particles size, hydrophobicity and flotation response · the accepted reaction bet·ween tmcs and a...
TRANSCRIPT
NOTE
This online version of the thesis may have different page formatting and pagination from the paper copy held in the Swinburne Library.
Centre for Applied Colloid Scien·ce Department of Applied Chemistry Swinburne Institute of Technology
PARTICLE SIZE, HYDROPHOBICITY AND FLOTATION RESPONSE
PARTICLE SIZE, HYDROPHOBICITY AND FLOTATION RESPONSE
A THESIS SUBHITTED BY
RUSSELL J CRAWFORD
FOR THE DEGREE OF HASTER OF APPLIED SCIENCE
APPLIED CHEHISTRY DEPARTHENT
SWINBURNE INSTITUTE OF TECHNOLOGY
DECEHBER 1986
This is to certify that this thesis has not been submitted in whole, or in part in respect of any other academic award.
Russell Crawford December 1986
ACKNOI'ILEDGE�IENTS
Research projects of this nature are profoundly influenced by the
quality of motivation, guidance and support provided throughout the
period of investigation.
Among the many whose assistance has been invaluable, I would like to
particularly thank the following:
The Australian Mineral Industries Research Association Ltd. Thanks
are extended to this Association for their support and sponsorship of
this project.
My principal supervisor, Professor John Ralston. John's support,
enthusiasm �nd friendship have been a constant source of energy and
inspiration, during the period of the project. Sincere thanks are
given to John for this.
My 'other supervisor', Dr Dianne Atkinson. Dianne's help was very
much appreciated when those day to day problems arose that couldn't
be solved with a phone call to Adelaide. Thanks are also extended
for helping to proof read this thesis.
My 11ife Jill. The thanks for all the love and encouragement can
never be appropriately expressed ..
Peter Kelly, Swinburne's glassworker. His skills as a glassworker
made design and construction of the precision glassware used in this
project a relatively easy task. His skills as a glass user helped
make this project more enjoyable.
Gayle Newcombe and Veronika Nyman. Thanks are given to these two
wonderful people for all the fun times we shared in the laboratory.
The many hours spent performing particle size analyses and the
accomodation on the frequent trips to Adelaide provided by Gayle v1ere
also very much appreciated.
i i
Dr Ian Jones (Head of Department) and the Academic Staff in the
Department of Chemistry at Swinburne. Ian's enthusiasm for
postgraduate research and his support of such programs at Swinburne
is commendable. The assistance of both Ian and the other members of
staff has been invaluable.
Dr David Mainwaring and the members of the Center for Applied Colloid
Science, Swinburne, for the fruitful discussions about the project.
John Endacott and the Technical Support Staff for both telling me
jokes and for listening to mine.
Audrey Killey for her skilful word ·processing abilities and for not
getting mad at me.
Flip Miller for teaching me how to use a \Wrd processor and not
getting mad at me.
Finally, a very special thankyou to my family, Dad, Mum, Nan, Bruce
and Leanne, You are all very special people.
Russell Crawford 1986
CHAPTER 1
CHAPTER 2
2.1
2.2
2.3
2.4
2.5
2.6
CHAPTER 3
3.1
3.2
3,3
3.4
CHAPTER 4
4.1
4.2
4.3
4.4
4.5
i i i
INTRODUCTION
REVIE\v
Introduction Flotation Recovery Bubble-Particle Collision and Attachment The Effect of Contact Angle on Flotation The Maximum Particle Size Limit in Flotation The Minimum Particle Size Limit in Flotation
THE PREPARATION AND SURFACE MODIFICATION OF QUARTZ
The Separation of Quartz into Various Size Ranges 3, 1, 1 Constant Flow Elutriation 3.1.2 Elutriation Particle Size Analysis Cleaning of the Quartz Surface 3.3.1 Reagents 3.3.2 Introduction 3.3.3 The Cleaning Process The Quantitative Methylation of Surface
the Quartz
3.4.1
3 .4. 2
Chemicals and Glassware
3.4.3
3.4.4
3 .4. 5
3.4. 6
•
Preparation of TMCS in Cyclohexane Solutions Analytical Determination of TMCS Concentrations Methylation of Quartz Particles �!ethylation of Quartz Plates Percentage Surface Coverage
THE FLOTATION BEHAVIOUR OF TAILORED QUARTZ PARTICLES
Experimental Method 4.1.1 Flotation Procedure 4.1.2 Flotation Recovery Results Assessment of Floated and Non-Floated Material Variation of Indifferent Electrolyte Concentration The Rate of Flotation 4.5.1 Introduction 4.5.2 Results: Flotation Recovery as a
Function of Time for a Given Particle Size
1
3
4
4
9
13
15
17
17
21
22
25
25
25
26
27
27
28
28
29
30
31
32
35
36
37
49
50
53
53
54
CHAPTER 5
5.1
5.2
5.3
5.4
5.5
CHAPTER 6
6.1
6.2
6.3
6.4
SUMMARY
APPENDICES
REFERENCES
iv
CONTACT ANGLE
The Young Equation Contact Angle Hysteresis The Cassie Equation The Measurement of Contact Angle
- 5.4.1 Quartz Plates 5.4.2 Quartz Particles 5.4.2.1 \Vetting Liquids 5.4.2.2 Preparation and Packing
Particles 5.4.3 Results
of Quartz
Comparison of Measured Contact Angles to Theoretical Contact Angles
DISCUSSION
Introduction Particle Size Limits in Flotation 6. 2 ,1 Coarse Particles 6.2.2 Fine Particles Induction Time The Rate of Flotation
59
61
63
67
67
72
76
77
80
81
84
84
85
90
93
100
1.
CHAPTER 1 INTRODUCTION
The purpose of this study is to examine the interrelationship of
particle size, hydrophobicity and flotation response in the flotation
process in the absence of soluble collectors and frothers. Such
species normally alter electrical double layer properties, surface
tension, bubble size distribution and film drainage rates among other
effects. As a result, any firm link between particle size,
hydrophobicity and flotation response has not been established to
date (li).
A model system was therefore required which would provide accurately
known levels of surface coverage for well defined, discrete particle
size ranges, The quartzjtrimethylchlorosilane (TMCS) model system
(3, 4, 36, 39, 40) fulfils these requirements.
The accepted reaction bet·ween TMCS and a surface silanol group on the
quartz surface is as follmvs:
� /
CH3 SI-0-Sl-CH + � "3 � CH3
HCI
The trimethylsilyl group is hydrophobic in nature whereas the
unreacted silanol groups are hydrophilic. Therefore a system is
obtained where a hydrophobic group is strongly chemically bonded to
the quartz allowing samples of accurately known surface coverage to
be obtained (3, 4).
The flotation response for quartz particles of various surface
coverages and diameters balm; 150 Jlm is measured. Similarly, the
rate of flotation of three particle size ranges is determined.
The contact angles of 'ilater on both quartz plates and powders are
measured. It is found that the composite contact angle may be
predicted by the Cassie equation for the model system.
2.
The results of the flotation studies ai)d the contact angle
measurements are interpreted in terms of the kinetic theory of
flotation for larger particles·. Current theory does not permit a
quantitative explanation of fine particle behaviour.
Calculated induction times, in conjunction with observed flotation
behaviour, indicate that the process of attachment of a bubble to a
particle is most efficient for particles of about 38 pm in
diameter under the experimental conditions of this study.
3.
CHAPTER 2 REVIEI'I
2.1 Introduction
Froth flotation is a separation process in which particles of
different surface characteristics are separated by firstly rendering
various particles selectively hydrophobic and then passing air
bubbles through the stirred pulp allo>Ting attachment of the
hydrophobic particles to the air bubbles. The bubble-particle
aggregates are then transported upward into a froth layer in the
flotation cell, leaving the hydrophilic particles behind.
Flotation is commonly used as a mineral dressing process. Ores such
as sulphides, salt minerals, scheelite, feldspar, mica and
cassiterite along \Vith ra"'v materials such as coal are enriched by
flotation. It has been estimated that about t>To thousand million
tons of various ores are concentrated by the mineral flotation
process annually worldwide (l).
The process of flotation is complex; a number of separate effects
such as collision of a bubble and a particle, the drainage of the
thin film formed bet>Teen the bubble and particle and the subsequent
attachment of the particle to the bubble, take place. These
processes are little understood and up until recently, comparatively
little research 'vas performed in this area as ores were readily
available and the flotation process, although only empirically
understood, was a reasonably efficient method for concentration of
minerals. In the future, hov1ever, the ready availability of ores
will decrease and an emphasis >Till be placed on the reprocessing of
the 1vaste materials from previous flotation processes to ?btain any
remaining minerals. The available grain size will therefore decrease
causing concentration by flotation to be more difficult, and hence
both a deeper understanding and a more effective control of the
parameters in the flotation process are required.
4.
2.2 Flotation Recovery
The flotation recovery, R, of a batchwise flotation system has been
shown to be first order (2). It can be shown that
(1 - R) -kt e
\Vhere k is the rate constant and t is the flotation time.
(2a)
The rate constant is dependent on many factors. This is shown in
equation (2b) (3, 4)
3Q.Ecoll'h k
2dbVR (2b)
Q volumetric gas flow rate
Ecoll collection efficiency
h cell height
db diameter of rising bubble
VR reference volume
The gas flow rate, cell height, bubble diameter and reference volume can
be kept constant to allow a direct study of the processes influencing the
efficiency of collection of the particles to be made, To understand this
the sub-processes in the collection of particles must be considered.
2.3 Bubble-Particle Collision and Attachment
The process of capture of a particle by a bubble occurs in three main
stages: (5)
(1) The Collision Stage: Here, the trajectories of both the bubble and
the particle are separated by only a small distance. The particle,
being much smaller than the bubbles in most cases, is essentially
approaching a planar gas-liquid interface. The distance between the
bubble and particle becomes so small that the liquid separating them
is a thin film.
5.
(2) Film Thinning Stage: If a bubble and particle are going to
attach, the second stage is that of thin film drainage. If the
bubble particle distance is small, molecular forces come into
play and cause the thin film to drain if the surface of the·
particle is hydrophobic. These forces give rise to the '1o1etting'
or 'disjoining' pressure, which eventually is responsible for the
rupture of the thin liquid film.
3. Film Recession Stage: This is the stage at which the liquid
around the point of rupture of the thin film formed draws back
and forms a finite contact angle with the particles.
The efficiency with which particles are collected, Ecoll is
dependent on the respective efficiencies associated with the three
stages discussed above; This is summarised in equation (2c).
(2c)
where Ec is the collision efficiency, Ea is the attachment
efficiency and Es is the stability efficiency of the
bubble/particle aggregate.
The parameter Ecoll' the collection efficiency, is convenient for
comparing experimental and theoretical collection rates 1 hmvever, the
Ecoll value of l can normally never be attained due to, for
example, hydrodynamic effects around the bubble causing smaller
particles to move aside from a vertically rising bubble (5).
Flint and Hm<arth (6) derived an equation to predict the motion of a.
particle around a stationary sphere, viz
+ (2d)
where
6.
particle density
particle volume
v velocity of the particle
u velocity of the component of the liquid field
caused by the presence of the bubble
G body force acting on the particle
cd particle drag co-efficient
(j refers to the direction of action of the above)
Derjaguin and Dukhin (7) had written Vp (Pp - Pf) [where Pf is
the density of the fluid] instead of the left hand term of equation
(2d), This led to a conclusion that particles did not deviate from
fluid str�amlines, and hence particles below a certain size could not
reach the zone very near to the surface of the bubble. Flint and
Howarth (6) solved the corrected equation with both potential flm•
and Stokes 'creeping' flow around the bubble, assuming that the
component of fluid velocity, uj , at the position of the particle
was the same as if the particle were not there. The drag on the
particle was calculated from Stokes Law. It was found that particle
behaviour was different for large and fine particles, as
characterised by the Fonda and Herne parameter K (8).
where
K
radius of the particle
velocity of the bubble
viscosity of the liquid
rb radius of the bubble
(2e)
7.
When K > 1 (for large particles), Ec, the collision efficiency, was
strongly dependent on inertial forces and Ec increased with
increasing bubble size. \Vhen K < 0.1 (for fine particles) the
collision efficiency was virtually independent of K but dependent on
G, defined as
G
where Pf g
2 (pp - Pf) r/g
9J.LUb
density of the fluid
acceleration due to gravity
(2f)
For low values of G (for fine particles) the collision efficiency
increased with decreasing bubble size.
Flint and Howarth's work defined efficiency of collection on the
assumption that a particle would be captured if the trajectory of the
centre of the particle made contact with the bubble. This assumption
has been disputed and Reay and Ratcliff (9) rectified this in their
hypothesis that collection would occur if both the bubble and
particle surfaces made grazing contact 1vith each other at a finite
contact angle. An assumption they made was that the flow pattern
around the front of a bubble is that of a Stokes or 'creeping' flow
around a solid sphere. Anfruns and Kitchener (10) however found that
the'collection efficiencies of spherical particles deviated
considerably from those predicted using the Stokes flow theory.
Reay and Ratcliff (9) and Flint and Howarth (6), from their
calculations of collision efficiency, concluded that
where the exponent N varies according to the Pp/Pf ratio.
(2g)
Reay and Ratcliff concluded that the exponent was 1.9 for particles for
Pp/ Pf � 1. 0 and 2. 05 for Ppl Pf � 2. 5 . . Flint and Howarth
obtained N � 2 because of their different definition of collision
efficiency. N is frequently equal to 1 in plant practice (11).
8.
Jameson et al (5) criticised both Reay and Ratcliff and Flint and
Howarth of over-simplification of the hydrodynamics involved,
suggesting that these assumptions lead to serious errors. Both
parties assumed that the drag on the particle near a bubble could be
calculated from Stokes Law, hmvever, when a particle comes close to a
risipg bubble the velocity field is distorted, and the hydrodynamic
drag becomes large. Other deficiencies in this work were the neglect
of the effect of bubble and particle charge and other surface forces
responsible for film drainage and bubble-particle contact.
Recalling equation (2c)
It carl be seen that the collision efficiency (Ec) would be the
determining factor for- efficient collection if it is assumed that the
other varibles Ea, Es are approximately equal to 1, as in the
work of Anfruns and Kitchener (10). Here, glass spheres and angular
quartz particles were rendered strongly hydrophobic with
trimethylchlorosilane. As the particle sizes used 'ivere within the
range 10-50 �m and the bubble size 500-1000 �m in diameter,
it was reasonable to assume that Ea and Es equal one as the high
contact angles and low turbulence conditions used 'iVould ensure
efficient attachment and subsequent stability of bubble-particle
aggregates. Thus the collision efficiency alone was assessed. It
was found that smooth glass spheres displayed a much lower collection
efficiency· than the angular quartz particles due to the rough surface
on the latter allowing a more efficient rupture of the film between
the bubble and particle. 1fuile Ec was reasonably able to be
predicted, the role of Ea and Es is less clearly understood.
Thin film studies (18, 34, 37) have revealed much information on the
role of 'surface forces 1 in flotation hmvever the role of contact
angle and its link to particle size and flotation kinetics has not
been identified satisfactorily.
9.
2.4 The Effect of Contact Angle on Flotation
\fuereas Ec is directly related to a function of the particle size,
Ea andEs, the attachment and stability efficiencies are directly
related to a function of the hydrophobicity (which is proportional to
surface coverage of trimethylsilyl groups in the model system) and
inversely related to the particle size (11) i.e.
f [ 8]
f[d)
·where 0 is the angle of contact of, for example, water on a solid
and is a measure of the hydrophobicity of the solid.
Trahar (11) remarked that 'There is a need for quantitative
information on the collector requirements of individual size
fractions of different minerals if the efficiency of selective
flotation of minerals from increasingly refractory ores is to be
improved. Experimental attempts to derive such relationships have
produced results which have been so variable that little recent
research in this topic has been undertaken.'
The model system chosen in this study allows not only a particle size
dependence in flotation to be assessed, but also permits the relevant
contact angles_
to be measured. If soluble collectors were used to
vary the surface hydrophobicity, many complications would arise,
including:
( i) The electrical double layer properties may vary with a
change in collector concentration. The zeta potential
1muld change, whereas with the TMCS/quartz model system
the presence of the TMS bonded layer has no measurable
effect on the zeta potential (3, 15). Also an ultra thin
layer of TMCS would have no appreciable effect on the
quartz/l•laterjair Hamaker constant (12, 13, 15).
(ii) The bubble size and surface tension >IOuld change with
varying collector concentration.
(iii)
10.
The 'sub-steps' of bubble particle collision (as discussed
earlier) may change. The effects of surfactants on thin
film drainage, kinetics of expansion of the three phase
line of contact etc. are poorly understood.
The deficiencies in (i) and (ii) are overcome with the quartz/TMCS
system used. Theoretical treatments of the limiting particle size in
flotation have been performed by various workers (l, 16-18).
Models for predicting the particle size limits of floatability have
arisen from resolution of the forces acting on a particle at a
gas/liquid interface. The problem of equilibrating forces on a
regularly shaped, isometric particle at an interface has been dealt
with by Schulze (16), Scheludko et al (17), Morris (18) and Nutt (20)
among others. The firSt extensive generalised treatment of forces on
particles was put fon;ard by Princen in 1969 (19).
For a spherical particle with a homogeneous, smooth surface and a
radius 1), attached to a bubble of radius Rb where Rb >> Rp (Figure
2.1) the forces acting on the particle can be summarised as follows:
zfyJ
t !.?air
Fi�ure 2.1
11.
(a) the force of gravity
(b) the static buoyancy of the immersed section
rr 3 2 3 Rp Pfg[(l - cos w) (2 + cos w)]
(c) the hydrostatic pressure of the liquid of height Z0 on the
contact area
(2h)
(2i)
(2j)
(d) the capillary force at the three phase contact point in the
vertical direction opposite to the field force.
JHJ (2k)
(e) additional detaching forces Fadd ;1hich are represented as
approximately the product of the particle mass and acceleration
bm in the flotation cell.
Fadd "' (21)
(f) the capillary pressure in the gas bubble on the contact area
which can be given approximately as follows:
where g acceleration due to gravity
vapourjliquid surface tension
radius of bubble
(2m)
12.
At equilibrium, the sum of all of these forces must be zero.
Difficulties arise in the use of the individual equations, so certain
assumptions must be made. The resulting summation expression is
cumbersome, the ·solution of ,;hich has been documented else,;here (1).
A summary of the assumptions and principles only ,.,ill be discussed
here.
The assumptions and simplifications made are as follo,;s:
(i) The particles are spherical.
(ii) In the flotation cell all particles experience an
(iii)
acceleration aeddy = ap due to the forces occurring in
the various eddies. These eddies are counteracted by
corresponding static buoyancies in the vortices.
If Rb, the bubble radius is much greater than the radius
of the particle, Rp, F1 is very small and may be
taken as zero.
Work must be done on a bubble-particle aggregate to cause the
particle to leave the equilibrium position it has obtained at the
vapour/liquid interface. This ,;ork can be described in terms of a
detachment energy, expressed by
(2n)
,;here hcrit is the critical displacement (from an equilibrium
position heq) for detachment. Shulze (1) provided solutions to
this expression for given conditions. His kinetic theory of
detachment is similar in some respects to the Scheludko et al theory
(17) ,;here the force resisting immersional wetting is calculated from
surface tension, particle size and contact angle data. Contact angle
and surface tension are factors ·determining the magnitude of Edet
(Equation 2n) and are both controllable entities.
13.
Particles with kinetic energies greater than Edet cannot float.
Schulze's theory assumes that bubble-particle attachment has occurred
and that it is the aggregate stability which controls flotation (the
particles may be 'shaken off' the bubble if their kinetic energy is
too large). Hydrodynamics is not important, yet it is known that the
collision mechanism differs for large and small particles so that
both a lower and upper particle size limit might exist for flotation,
the upper limit also being dependent on the buoyancy of the
bubble-particle aggregate and hence the bubble size. The lower limit
is likely to be linked to the time of contact with the bubble. If
this time is too short, the thin film rupture may not occur under
flotation conditions.
2.5 The Maximum Particle Size Limit in Flotation
The upper particle size limit is determined by the relationship of
the particle's kinetic energy to the energy required for the particle
to detach. Clearly this energy will be different in static compared
to turbulent conditions. Rp,max,g is defined as the maximum
particle size that can be floated under non-turbulent conditions
i.e. acting only under the influence of gravity.
This value can be calculated from equation (2o) (1).
Rp, max, g � (% 1 sin w* sin (w* + 8)) 1/2
b.pg + ppbm
where surface tension of liquid
Pp density of particle
g acceleration due to gravity
bm acceleration of particle ( � 0)
(2o)
b.p density difference between particle and liquid
8 contact angle
w* 180 - 8/2
The maximum limit of particle size is less than that calculated from
equation (2o) in the case of turbulent conditions. This value may be
calculated two ways, the equation for the energy balance of the equation
for the balance of forces:
14.
i) Energy Balance
2 "R 3 p v 2 3 p p t
+ 3h 2Rp
sin2w
rr(Rp sin w)2 {
3 (w + 8)} sin w sin
a2R 2 p
2"1 2Rbpfg})dh.
Rb
(ii) Force Balance
4 "Rp
3ppbm 3
where
a
{� 3 (1
2pp cos3 w* 1rRP Pgg
Pf
3h sin2w*
3 (w* + 8 � + sin W'i'< sin 2Rp 2R 2 a p
radius
radius
of particle (here Rp of bubble
particle acceleration
max,
- ;:fg capillary or Laplace constant -
,
turbulent)
sedimentation velocity of the particle in relation
to the ascending bubble*
* Since the sedimentation velocity is usually much smaller than the ascent velocity of the bubbles in flotation, vt is approximately equal to the velocity of the rising bubble (1, 17).
vbubble vbubble
vparticle
15.
Numerical solutions to the above equations under various conditions
are available (1, 17). The majority of symbols and definitions are
shown in Figure 2.1.
2.6 The Hinimum Particle Size Limit in Flotation
A theory for the determination of the lower particle size limit has
been advanced by Scheludko et al (17). The critical work of
expansion of a three phase contact (i.e. the work necessary to form a
'hole' v1hen a bubble just makes contact with a particle) tvas equated
with the kinetic energy of the particles. This yields a minimum
particle diameter for flotation as given in equation (2r).
'\vhere I<
vb
�p
1
e
is
is
is
2 .( -2
3,._2 ]1/3
vb �P 1 (1 - cos 8)
the tension in a line or 'line
the rising bubble velocity
the density difference between
the particle and the liquid
is the air/liquid surface tension
i_s the contact angle
(2r)
tension'
The line tension term in equation (2r) opposes 'hole' formation; its
magnitude poses great uncertainty. Its existence was first suggested
by G�bbs (21) and further analyses have been performed by Harkins
(22), De Feijter and Vrij (23), Lane (24), Pethica (25) and others.
Experimental data is scarce and hence calculations involving line
tension are fraught with uncertainties. Scheludko et al (17)
estimated 1< for contact angles usually encountered in flotation;
bet'i7een 20° and 40°. For these values the line tension was
found to range from 2.8xlo-10N to 5.6xlo-10N. This is to be
expected as line tension should vary with contact angle (16, 104).
According to Scheludko et al, the collision efficiency, Ec, can
16.
become zero if the line tension prevents the formation of the primary
three phase contact «ith the bubble. Generally the kinetic energy of
fine particles is about l0-15J (1) and the "ork required to form
the primary contact is of the same order. The lo«er grain size
limit, according to Scheludko et al, varies from 2.3 to l.l�m
for contact angles of 20o and 40• respectively, assuming
,. � 2.8xlo-10N. For �< � 5.6xlo-10N, the lower grain size
limit varies. from 3. 7 to 1. 7 p.m for the same contact angles.
Particles of all sizes have a finite collision probability (5)
however bubble-particle contact may not occur. In practice,
particles «ith diameters less than 4p.m report to a concentrate
principally by entrainment.
17.
CHAPTER 3 THE PREPARATION AND SURFACE MODIFICATION OF QUARTZ
3.1 The Separation of Quartz ihto Various Size Ranges
In this study of particle size and hydrophobicity effects in
flotation various particle size ranges of quartz were required,
Two kilogram of optical grade high purity quartz (G. Bottley Pty Ltd,
London) was crushed to less than 5mm in size and then dry ground in a
5 litre ceramic mill with ceramic balls. Any material less than
200 �m was periodically removed to ensure that a high proportion
of larger sized material was retained and not ground to a fine
powder. The quartz was then sized by standard wet and dry sieving
techniques using Endecott sieves down to 45 �m. Material less
than 45 �m was separated by either constant flow elutriation or
beaker decantation. The separation process is shown in Figure 3.1.
3 .l.l Constant Flow Elutriation
The sub-sieve size ranges were obtained by elutriation
techniques. Elutriation is the process by which a sample of
particulate material is fractionated by a vertically moving
liquid. This technique has been used extensively (26-28) and has
been shown to be an efficient method of obtaining discrete size
ranges (29).
In a vertical cylinder of known internal diameter, particles rise
or fall in an upward flo\• of liquid depending on whether their
settling velocity is greater or less than the velocity of the
liquid. The Stokes settling velocity for a given particle is
given by
-45 f.'ill
I Elutriation
1 -45 + 40 f.'ill
-40 + 30 f.'ill
-.30 + 23 J.tm -23 + 18 J.tm -18 + 14 J.tm
18.
High Grade Optical Purity
Quartz Pieces ,r,, Hammer to Pieces <5 mm
l Dry grinding to less than 150 J.tm in a 5 litre ceramic mill >Iith ceramic balls initially cleaned 1vith coarse clean sand for 2 hours and flushed >Iith distilled >later
l /"'"'"'�
fraction -150 + 45 f-LID fraction
~ Decantation
j -14 + 5 J.tm - 5 + 0 J.tffi
Figure 3.1
\ wet sreening
-150 + 125 J.tm -125 + 106 J.tm -106 + 90 J.tm
90 + 75 J.tm 75 + 63 J.tm 63 + 53 J.tm
45 J.tm 53 +
v
1-'
p
19.
ms-1 (3a)
equivalent particle diameter. It applies to an
irr7gular particle which has an equivalent diameter
to that of a spherical particle of equal density
,.,hich settles at the same rate as does the
irregular particle
viscosity of the liquid
specific gravity of the particle
specific gravity of the liquid
The Poiseulle Equation of laminar flow (30) enables the velocity
of flow of a liquid through a cylinder to be calculated. The
velocity of flow varies across the cylinder such that the maximum
velocity is along the axis of the cylinder, and the minimum
velocity (zero) is at the point of contact of the liquid with the
cylinder wall. It is the maximum velocity which must be
considered in elutriation techniques as every particle will
experience this velocity at some time.
It can be taken that the average velocity of flow (u) through a
cylinder is equal to the volume of liquid per unit time divided
by the cross-sectional area of the cylinder (A) (28).
Q A
(3b)
The maximum velocity of flow, or axial velocity is equal to t'·lice
the average velocity, viz
umax = 2U Q A
,.,here r is the internal radius of the cylinder.
(3c)
20.
Therefore, combining the Stokes settling velocity [equation (3a)]
with the maximum velocity of flow [equation (3c)] a suitable
internal radius of a cylinder required to retain particles of a
given size and carry over any smaller can be calculated given a
knowledge of the flowrate and upward flow velocity of the liquid.
The elutriation apparatus used is shmm in Figure 3. 2. The
outflow from each tube was connected to the inflow of a tube of
smaller diameter. All undersize material >·ms then lifted up and
over in�o the next tube. This allowed a continuous separation of
quartz samples. Separation of a three gram charge took about
twelve hours, after which time the top halves of the tubes were
clear. This process was repeated until sufficient quartz was
obtained for the study.
A water flowrate of 7 cm3 per minute allowed particle size
ranges to be obtained from tubes of the follm1ing indicated
_internal diameters.
Internal diameter of tube (mm) Calculated Maximum Equivalent Diameter of Particle (Assuming max. velocity)
(I'm)
14 40 19 30 25 23 31 18 47 14
(Actual particle size distributions for the particle size ranges
used are given in Section 3.2.)
21.
All sections of the elutriator were made of either glass or
Teflon to facilitate cleaning and to minimise impurities which
may adsorb onto the quartz. Connection tubes were of small
diameter to ensure an efficient transportation of undersize
material into the larger tubes. (The velocity of liquid flow was
high in these smaller diameter tubes.)
FLOW
METER
LOADING RESERVOIR
METERING PUMP
3.1.2 Decantation
2
'AIR BLEEO'TEFLON TAPS
3
Figure 3.2
4
THREE WAY� TEFLON TAPS
5
Quartz particles less than 14 J.Lm in diameter were
fractionated by a standard decantation technique (31). The
Stokes equation was used to calculate settling times for
particles of an equivalent spherical diameter (28).
UNDERSIZE MATERIAL OUTLET
22.
18p1 x 10-7
metres (3d)
This equation enables one to calculate the time (t) that a
particle of given equivalent diameter (de) and specific gravity
(p) will take to fall through a height (L) after being
dispersed in a liquid of known viscosity (p) and specific
gravity (p0).
A 2% by weight suspension of quartz in ·water ·was stirred in an
ultrasonic bath to disperse the quartz. The appropriate settling
time \'las allowed, then the supernatant decanted. This process
was repeated several times until all supernatant material was
removed.
3.2 Particle Size Analysis
The quartz particle size distribution for the separate size ranges
was measured by three instruments; the Cilas Granulometer 715 F429,
the HIAC-ROYCO Particle Counter and the Malvern Particle and Droplet
Sizer 2600C. The Cilas Granulometer, used to measure the particle
size distribution of all particle size ranges, shines a beam from a
Ne-He gas laser through a suspension of particles. The transmitted
beam intensity is related to the size distribution of the suspended
particles. The HIAC-ROYCO counter measures particle size
distribution by directing a collimated beam of light from a quartz
halogen lamp through a stirred suspension of particles on to a
sensor. The greatest projected area of the particles (as they tumble
through the turbulent zone of the sensor) is measured and is
proportional to the particle size. The Malvern Particle and Droplet
Sizer is similar to the Cilas Granulometer in that a He-Ne laser beam
is shone through a suspension of particles, and the diffracted light
is collected by a lens and then focussed on a special detector
placed on the focal plane of the lens. The detector consists of 30
concentric, semicircular photosensitive rings. The data from the
detector is processed, and a distribution of 'best fit' is obtained.
The average particle sizes are shown in Table 3.1.
23.
TABLE 3.1
Average Particle Sizes r r-N_
o_m
_i_n_a_l
----�- - - C-i
-l�a
-s
�--�T-H-
I_A
_ C ___ R
_ O_Y
_C_O __ ,-_MA
__
L_�_
E_RN ___
2
_6
_0
_0
_C �-A-v
_e_
r_a
_g
_e
__
o_f _______ l
Particle Granulo meter I Three Instruments I Size Range and Range within 1
I (I'm) i
-150 +'125
-106 + 90 I - 9o + 7 s 1 - 7 s + 63
- s3 + 45 1
Ill � �� : i� I - 30 + 23 i - 14 + 5 i
(I'm)
120
102
70
62
50
47
37
26
14
(I'm)
47
37
28
16
i i which 90% of I ·· -I. Particles are I
(I'm)
121
96
72
65
56
45
36
27
14
' found i j (I'm) I
121±19
99±17
71±12
64±11
53±9
46±8
37±8
27±8
15±5
I
The quartz particles were photographed by electron microscopy. The
electron micrographs for particles of various particle size ranges are shown in Plates 1 to 3. The surface of the particles are
rough. The effects of this roughness will be discussed in C
hapter 5.
24.
\
Plate 1
Plate 2
Plate 3
3.3 Cleaning of the Quartz Surface
3.3.1 Reagents
25.
(a) Conductivity_
\-later High purity water, or 'conductivity'
water was prepared by passing once distilled water through
activated charcoal, followed by a mixed bed ion exchange
resin before being distilled again into Pyrex containers.
The conductivity '·later had a surface tension of
72.8 mNm-1 at 20°C, pH of 5.70 and a maximum
specific conductivity of 1.0 x lo-6n-1cm-1.
The water was in equilibrium with air.
(b) Nitric Acid Analytical Reagent Quality.
(c) Potassium Nitrate Analytical Reagent Quality,
recrystallised, and baked at 220°C.
(d) Potassium Hydroxide Analytical Reagent Quality
3.3.2 Introduction
Low levels of surface contamination will affect both the
flotation responses and contact angle measurement on the quartz
particles and.
plates, hence a meticulously cleaned surface is
required before any surface modification can take place.
Vig el al (32) showed that a well cleaned quartz plate forms
continuous \'letting films \Vhen exposed to water vapour. The
�resence of an impurity causes microdroplets to form on the
surface under similar conditions. Similarly, particles of quartz
can be tested for cleanliness by a process described by Leja
(33). Here, an air bubble in water is pressed against a bed of
quartz. If any particles cling to the bubble, the surface is
contaminated ,iith hydrophobic material. Clean quartz particles
are hydrophilic and will not adhere to an air bubble in such a
situation.
26.
Various. methods have been used to clean the surface of glass and
quartz (32-38). It has been shown by various techniques
(including ellipsometry) that washing the quartz surface with
hot, concentrated nitric acid follm;ed by brief immersion in 30%
hydroxide solution followed by rinsing with conductivity water
provides a clean surface free of any gelatinous polysilicic acid
groups (34, 35, 38).
3.3.3 The Cleaning Process
The quartz powders and plates used in this study were cleaned by
the following method:
(a) Immersion in hot Nitric Acid for two hours.
(b) The acid was then decanted and the quartz washed with
copious quantities of conductivity w�ter.
(c) Immersion in hot 30% Potassium Hydroxide solution for
thirty seconds.
(d) The hydroxide solution was decanted and the quartz was
washed again with conductivity •mter until the pH of the
washing solution had returned to that of conductivity
·water.
(e) The plates and pm;ders were assessed for cleanliness by
the methods previously described (i.e. The 'steam' and
'bubble cling' tests).
The clean quartz was dried in a clean oven at llO"C, cooled
in a vacuum desiccator and stored in ground glass sealed
containers within the desiccator until needed. Subsequent
'steam' and 'bubble cling' tests showed that no detectable
hydrophobic surface contamination occurred during drying or
storage.
27.
3.4 The Quantitative Methylation of the Quartz Surface
The quartz/TMCS surface modification technique has been used
extensively .as a method for rendering quartz and glass surfaces
hydrophobic (38-40). In previous to�ork the surface coverages to�ere
only qualitatively controlled by variation of the methylating
solution concentration. No stoichiometric, quantitative method had
been produced to determine the degree of surface coverage until Blake
and Ralston (3, 4) developed the technique in 1983.
The reaction between TMCS and a surface silanol group on quartz is
sh01m schematically belm;:
� ;a-0-H +
/CH3 CI-Si-CH
�CH3 3
3.4.1 Chemicals and Glassto�are
HCI
The surface modification process requires very lpw concentrations
of TMCS in cyclohexane, hence further purification of the
reagents was necessary to remove trace impurities such as 1vater
to�hich could lead to errors in the subsequent analyses. TMCS
(>99%, Merck) and Cyclohexane (A.R., Ajax) to�ere dried with fresh
phosphorus pentoxide folloHed by tHo distillations under a dry
nitrogen environment (99.99%, GIG). These reagents Here then
stored in glass containers within a dry nitrogen envirOnment
until needed. High sensitivity NMR and mass spectrometric
analyses to�ere performed. It Has found that these reagents
contained no detectable levels of impurities such as
hexamethyldisiloxane [ (CH3)3SiQSi(CH3)3] or higher
molecular Height species (41). The methylation procedure •ms
performed Hithin a polyethylene glove bag (Model X-27-27,
Instruments for Research and Industry) filled to�ith high purity
oxygen free nitrogen (99.99%, GIG) and dried Hith phosphorus
pentoxide (AR, BDH).
28.
Glassware used for any purpose involving contact with TMCS was
initially cleaned by the same method as for the quartz plates and
powders (see Section 3.3.3). The glassware was then conditioned
by rinsing 1·1ith a concentrated solution of freshly distilled TMCS
in cyclohexane1 rinsed with cyclohexane several times, then
placed in a clean oven at 160'. This process provided a
durable· hydrophobic surface which was shown not to react further
with any TMCS in cyclohexane solutions used in this study.
3.4.2 Preparation of THCS in Cyclohexane Solutions
TMCS in cyclohexane solutions ranging in concentration from
2.0 x·lo-4H to 0.5 x 10-4H were used as the methylating
solutions. These solutions were prepared by diluting varying
amounts of a 2.0 x 10-4M stock solution which was initially
obtained by delivering a known volume of pure, dry TMCS with a
calibrated Agla micrometer syringe (42) into a standard flask
containing cyclohexane. All TMCS solution concentrations were
evaluated separately by the pH difference technique described in
Section 3.4.3. All manipulations were performed within a dry
nitrogen environment.
3.4.3 Analytical Determination of TMCS Concentrations
Blake and Ralston (3,4) developed a technique for determination
of TMCS in cyclohexane solution concentration. This technique is
based ot1 the stoichiometry of the fol101dng reaction:
reacts readily with �;ater.)
CH 3, _;
CH:rSi-CI CH:Y
3
+ H-0-H
(TMCS
+ HCI
29.
A given volume of conductivity \•later of knmm pH was shaken with
the same volume of THCS in cyclohexane solution in a sealed
separating funnel and the phases were allowed to separate. The
aqueous phase �Vas then tested for pH using a calibrated Orion
Research Model 701A pH meter, and subsequently the amount of HCl
liberated was deduced from the change in pH. From this the TMCS
concentration 1vas able to be calculated. All measurements \vere
taken in duplicate at least and at 25± 1•c.
3.4.4 Methylation of Quartz Particles
A quartz charge, typically 5.00g was placed in a glass reaction
vessel (Figure 3.3) and baked at 160• overnight.
0 N �
NOT TO SCALE
n Ground GlasS Tap
( ) �Quick· Fit Top
Approx\ Pulp
Height 1���������- �-::::::=---' -
-- - - :.=::
1-- -_-::.._-_-_-_-_-_- _ _:_ =
F-- ---=-=-= --=::
Glass Mag� Follower
48
\Quartz Disc
Figure 3.3
30.
The vessel was then sealed and transferred to a nitrogen filled
glove-bag whilst still hot. After cooling for two hours,
100 cm3 of previously prepared THCS solution was added rapidly
and the vessel resealed. Methylation was then commenced for a
specified time, usually 40 minutes, after which time stirring was
ceased and the qu!"rtz was allowed to settle. The supernatant
solution was then decanted and stored in sealed glass flasks for
subsequent analysis. The remaining quartz was rinsed twice \Vi th
50cm3 of cyclohexane to remove any residual TMCS. The quartz
was then transferred to a clean oven for two hours .at 110°
and stored.
The degree of.
surface coverage was obtained from the TMCS
concentrations before and after reaction with the quartz. A
sample calculation is shown in Appendix 1.
The HCl produced by the TMCS/quartz reaction •·1as assumed by Blake
and Ralston (4) to enter the available free space above the
dispersion level within the methylation vessel This assumption
was based on the fact that the vapour pressure of HCl is very
large (40 atm at 18"C (43)) and that the solubility of HCl in
cyclohexane is very low (44). This was confirmed in this study
by methylating a sufficient quantity of quartz to ensure a
complete consumption of all the THCS. No detectable change 'in pH
occurred >Jhen the organic phase >Jas brought into contact with
conductivity water (see Appendix 2).
�ence, no HCl was present in the cyclohexane to affect the TMCS
concentration determinations.
3.4.5 Methylation of Quartz Plates
Quartz plates were methylated along >Iith the quartz powders by
the same method as described in Section 3.4.4. The plates were
considered to be another particle in the reaction vessel, and as
such should receive the same degree of surface coverage as the
pmvders. This procedure is discussed further in Section 5. 4. 1.
0 0 r
X
"rn "' 0
6
Vi. .-, :r: g
r:-,
31.
3.4.6 Percentage Surface Coverage
The percentage surface coverage was calculated as follows:
% Surface Coverage
r (CH3) 3si
r(CH3)3Simaximum
X
100
1
r(CH3)3Si is the actual surface concentration of (CH3)3si
groups in mole g-1.
r(CH ) Si represents the maximum surface coverage per gram 3 3 max
of trimethylsilyl groups for a given particle size. This value
was obtained by determining the surface concentration (r(CH ) Si) . 3 3
at various time intervals (see Figure 3.4). The maximum surface
concentration per gram is obtained from the plateau value. This process
was repeated at least three times to obtain an average r(CH3)3Si maximum
20 FIGURE 3.4
• •
Uptake of 15 trimethyl silyl
groups by quartz ( -45 -40)') as
10. a function of time. (2.0 x 10-4M
5 TMCS in cyclohexane as methylating agent).
20 40 60 80 100 120
[�EACTION TlfViE (IV/INS.)
32.
CHAPTER 4 THE FLOTATION BEHAVIOUR OF TAILORED QUARTZ PARTICLES
4.1 Experimental Method
The flotation recoveries of quartz with varying degrees of known
surface coverage for a given size range w·e-re measured using a
1nodification of the Ha11imond tube (45, 46), (Figure 4.1).
NOT TO SCALE
· � �L
Gas Source
73
�Solution Level
_____--collection Tube
Glass Magnetic Follower
"' "' N
L =����::::-::::-::::-::::-::::-�S�I n�t�e":'r e:cd�G�I�as�s;_I F�r :!!l t:_ _____ _j_
Figure 4.1
33.
The modified Hallimond tube included similar modifications made by
Blake (3):
(a) The tube height 1-1as increased to minimise mechanical 'carry over'
or 'entrainment' of particles.
(b) A sintered glass frit of uniform porosity together with a glass
magnetic stirrer allm·Js a reproducible bubble distribution to
emanate from the base of the cell.
(c) A gas lock was included to prevent any environmental impurities
entering the cell.
The tube was attached to the gas source via three way ground glass
tap and a gas flowmeter as in Figure 4.2.
A c D
Figure 4. 2
A. Nitrogen Source
B. Silica/Conductivity water slurries
C. Fischer-Porter flowrator
F
E
D. Teflon tubing
E. Three way ground glass
tap
F. Flotation Cell
G. Magnetic Stirrer
34.
To allo>" a direct comparison of flotation response bet>"een different
particle size ranges, the follo>"ing parameters >"ere kept constant at
the given levels for the duration of the trials:
(a) Gas Flow Rate
High purity oxygen free Nitrogen gas (99.99%, GIG) >"as used for
all flotation trials. The flowrate was adjusted to 60 cm3 per
minute and >"as monitored by a Fischer Porter calibrated Flm<rator
(48). The nitrogen >"as scrubbed through two silicaj>"ater
slurries in order to remove impurities before passing through the
flotation cell.
The bubble size distribution was measured by firstly
photographing the rising bubbles >"ith a high speed camera, then
measuring the bubble size from the graduated scale. A typical
photograph is sho>"n in Figure 4.3.
Figure 4.3
A number average bubble size of 1.0±0.7 mm >"as obtained. This
value covers the entire range from the smallest disce.rnible to
the largest bubbles, About 90% of the bubbles >"ere 1. 2±0. 2 mm in
diameter. The bubble size distribution did not alter during
flotation experiments.
This average bubble size corresponds to a bubble velocity of
25±5 em s-1
(33). The bubbles were rising through
uncontaminated dilute aqueous KN03 solutions. It is well known
(47) that bubble coalescence and velocity is not affected until
the salt concentration exceeds about 0.5M.
35.
(b) Pulp Volume
A constant stirring rate, corresponding to a pulp height of
2.5 em, was used for all particle size ranges. This ensured that
the particles were lifted off the glass frit prior to
encountering the nitrogen bubbles. In all cases a one gram
charge qf quartz was used for flotation experiments. There was
no detectable effect on the flotation recovery curves or
threshold values for variations in pulp density between 0.1 and
4%.
(c) Ionic Strength
Analytical Grade Potassium Nitrate, further purified by
recrystallisation followed by baking at 200° was used to
prepare the indifferent (49) electrolyte used in all flotation
trials. A concentration of 10-3
M KN03 of surface tension
72.60±0.05 mNm-1 and pH 5.7±0.2 was normally used although the
effect of variation of indifferent electrolyte concentration was
also studied. [The pH of the KN03 solution was measured before
and after the flotation trial and was found not to vary
appreciably. It remained within the limits 5. 7±0. 2 .]
(d) Flotation Time
A constant flotation time of five minutes was normally used
although the rate of flotation was also studied by varying the
flotation time.
(e) Conditioning Time
The quartz particles were stirred in 10-3
M KN03 solution for
a period of five minutes prior to the commencement of flotation
t:o ensure that the particles were properly dispersed,
4.1.1 Flotation Procedure
The follm·ling procedure was adopted for each flotation trial.
(i) The vertical section of the flotation cell (Figure 4.1)
was filled with KN03 solution.
(ii) A one gram charge was introduced into the agitated
<3olution
36.
(iii) The remaining sections of the flotation cell were
connected.
(iv) The cell was filled to the required level with KN03
solution.
(v) The stirring rate was adjusted to give a pulp height of
z.scm.
(vi) The pulp was stirred for five minutes.
(vii) The gas flow was commenced and flotation occurred for a
fixed period.
(viii) After the particles were allowed to settle, the collection
tube was removed and placed in a large beaker into which
the residual particles remaining on the walls of the cell
were ·washed.
(ix) The floated material was then filtered through a
pre-weighed sintered glass crucible, dried, then weighed.
4.1.2 Flotation Recovery
The increased flotation cell height >laS designed to reduce
mechanical 1carry over' or 'entrainment', however a certain
degree of entrainment still occurred. This value was subtracted
from each flotation recovery value to enable the true flotation
recovery to be evaluated.
The entrainment was determined by performing a flotation trial on
a clean quartz sample (of a given size range free of surface
trimethylsilyl groups). The percentage recovered was taken as a
measure of entrainment.
Hence,
Real flotation recovery Actual Flotation Recovery - Entrainment
The percentage recovery was calculated as follm·lS:
% Recovery mass of floated material-mass entrained x 100
mass of initial charge 1
37.
4.2 Results
Table 4(a) Flotation recovery as a function of surface coverage
for -150+125pm quartz particles.
r(CH3)3 Si
mole g-l (x 107)
1. 58
1. 60
1. 61
1. 66
1.94
3.47
4.93
6.05
6.43
(Entrainment 0%)
B 1;; w
100
80
6 60 u w "'
z 0
(i' b 40 � u.
20
20
Percentage Surface Real Flotation
Coverage Recovery (Percentage)
25 6±1
25 17±2
25 26±2
26 23±2
30 49±1
54 81±2
77 91±2
94 97±2
100 96±2
Figure 4.5(a)
40 60 80 100
SURFACE COVERAGE ('l.J
38.
Table 4(b) Flotation recovery as a function of surface coverage for
-106+90pm quartz particles.
r(CH3)3 Si Percentage Surface
mole g-1 (x 107) Coverage
l. 91 22
2.00 23
2.37 27
2. 73 31
2.92 34
3.05 35
4.09 47
6.96 80
7.22 83
8.18 94
8.70 100
8.70 100
(Entrainment 1%)
100
80
fu � 60 u w "'
z 0
� b 40 � u.
t � "'
20 r 9
I 20 40 60 80
SURFACE COVERAGE !Xl
Real Flotation
Recovery (Percentage)
1±1
12±1
35±1
56±2
54±2
56±2
80±2
96±1
95±2
95±1
96±2
97±1
Figure 4.5(b)
100
39.
Table 4(c) Flotation recovery as a function of surface coverage for
-90+75pm quartz particles.
r(CH3)3 Si
mole g-l (x 107)
2.82
2.92
3.25
3.59
4.42
4.44
5.94
6.68
8.57
12.93
13.43
(Entrainment 1%)
2 0
�
100
80
b 40 rr
20
9
I 9
20
Percentage Surface Real Flotation
Coverage Recovery (Percentage)
21 2±1
22 14±1
24 58±1
27 67±2
33 70±1
33 74±2
44 91±2
50 94±1
64 96±1
96 97±1
100 97±1
Figure 4.5(c)
40 60 80 100
SURFACE COVERAGE l'l.l
40.
Table 4(d) Flotation recovery as a function of surface· coverage for
-75+63pm quartz particles.
r(CH3)3 Si
mole g-1 (x 107)
1.84
2.31
2. 72
3.41
5.47
5.55
5.85
8.00
9. 92
14.01
14.35
(Entrainment 2%)
100
Percentage Surface
Coverage
13
16
19
24
38
39
41
56
69
98
100
9 �?-
80
II;
;!
>-"' '"
6,0 6 u ? '" "'
z 0
� 40 0
� u.
� <( '" "'
20
20 40 60 80
SURFACE COVERAGE !%!
Real Flotation
Recovery (Percentage)
1±1
6±1
6±1
59±2
81±2
87±1
80±1
88±2
92±2
96±1
96±1
99
Figure 4.5(d2
100
41.
Table 4(e) Flotation recovery as a function of surface coverage for
-53+45pm quartz particles.
r(CH3)3 Si
mole g-l (x 107)
2.25
2.54
2.93
3.02
3.11
4.32
5.43
5.52
8.69
13.31
16.10
(Entrainment 3%)
100
80
/z s ,.. "' w
6.0
( ? >
0 u w "'
z 0
to >- 40 0 ll -' u..
-' t "' w "'
j 20
I ¢
20
Percentage Surface Real Flotation
Coverage Recovery (Percentage)
14 3±1
16 18±1
18 30±2
19 33±1
19 38±2
27 60±2
34 60±2
34 71±2
54 91±2
83 88±2
100 88±1
Fifl:ure 4.5(e}
40 60 80 100 SURFACE COVERAGE 1/.l
42.
Table 4(f) Flotation recovery as a function of surface coverage for
-45+40pm quartz particles.
r(cH3)3 Si
mole g-l (x 107)
2.02
2.02
3.19
3.53
4.03
4.53
8.38
12.39
14.61
16.80
(Entrainment 4%)
2 0
100
80
� b 40 rr'
20
20
Percentage Surface Real Flotation
Coverage Recovery (Percentage)
12 6±1
12 12±2
19 34±2
21 38±1
24 38±2
27 49±1
50 71±2
74 81±2
87 85±2
100 88±1
Figure 4.5(f)
40 60 80 100 SURFACE COVERAGE !'l.l
43.
Table 4(g) Flotation recovery as a function of surface coverage for
-40+30pm quartz particles.
r(CH3)3 Si
mole g-1 (x 107)
1.01
1.05
2.16
2.80
2.93
2.94
3.19
4.34
5.78
9.70
10.70
15.62
17.70
(Entrainment 4%)
100
80
i'< � 60 8 w "'
2 0
!;; b 40 rC
20
20
Percentage Surface Real Flotation
Coverage Recovery (Percentage)
3 0±1
6 4±2
12 16±2
16 13±2
17 22±2
17 25±2
18 21±2
25 24±1
33 35±1
55 45±2
60 45±2
8 8 52±2
100 52±2
Figure 4.5(g)
40 60 80 SURFACE COVERAGE (:t.,)
44.
Table 4(h) Flotation recovery as a function of surface coverage for
-30+23pm quartz particles.
r(cH3)3 Si
mole g-l (x 107)
1. 37
2.40
5.26
5. 72
5.99
7.20
11.62
17.52
19.35
19.94
21.01
(Entrainment 14%)
g 1;:
100
80
w
> 60
� "'
z 0
� b 40 � lL
20
Percentage Surface
Coverage
7
11
25
27
29
34
55
83
92
95
100
SURFACE COVERAGE l'l.l
Real Flotation
Recovery (Percentage)
0±2
5±1
12±1
18±2
19±2
19±1
25±2
32±1
34±2
36±2
35±1
Figure 4. 5 (h)
45.
Table 4(i) Flotation recovery as a function of surface coverage for
-14+5pm quartz particles.
r(CH3)3 Si
mole g-l (x 107)
1.15
1. 98
3.51
4. 52
4.86
4.87
6.04
7.02
7.48
7.98
10.75
11.11
12.13
15.26
15.44
22.23
24.77
25.02
(Entrainment 20%)
100
80
20
Percentage Surface
Coverage
5
8
14
18
19
19
24
28
30
32
43
44
48
61
62
89
99
100
20 qo 60
SURFACE COVERAGE !'l.l
Real Flotation
Recovery (Percentage)
1±2
0±2
0±2
4±1
5±1
7±2
8±1
9±1
8±2
10±1
14±2
15±2
15±2
19±2
20±1
24±1
29±1
28±1
Figure 4.5(i)
80 100
46.
A summary of the flotation response curves is shown in Figure 4.6(a)
and (b). Two separate sets of curves are used to more clearly
display the trends in the curves over the range of particle sizes
studied.
100
80
B > "' w
60 6 u w "'
z 0
s 40 0
� u.
� . ..:
w "'
20 •!Jm
20 40 60 80 100
SURFACE COVERAGE (/.J
Figure 4.6(a)
100
z 0
�
80
b 40 It
20
20 40 SURFACE
47.
Figure 4.6(b)
*
-1�"'""'
*f.lm
60 80 100
COVERAGE 11.)
Important points obtained from these curves are:
( i)
(ii)
For particles of 100% coverage, as the particle size
decreases from -150+125�m to -90+75�m there is a
slight increase in the flotation recovery. Further
reduction in particle size from -75+63�m to
-14+5�m resulted in a decrease in flotation recovery
at the same degree of surface coverage.
There is a critical surface coverage below which particles
of a given size range will not float. For example, a
sample of quartz of particle size -l4+5�m \•lith a
surface coverage below 14% will not float (Figure
4.3(i)). -l4+5�m quartz particles with surface
coverages below this value were prepared and, upon
flotation testing, it was found that no true flotation
occurred. These particles were tested for hydrophobicity
using the bubble pickup technique (Section 5.4.1). Here, a
captive bubble was pressed against a packed bed of the
particles. Appreciable bubble-particle cling was observed
whereas no adhesion occurred with clean quartz.
48.
The variation of critical surface coverage with changing particle
size is shown in Table 4(j) and in Figure 4.7. The average particle
size was taken as the midpoint of the range.
Nominal Particle Size Range (�m)
-150+12;5
-106+ 90
- 90+ 75
75+ 63
- 53+ 45
- 45+ 40
- 40+ 30
30+ 23
14+ 5
:r:ab:J,�_4jjJ
Average Instrumental Actual Particle Size (�m)
121
99
71
64
53
46
37
27
15
----- --------
140
Critical %
Surface Coverage
25
23
21
18
14
11
3
7
14
Fi�ure 4.7
Critical surface Coverage C'l.)
Fron these results it can be seen that a quartz sample -,;;vith a particle size
and surface coverage corresponding to a point to the right of the line in
figure 4.7 will not float.
49.
4.3 Assessment of Floated and Non-floated Material
The surface characteristics of the floated and non-floated fractions
were assessed by bubble cling tests (50) just after flotation. A
similar amount of bubble-particle cling was observed for both
fractions. Contact angle determinations on the quartz powders
(Section 5 .4.2) indicat.ed that all particles possessed the same
degree of surface coverage because the contact angles obtained were
equal to those on quartz plates of the same surface coverage. Blake
and Ralston (4) found that the maximum surface excess concentration
r(CH ) Si in mol m -2 was the same for all of the particle 3 3 max
size ranges studied, indicating that the free energy per. unit area was
the same. Therefore large particles (-l50pm) would behave the
same way as small particles (-14pm) with regard to trimethylsilyl
group untake.
The particle size distribution was measured for both the floated and
non-floated fractions. These results showed that for the 37±12,um
particles of 34% coverage, for example, the floated fraction was
enriched in coarser particles compared to that of the non-floated
rnater{al.
Examples of the results obtained are shown in Table 4(k).
Table 4Ck)
SAl'IPLE PARTICLE SIZE DISTRIBUTION (,urn)
Original Sample 36±12
Floated Fraction 39±10
·Fraction unfloated 31±7
Other particle sizes displayed similar enrichment of coarse particles
in the floated fraction.
!
100
80
s >-"' w
6 60 u w "'
2 0
� 1- 40 0 � u.
� <( w "'
20
50.
4.4 Variation of Indifferent Electrolyte Concentration
Flotation trials were performed to assess the influence of
indifferent electrolyte concentration on flotation recovery for three
particle size ranges. Potassium Nitrate solutions varying from
10-lM to 10-5M were used and the flotation recovery was measured.
Figures 4.8(a)-4.8(c) show the flotation recovery dependence on ionic
strength for particle size ranges of variable surface coverage.
•.:========-••-n • I
_y: Figure 4.8(a)
1/
f . Flotation Recovery
as a function of • &
surface coverage I
II
at various
:;. ·-· 10-'M
indifferent
10-'M ·---· electrolyte 10-'M
(KN03) I
I concentrations for
-106+90Jlm •
'
• ,quartz particles .
20 40 60 80 100 SURFACE COVERAGE l'l.l
100
2 0
�
80
5 40 it
20
100
80
� >-"' w
60 > 0 u w "' 2 0
� .... 40 0
� u.
� "' w "'
20
'SURFACE COVERAGE (/.)
•
20 40 60
SURFACE COVERAGE ('l.)
51.
•-• 10-'M
,.____ 10 _, M 10 _, M '
80 100
Fi�ure 4.8(b)
Flotation Recovery
as a function of
surface coverage
at various
indifferent
electrolyte
(KNo3) concentrations for
-45+40�tm
quartz particles.
Figure 4.8(c)
Flotation Recovery
as a function of
surface coverage
at various
indifferent
electrolyte
(KN03)
concentrations for
-14+5�tm quartz
particles.
52.
These curves show a small increase in flotation recovery as the
background electrolyte concentration is increased from l0-5H to
-1 10 H KN03. The critical surface coverage is decreased as the
background electrolyte concentration is increased. This trend is
depicted in Figure 4.9. The two sets of points were obtained for
three particle size ranges.
100 n
E ::L u
Q) N
U1
Q)
u
+-> ...._ ro
D.
c ro Q)
�
80 10-1M 10-5M, 10-3M
60
40
20
5 10 15 20 25
Critical surface coverage C%) Figure 4.9
Hean particle size as a function of the minimum surface
coverage required to initiate flotation for various
indifferent electrolyte (KNo3 solution) concentrations.
These results are consistent with those of Laskowski and Kitchener
(15) and Anfruns and Kitchener (51) in that the flotation recovery
increased with increasing ionic strength. As the background
electrolyte concentration increases1 the thickness of the electrical
double layer (1/�<) decreases. Therefore the equilibrium
thickness of wetting films on the quartz particles is reduced
53.
resulting in a more rapid thin film drainage between a bubble and a
particle. The result is more efficient flotation due to the overall
reduction in electrostatic repulsion.
4.5 The Rate of Flotation
4.5.1 Introduction
For a monodisperse particle size flotation system1
l - R -kt e (4a)
and a plot of ln(l - R) vs t would be linear (2). To enable
analysis of the flotation rate data for a polydisperse sample,
the following terms may be introduced: (52)
Assuming that the system shows two component behaviour, let
kf rate constant of fast floating component
ks - rate constant of slow floating component
Ff fraction of sample which is fast floating
Fs fraction of sample which is slmv floating
l (4b)
hence -k t -kft
(1 R) F e s + Ffe s (4c)
or -k t -kft
(1 - R) F e 8 + (l - F8
)e s (4d)
From a plot of ln(l - R) vs t which is non-linear, such as in
Figure 4.10, the kf and ks values may be obtained from the
initial and final gradients respectively: Fs, the fraction of
the sample which is slow floating, may be obtained from
extrapolation of this region of the curve to t - 0. It is
assumed that all of the fast floating component has disappeared
at this point and does not contribute to the flotation recovery.
at t- 0, ln(l - R) � lnFs (4e)
54.
4.5.2 Results : The Flotation Recovery as a Function of Time for
a Given Particle Size Range
The rate of flotation was measured for three particle size ranges
by determining the flotation recovery at various time intervals
up to a maximum of ten minutes flotation time. All other
variables such as pulp volume and gas flowrate were kept constant
(Section 4.1).
100
EO
20
2
The results are shown in Figure 4.10(a)-(c).
4 B 10
FLOTATION TIME (MJNJ
Figure 4.10 (a)
Flotation recovery
as a function of
time for quartz
(-106+90um) of
various surface
coverages
1; 100%
... 70%
D 64%
• 41%
0 38%
• 26%
100
100
BO
55.
FLOTATION TIME IMIN.l
-------------·----------�·--------·
-----· __. / -----·-20 �· .-----· ,_--0
..,-- o·- ------ ---- o D-o
.---• �:=:=:=:=:=:=o�======� 2 4 B 10
FlOTATION TIME lMIN.J
Figure 4.10 (b) Flotation recovery
as a function of
time for quartz
( -45+40!!ml of
various surface
coverages
h. 100%
... 60%
D 31%
• 27%
0 19%
• 14%
Figure 4.10 (c)
Flotation recovery
as a function of
time for quartz
(-14+5!!m) of
various surface
coverages
h. 100%
... 66%
D . 45%
• 19%
0 18%
To obtaln rate curves, · the
-----�4�.l�l�(�a�)�- (�
cA;)m)�. �� TIME !MIN.I 8 FlOTATION 6 4 2
-2
56.
. . plotted ln(l - R) ls . e (Figures against tlm
10 ®
•
Figure 4.1l
Flotatlon . rate for quartz curves
(a) -106+90pm
(b) -45+40pm (c) -14+5pm
(symbols for iven i n lines as g
Figure 4.10)
2 FlOTATION TIME61MIN.I
4 8
10
� •
:-------o----
-3
• 0�
·� :.·-_: ------------------· 0
•
�l •\o�o---o•- o • 8 10
-1
-2 ©
-3
57.
For quartz particles (-45+40pm) of 100% and 60% coverage
respectively, this dissection of the 1n(1 - R) curve is shown in Figure 4.12.
-3
(b)
FLOTATION . TIME (M!N.l 2 4 6 8
Figure 4.12
60% surface coverage
10
601. •
1007. •
at t - o, ln(1 - R) 1nFs Fs
Ff � 1 - F8 � 0.781 kf (-gradient) � 0.550 min-1
ks (-gradient) - 0.035 min-1
(a)lOO% surface
coverage
at t 0, ln(l - R)
e-2.05 1nFs
:. Fs 0.129
Ff � 1 - F8 - 0.871
kf (-gradient) - 0.896 min-1
k (-gradient) s 0.047 min-1
Hence, the equation of the curve at 100% surface
coverage is
(1 - R) 0.87le-0.896t + 0.129e-0.047t
e -l. 52 0.219
Hence the equation of the curve at 60% surface coverage is
(1 - R) - 0.781e-0.550t + 0.219e-0.035t
58.
The equations closely reproduce the experimental curves obtained in
Figure 4.12. Similar data may be obtained from other rate of
flotation trials for quartz of known particle size and surface
coverage. Some examples are given in Table 4 (1).
Table 4(1)
Particle I . I I
Surf. e k * kf F
f I Fs s
Size Gov.
I (Jtm) (%) (degrees) (min-1
)
I (min-
1)
I
I '
i '
r
l !
100 88 I 2.8±0.2 0.96
70 71 2.1±0.2 0.95
64 68 (0.024) 1.1±0.1 0.94
-106+90 41 53 (0.020) 0.6±0.1 0.28±0.03
38 51 (0.019) 0.4±0.05 0.25±0.03
26 41 (0.014) 0.1±0.02 0.67±0.02
;
i 100 88 (0.047) 0.9 ±0.1 0. 94
60 65 (0.035) 0.5 ±0.1 0.78±0.02
31 46 0.22±0.05 0.45±0.05
-45+40 27 42 (0.026) 0.20±0.05 0.42±0.05 I
19 35 0.10±0.02 I 0.33±0.03
14 30 0.04±0.05 I 0.20±0.03 I
I !
i. 100 88 0.4 ±0.2 I
0.30±0.04
I :
I -14+5 66 69 0.10±0.06 0.20±0.02
45 56 0.07±0.03 i 0 .13±0. 02 I
19 35 0.04±0.02 0.07±0.02
* k8 is given in some cases but not when either Ff was large
(<:0.8) or when the inaccuracy inks was so large (<:50%)
as to not permit any realistic trends to be observed,
0.04
0.05
0. 06
0.72±0.03
0.75±0.03
0.33±0.02
0.06
0.22±0.02
0.55±0.05
0.58±0.05
0.67±0.03
0. 80±0. 03
0.70±0.04
0.80±0.02
0. 87±0. 02
0.93±0.02
I I
I I
59.
CHAPTER 5 CONTACT ANGLE
5.1 The Young Equation
Bubble to mineral adhesion in flotation is linked with the contact
angle at the air/mineral/water line of contact. The Young Equation
gives a measure of this adhesion per unit length of triple contact
(53 - 55). A liquid droplet placed on a solid is shown in Figure
5 .1.
'a!fv VAPOUR
SOLID 'ds/1 lis·
Figure 5.1
The terms used are as follows:
8
Liquid/Vapour surface tension
Solid/Liquid interfacial tension
Solid/Vapour surface tension of solid interface
when the vapour from the liquid and the solid
are in equilibrium
Solid/Air surface tension of solid interface in
equilibrium ><ith its o\m vapour.
Equilibrium spreading pressure
Contact Angle, measured through the liquid phase.
60.
Initially, considering the solid surface in the absence of adsorbed
vapour molecules from the liquid,
7L/V cos 8 + 7S/L (Sa)
vihen all three phases are at equilibrium it must be realised that the
solid surface has an adsorbed film of the liquid of surface pressure
hence
7L/V cos 8 + 7S/L
n8, the equilibrium film pressure, is defined as the reduction
in 7so due to adsorption of molecules from the vapourised
liquid component at equilibrium (56).
7s;v
(5b)
(5c)
The work of adhesion of a liquid to a solid is related to the
interfacial surface energies as discussed by Fowkes (57) and shown in
equation (5d).
(5d)
Combining equations (5d) and (5b) we obtain an expression for
calculatiort of the work of adhesion of a liquid on a clean surface.
7L/V (l + cos 8) + �e (5e)
If the solid surface is in equilibrium with a vapour of the liquid,
this reduces to
7L/V (1 + cos 8) (Sf)
where WAD is the work required to part unit area of solid and
liquid, the final solid surface being covered with an equilibrium
61.
· adsorbed film. It can be seen that contact angle measurement is a
definitive technique for measuring the strength of adhesion bet,;een a
liquid and a solid. The same principle can be applied to the case of
an air bubble/mineral aggregate in flotation. For efficient
flotation, the HAD bet,;een a bubble and a particle must be high.
This occurs ,;hen 0, the contact angle (measured through the
liquid) is high.
Roughness, surface chemical heterogeneity and surface contamination
can influence the measurement of contact angles.
5.2 Contact Angle Hysteresis
Detailed discussions are available (58, 59, 61) on the factors ,;hich
contribute to differences bet,;een advancing and receding contact
angles. For the example sho,;n in Figure 5.1, the advancing contact
angle corresponds to liquid advancing over a previously uncovered
solid surface whereas the receding contact angle corresponds to
liquid receding from a previously covered solid surface. The
measured contact angle may be influenced by:
(1) Contamination
The liquid or the solid surface may become contaminated causing a
change in the equilibrium spreading pressure, rre, a change
in the solid/vapour surface tension, "�S/V• or a change in
the liquid/vapour surface tension, "�L/V'
(2) Roughness
The surface of the solid may be rough and if so, the microscopic
and macroscopic contact angles will be different. Many workers
have investigated the effects of surface roughness (58 - 63) and
the major features only are summarised here. Henzel (63) derived
an equation relating the contact angle on a molecularly smooth
surface (Os) to the observed or apparent contact angle
(Or) (equation 5g)
r cos Os (5g)
r is an empirically determined roughness factor (�1).
62.
Huh and Mason (62) derived a modified Wenzel equation for a
random surface roughness relating the average apparent contact
angle, Or to r, Os, and a surface texture factor �.
cos Os [r + (r - 1) �] (5h)
It has been shown (62) that when the drop size is large compared
to the surface roughness, the surface texture factor�
approaches zero and the original Henzel equation (5g) applies,
For a smooth plate \<here no detectable surface roughness is
evident upon microscopic examination, Or and 88 are
likely to agree well. Johnson and Dettre (58) demonstrated the
effect of surface roughness on contact angle in their model
(Figure 5.3). It can be seen that two very different observed
advancing and receding contact angles (8 a• Or)· may be
obtained on a surface l'Jhich is rough, On a microscopic scale,
however, both the advancing and receding angles are the same
Figure 5.3
(3) Surface Chemical Heterogeneity
Surfaces with different areas of chemical composition will result
in contact angles different from the 'pure' component
contributions. This issue is discussed further in Section 5.3.
63.
In general, surfaces are both ·rough and heterogeneous. Surface
heterogeneity is the principal cause of hysteresis unless the surface
roughness is particularly large (56). Johnson and Dettre (58)
suggest that surface roughness is not a serious cause of hysteresis
unless the rugosities are larger than about 0.5pm. The case of
surface he·terogene.ity requires deeper examination.
5.3 The Cassie Equation
Cassie in 1948 (14) proposed that a 'composite' contact angle,
ec, could be calculated for a microheterogeneous surface
consisting of a random arrangement of t'\10 separate compo.nents, viz:
cos ec (5i)
f1 is the area fraction of the surface with intrinsic contact angle
e1 and f2 is the area fraction of the surface with intrinsic
contact angle e2.
Although applications of equation (5i) are limited (58), it has been
used to describe surfaces such as those in the current study (36, 58,
64, 65). This equation enables us to derive a surface population
profile of a mixed surface (f1, f2) from observed contact angles
cec, el, 82) or vice versa.
Johnson and Dettre (58) postulated that as the size of the surface
heterogeneities become smaller, the contact angles measured tend to
be closer to those predicted by Cassie. Hence for the modified
quar�z surface in the TMCS/quartz model system where a random
arrangement of trimethylsilyl and surface silanol groups exists, the
Cassie equation is likely to be valid, as the chemical
heterogeneities are indeed very small.
64.
The advancing and receding contact angles.on fully methylated quartz
have been extensively studied. Similarly, the advancing and receding
angles have been measured for pure, clean quartz and paraffinic
surfaces with only -cH3 groups
' 02 � 0 (15, 34, 61, 64) and ,a
exposed, Using o1·a - 110±2 . .
Be a (the advancing angle on
' .
fully methylated quartz) � 88±9 (34 - 36, 64).
' cos 88 fl cos 110' + f2 cos 0'
fl cos 110' + (1 - fl) cos 0'
f1 becomes 0.72 ± 0.10
' (66 - 69),
Similarly, using the receding angles, 01 r � 88±10'(66, 67, 71), •
o2,r - 0' (15, 34, 61, 64) and oc,r � 72' (36).
cos 72'
0,72±0.15
This value agrees quite closely with one possible packing of spheres
on a surface (Figure 5.4).
65,
Figure 5.4
Unit Area
Sphere Area
Fraction of surface covered \vith spheres
0.79
The area fraction of 0, 72 also agrees 1olith the fact that a maximum of
2.6 surface hydroxyl groups per nrn2 quartz are capable of reacting
with TMCS, This was first estimated by Kiselev (70) and supported by
Knozinger (71). Blake and Ralston (4) later verified this through
adsorption studies of TMCS on to quartz particles. The value of 2.6,
when multiplied by the circular cross-sectional area of a
trimethylsilyl group, gives an area fraction of 0.72. Hence this
0.72 area fraction is self consistent.
100
Q:! LU ...J
80
� 60 c(
t; � 40 z
8 20
66.
The Cassie Equation therefore provides a means by 1o1hich a composite
contact angle can be predicted for a microheterogeneous surface such
as the one used in this study.
Composite contact angles (advancing and receding) for
waterjairjquartz for varying degrees of surface coverage with
trimethylsilyl groups are shown in Figure 5.5. A sample calculation
is given below. It should be noted that the maximum receding contact
angle of 72' predicted by this method corresponds to that
measured by Lamb and Furlong (36) for a fully methylated quartz
plate.
-Cassie Equation.
20
Sample Calculation
40 60
SURFACE COVERAGE !/.)
Figure 5.5
80
For a sample of quartz with 50% surface coverage (compared with
maximum uptake (4))
fl 0,5 X 0. 72 0.36
f2 1 - fl 0.64
Advancing: cos 8c a 0.36 cos 110' + 0.64 cos 0' •
8c a sg· •
Receding: cos 8c r 0.36 cos 88 0
+ 0.64 cos 0' •
8c r 49° •
100
67.
5.4 The Measurement of Contact Angle
5.4.1 Quartz Plates
A high purity optic·al grade quartz plate (as a 9mm diameter disc)
was cleaned according to the procedures described in Section
3.3. To modify its surface it was placed in the reaction vessel
so that it contacted the TMCS solution without contacting any
quartz particles (Figure 5.6). This was important as any induced
roughness that could arise from particle/plate contact was
avoided .
.-------------- �
In In
Ground Glass Tap
()-------() �Qulck·Flt Top
Side
/"�""'""' ';1
Approx\ Pulp
Height t�����i��� 1----
,__-::--
- �-
\ Quartz
Disc In "'
-- -- ---- _.:..=c
::- __ -
___ -- - -_-
Glass Mag� Follower
48
Figure 5.6
68.
The plates, initially pitch polished, were observed under an
optical microscope at 200X magnification. At this magnification
level no surface scratches or holes were detected.
After methylation the disc �<as removed, rinsed with purified dry
cyclohexane and then placed in a clean oven to dry at 110.°C,
After drying, the disc 10as stored in a ground glass container in
a vacuum desiccator over silica gel until needed,
Contact angle measurements were made by the well kno�<n captive
drop or bubble technique. The apparatus used was an adaption of
the 'Bubb.le Pickup Apparatus' described by Lee (50). It
consisted of a modified microscope with an attachment for
mounting a micrometer syringe (Figure 5.7).
E
Figure 5.7
D
The modified plate (A) was placed in the thermostatted sample
cell (B) on a movable platform (C) at 25.0 ± 0,5°G, [the cell
,.,as then filled with conductivity water at 25°G if a bubble
69.
profile was to be photographed] and allowed to equilibrate for
ten minutes. The cell was· illuminated with a standard microscope
illuminator (D) placed directly behind the sample cell.
A bubble of air in conductivity water or a drop of conductivity
water in air of approximately 2mm in diameter was formed at the
end of the micrometer syringe tip by advancing the micrometer
head (E).
For the air bubble, a receding water contact angle was obtained
by pressing the bubble against the plate until contact just
occurred. The advancing angle was obtained by withdrawing the
bubble from the surface. (The advancing and receding angles for
water ,.,ere obtained by pressing a water droplet against the
surface and withdrawing it respectively.) In practice these
events occur as minor (-1%) volume changes are made to the bubble
and droplet with the micrometer syringe. Great care ,;as taken to
ensure proper equilibration as well as the absence of mechanical
distortion. A photograph was taken (with a Pentax SlA camera
through a microscope viewing arrangement (F) (with a X9 eyepiece
and a X4 objective lens) of the drop or bubble profile. Large
photographs of the bubbles/drops were obtained and were further
increased in size by an enlarging photocopier. The contact angle
was obtained by measuring it directly with a protractor to an
accuracy of ±2°. The entire contact angle measurement
apparatus was placed on a thick rubber matting to reduce any
vibration effects. The syringe and the sample cell were
�arefully cleaned to minimise any contamination of the quartz
surface. Even very lmv levels of surface contamination \Vill
result in inaccurate contact angles.
70.
The results obtained are the average of at least two separate
experiments performed with drops and bubbles. No difference in
angle was obtained for drops and bubbles for a given surface
coverage (within experimental error). The results are shown in
Figure 5.8 and tabulated in Appendix 6. Sample photographs of
drops and bubbles are given in Plates 4(a) to (d ). A clean
plate was shown to have a zero contact .angle both by measurement
(Plate 4 (e) 0 .• ;,. 0), by the absence of any detectable cling as
a bubble is '"ithdra>m from its surface and by the presence of
excellent interference fringes. Experimentally it is very
difficult to distinguish a very small contact angle (say 2")
from 0". No recourse was made to a method proposed by Fisher
(101) since the primary interest in this study was for angles in
excess of about 25". Therefore in the absence of unequivocal
evidence to the contrary, a clean plate was taken to have a
contact angle of zero.
-Cassie Equation
100 o Advancing
- 80 CD
� <.? '60 z ..:
,_ u
� 40 z 0 u
20
®Receding
20 40 60 80
SURFACE COVERAGE 1'/.l
Figure 5.8
100
71.
39% coverage
Receding air
Advancing 1120
Plate·4(b)
39% coverage:.·
Advancing ·air
39% coverage
Receding air
7la.
Plate 4 (d)
39% coverage
Advancing air
Plate 4 (e)
. 0% coverage
Advancing air
72 .
It can Pe seen that the measured contact angles are in very good
agreement with those predicted by the Cassie equation for both
advancing and receding angles.
5.4.2 Quartz Particles
Many methods have been employed in the attempt to measure the
contact. angle of particles (72). There are two main categories
into which these methods can be divided
(a) Dynamic methods
(b) Equilibrium methods
Dynamic methods such as that proposed by \Vashburn in 1921 (73)
(where the rate of penetration of a liquid into a packed bed is
related to the contact angle) suffer from disadvantages if
soluble surfactants are present (72).
Equilibrium methods such as the Bartell et al method (74 - 76,
102) and the \Vhite and Dunstan method (77) where the pressure
necessary to balance the Laplace pressure (which drives liquid
into a capillary bed) is measured are potentially much more
useful methods. Dunstan (40) developed an apparatus for
measuring this capillary pressure across a powder plug. This
technique is yet to be refined (77). The technique suffers from
a drawback in that the effective pore radius (reff) must be
known.
2(1
(where �p is the volume fraction occupied by the particles)
AP'· the specific surface area of the particles is also
required, which may present problems for coarse particles where
surface area measurements tend to be inaccurate.
73.
A straightforward method for determining the contact angle of
;·mter on quartz particles is the method first described by
Washburn (73) and later by Rideal (78). The method was modified
by Studebaker and Snow (79), subsequently used by other workers
(80 - 82) and tested thoroughly by Fisher and Lark (84).
This method is suitable for the Tl1CS/quartz model because the
trimethylsilyl groups [(CH3)3 Si] are firmly 'anchored' to
the quartz surface (4) and are not soluble. l1easurement of the
unknown reff could be factored out by using a liquid which wets
the surface completely, thus removing any need for a separately
determined reff value.
Szekely, Newman and Chuang (83) derived a usable form of the
Washburn equation by equating the Laplace equation pressure to
that of the Poisseulle equation for viscous drag in conditions of
·steady flow. They proposed that the rate of wetting of the
powder .ras given by
8
'1
t
tortuosity factor
liquid/vapour surface tension of the
penetrating liquid
contact angle
viscosity of the penetrating liquid
(5j)
Good and Lin (85 - 87) modified the Washburn equation further to
incorporate an equilibrium spreading pressure term (Ke - K0)
t
K (7LjV COS 8 + Ke-Ko)
2'1 (5k)
74.
rre equilibrium spreading pressure
rr0 spreading pressure at zero time
The reason for this modification is as follows:
If a porous body is initially devoid of an adsorbed layer of the
penetrating liquid and if the molecules of the penetrating liquid
are not, transported ahead of (or equal to) the moving liquid
front at a rapid rate by diffusion, then the rate of penetration
will be faster than that predicted by the I.Jashburn equation.
This is due to the fact that an adsorbed film or the surface of a
solid results in an overall reduction in the free energy of the
solid (87).
This theory is related to the 'initial spreading coefficient'
theory proposed by Harkins (88). Surfaces without an adsorbed
film contribute 1so, not 1s;v• to the driving force for
penetration. If transport processes (such as diffusion) are not
at least as fast as the advancing liquid front then there is a
driving force for penetration which is given as the spreading
pressure. Equation (5j) is applicable to a solid which has been
exposed to a saturated vapour of the liquid to be used as the
penetrating medium.
"e is often very low (and may be taken as zero) for mariy
low energy surfaces, however for high energy surfaces such as
that of quartz, the �e term cannot necessarily be taken as
zero (96). The "e contribution to contact angle can be
evaluated by comparison of contact angles on powders devoid of
any adsorbed film to those in equilibrium with the vapour of the
proposed penetrating liquid.
The form of the I.Jashburn equation derived by Szekely, Ne;nnan and
Chuang (83) incorporates a tortuosity factor "' to allow
within the network of capillaries of varying internal radius
within a powder plug. If an effective pore radius is known, the
75.
tortuosity factor can be approximated and hence a contact angle
can be obtained from the rate of penetration.
Methods for determining the pore radius of a packed bed of
particles include:
(a) Liquid Intrusion Methods (28, 90 - 92) such as Mercury
Porosimetry assume a constant contact angle of mercury on
the solid to be 130". This \Oould seem an unrealistic
assumption to make for quartz of various surface coverages
ranging from 0 to 100% coverage. Hysteresis is also
ignored with this method.
(b) Calculation l�ite (89) proposed a method for calculating
reff for a powder with known specific surface area, volume fraction and density.
(c) Rate of penetration measurement lVith a vretting liquid If a liquid known to have a zero contact angle with a solid is used to measure the rate of penetration of a packed co'lumn of that solid, equation (Sj) reduces to:
t
As "�L/V and
penetration � are constants and the rate of
12
/t is measurable, �. the tortuosity
factor can be evaluated. Hence reff can be obtained.
Experimentally this process is performed by direct comparisons of rate of penetration measurements. If 'i'le
define the follo\Oing terms:
(51)
the rate of penetration gradient for a non-wetting
liquid
the rate of penetration gradient for a \Oetting
liquid
76.
"�U/A surface tension
"�H/A surface tension
�u viscosity of
�,., viscosity of
then it follows that
C2
)u --C).
�<(?u;A cos
2�u
�<(?1'1/A cos
2�w
and as cos Ow l
the
the
Ou)
Ow)
of the non-wetting liquid
of the wetting liquid
non-wetting liquid
wetting liquid
gradient of non-wetting liquid
gradient of I·Tetting liquid
5.4.2.1 Hetting Liquids
Cyclohexane and toluene were the two liquids chosen as the
wetting liquids because
(5m)
�u (Sn)
(i) Upon testing they were shown to spread readily and quickly
over the quartz surfaces; and
(ii) Organic liquids possess low specific surface free energies
and hence spread on solids of high surface free energy
(such as quartz) resulting in an overall decrease in the
free energy of the system (68).
Uniform wetting line gradients were obtained for all quartz
samples. As the contact angles obtained were very close to those
predicted by the Cassie equation for both the trials using
cyclohexane and toluene as wetting liquids, it can be concluded
that these liquids form a zero, or near zero contact angle.
77.
The following gradients were obtained for clean quartz.
t \'Jetting Liquids Non-l'letting Liquid
Cyclohexane 0.103±0.001 Hater 0.299±0.001
Toluene 0.199±0.001
I I
The contact angles corresponding to these values (from equation
5n) are as follm;s:
Hetting.Liquid Contact Angles
Cyclohexane 1.8±9.4"
Toluene 1. 6±7. 6 °
The large error is a function of the equation at low contact
angles (the cosine is very sensitive). Higher contact angles
result in an error of only one or two degrees maximum.
5.4.2.2 Preparation and Packing of Quartz Particles
Samples of quartz particles with various degrees of surface
coverage were prepared by the technique described in Section
3.4. A six gram charge of quartz was prepared for all contact
angle measurement studies.
The t,;o types of quartz prepared were:
(i) Quartz exposed to a saturated vapour of the proposed
penetrating liquid.
(ii) Quartz from a dry environment free of adsorbed liquid
layers.
I
Samples of type (i) were prepared by equilibrating the dry quartz
particles with the vapour of the proposed penetrating liquid for
a period of two hours in a closed container at 25"C (Figure
5.9). The glass capillary tubes used for the rate of penetration
measurements tvere then packed and stored within this environment
until needed.
78.
f---BEAKER
WEIGHING-(--\--/ BOTTLE
Figure 5.9
\QUARTZ
The use of equation (5n) assumes a constant tortuosity factor
(�<) for both the >letting and non-wetting liquids and hence it
;ms important that the capillary tubes were packed in a
homogeneous and reproducible manner.
Patrick (94) and' Van Brakel and Heertjes (95) have described
methods for producing an homogeneous powder bed in which
horizontal vibration and applied to a bed as particles were
deposited on to the bed surface. These techniques required
detailed frequency of vibration studies for a given particle size
range in order to obtain optimum packing uniformity. Anderson et
al (97), Crm;l and \?oolridge (81) and Dunstan and \fuite (77, 99)
have obtained reproducible contact angles on packed beds using a
manual packing technique. Here, small amounts of powder were
placed in the tube whilst the tube was tapped in a uniform
manner.
In this study, a cleaned glass wool plug was placed in a
capillary tube. Quartz was added in small.quantities with
constant tapping. All tubes destined to contain the same quartz
sample type were packed at the same time to ensure as uniform a
packing as possible. The tube was then placed against a
graduated scale as in Figure 5.10.
GRADUAT ED
SCALE
PE TRI DISH
79.
Figure 5.10
0
LIQUID LEVEL
STAND
RUBBER BAND
SILICA POWDER
GLASS T UBE
The penetrating liquid was placed in the petri dish and allowed to
contact the bottom of the capillary tube . . Timing commenced as the
liquid front passed the '0' point on the graduated scale (see Figure
5.10) i.e., the time recordings were all taken as the liquid fr?nt
was �oving (100). The time taken for the advancing liquid front
to ascend through a certain height t·las recorded. To assist the
visual observation of the liquid front a light source was placed to
one side of the tube.
Substituting the appropriate viscosities and surface tensions the
follot<ing expressions were obtained.
80.
r(grad�ent water line ' )
11 grad1ent cyclohexane line
r(' gradient water line ) � gradient toluene line
These expressions permitted calculation of advancing contact
angles from rates of penetration of water, cyclohexane and
toluene into a packed bed of quartz particles.
5.4.3 Results
The advancing water contact angles of both the dry quartz powders
and the quartz powders in equilibrium with water vapour are shown
in Figure 5.11 and in Appendix 3. The points shown are an
average of at least three separate experiments. The rate of
penetration graphs are given in Appendix 7 and the gradients of
the wetting lines given in Appendix 4 .
.,-Cassie Equation
100 o Dry Powder
- 80
·�
� o ·Go z <
1-u � 110 z
8 20
1::1 Powder in Equilibrium with VaROUr
20
oo
110 60 80
SURFACE COVERAGE (/.)
Figure 5.11
100
81.
The results obtained are in close agreement to those angles
predicted by the Cassie Equation except at ma�imum surface
coverage ·where the measured angle is somewhat lower than
predicted. The· value of 72° is similar to that measured by
Garhsva et al (103) by the same technique; the precise reason
for this reproducible effect is not clear. Haximum uptake
studies of THCS on quartz particles were performed (see also
Section 3. 4. 6) and it ,;as confirmed that maximum surface coverage
samples 1vere used for the \·Jashburn contact a�gle measurements,
both with, and devoid of an adsorbed layer of the proposed
penetrating liquid. Plates methylated to the same extent gave
contact angles of.ss•.
5.5 Comparison of Heasured Contact Angles to Theoretical Contact
Angles
The measured contact angles on both plates and particles appear
to equal those predicted by the Cassie Equation. To directly
compare these two techniques, particles and plates of the same
surface coverage were prepared at the same time in the one
reaction vessel. The results are shown in Table 5(a) showing a
good concordancy bet1-1een methods.
82.
Table S(a)
Measured Angles
I I I Angles Predicted by l
!Particle Powders Plates I Surface Cassie Eguation I
[size (Jlm) Coverage (%) AdvancingiReceding !Advancing ! Advancing d" ' Rece �ng•
I ! I
I
I ' '
' I
! '
i ' I 21 3r 32' 35' 40' ' '
29 I 44' 37' i 40' 45' I
' I
35 49' 41' I so· 49' ' I
-40+30 40 '
52' 44' I so· sr I I
'
43 54' 45' : 52' 54' '
I
50 59' 49' 56' 59'
56 i
63' 52' 63' 63' I
i :
' '
'
'
' 34 48' 40' 48' 49' i I
-45+40 38 i 51' 42' 51' 51'
39 I 52' 43' 52' 52"
I 44 i 55' 45' 55'
I 55'
I From these results the following conclusions may be drawn
(i) \Vithin experimental error
8cassie � 8plate �
8powder (except at very high coverage when epowder is less)
(ii) It appears that over the particle size ranges studied, the
particle size exerts no influence on the contact angles
measured. Angles for both the -40 + 30}lm and -45 + 40Jlm
size ranges are in agreement with the angles calculated by
the Cassie equation. (Individual trials on larger and
smaller particle size ranges were performed and it was
found that for up to about 70% surface coverage the
contact angles obtained were in agreement with the
Cassie equation. To test all particle size ranges and
surface coverages was unnecessary and too time consuming.)
31'
37'
40'
44' I I
44' I
i 48' I
53' I I
38'
42'
42'
43'
83.
(iii) The packing of the capillary tubes appeared to be uniform
for a given surface coverage. This was indicated by the
close agreement of the contact angles obtained by using
both cyclohexane and toluene as wetting liquids on quite
different samples.
(iv) There was no detectable difference in contact angles
obtained on dry powders compared with those previously
exposed to a vapour of the proposed penetrating liquid.
This indicates that the equilibrium spreading pressure
term (rre-rr0) has no detectable effect on the
measured contact angle by the Washburn technique (within
experimental error) for the modified quartz surface.
Hence, the original form of the Washburn equation (Sj)
applies.
(v) Irregularities on quartz particles have no appreciable
influence on the contact angles on the powder samples
(Opowder). Electron micrographs of the surface of
the quartz particles indicate the presence of undulations
on the fracture surfaces (conchoidal fractures). The
contact angle of an individual particle may perhaps vary
from particle to particle, however the Washburn contact
angle is an average of the contact angles determined on an
assemblage of particles.
Overall, Opowder � Oplate =
Ocassie
84.
CHAPTER 6 DISCUSSION
6.1 Introduction
In this chapter discussion of the limits of flotation, induction
times and rate constants will be dealt with in sequence.
6.2 Particle Size Limits in Flotation
It has been sho'im that for a given particle size range there is a
definite surface coverage and advancing water contact angle belm·l
which the particles will not float. This is shmm in Table 6(a) and
displayed in Figure 6.1.
Table 6(a)
I Nominal Particle I Mean Instrumental I Critical 'Critical'
I Size Range (I'm) I Particle Size I % Surface Cassie Contact Angles
I (I'm) I
Coverage (Degrees) ±20 I I I I I Advancing Receding ! I I
i I
-150 I
+ 125 121 I 25 41 35 I
-106 + 90 99
I 23 39 33
- 90 + 75 71 21 37 32
- 75 + 63 64 18 34 29
- 53 + 45 I 53 14 30 26 I !
!
I - 45 + 40 46 11 "26 22
- 40 + 30 37 3 12 9 ! I I i - 30 + 23 27
I 7 21 17
;
I i - 14 + 5 15
I 14 30 26
! I
I
I I
I
I
140
120
{")
�100 u
w ,t:! Vl 80 w u p .... "' 60 a.
c ro w ;::;; 40
20
85.
Advancing Water Contact Angle
35· s2· 55· 77" sa·
no flotation
flotation
no flotation
20 40 60 80 100
Critical surface Coverage C%)
Figure 6.1 · ;pag_i_ccJ_e __ s_il'.te ... aS. . .!l fu!l<e1:i2I1 _oJ
c;r_tl;i_c_al "'n:fac_f! _ _cc.o_Y?rag"- ai1d
97Q!l1:!l.c.t.i!ngle
For each of the particle size ranges studied there is a minimum
contact angle· required for initiation of flotation,
6.2.1 Coarse Particles
In the absence of turbulence, the maximum particle size which can
be floated is dependent on the balance of capillary and
gravitational forces acting on the particle, For particles less
than or equal to about 300 to 500 �m and for bubbles greater
than or equal to about O.Smm in diameter, hydrostatic and
capillary pressure influences may be neglected (1, 16) so that
the maximum diameter of particles which can be floated is given
b y
dp, max, g
86.
1 sin w* sin (w''< + O)j llpg + ppbm
(6a)
where _dp, max, g -refers to the maximum diameter which can be lifted
by a bubble due to gravitational limits, 1 is the water/vapour
surface tension, 0 is the water contact angle, w* - 180' - 0/2
for 0<90' and refers to the location of the particles at the
water/vapour surface, llp is the density difference between
the particle and fluid, g is the gravitational constant and bm is
the bubble acceleration, which under gravitational conditions is
equal to zero.
Scheludko et al (17) derived a similar expression for spheres located
at a '\Vaterjvapour surface assuming that the volume of contact above
the wetting perimeter was small in comparison with the total volume
of the sphere (i.e. for 0<40')
d -p,max,g sin
o
2
Huh and Mason (113) have given a more general analysis of the
Scheludko et al result.
Taking 1- 72 mNm-1, g- 9.81 ms -l and the density of quartz
as 2. 5 X 103
kg m-3
, 1 f d b 1 1 d f va ues o p,max,g can e ca cu ate or
various contact angles using equation (6a).
(6b)
The value of 2.5 x 103
kg m-3
was taken as the density of quartz
to allm• a consistent comparison '·lith subsequent calculations. There
is only a slight difference in calculated particle diameter using the
actual density of quartz as 2.65 x 103
kg m-3
(43). d p,rnax,g as a function of contact angle is given in Appendix 8 and represented
in Figure 6.2
87.
Equations (6a) and (6b) do not describe the dependence of particle
size on contact angle under the turbulent conditions in a flotation
cell. d refers to the maximum particle diameter which may p,max,g be lifted by a captive bubble, heJd at the end of a capillary. Under
such static, condit-ions, the bubble may or may not lift the particle
depending on whether the conditions described in equations (6a) and
(6b) are satisfied.
The most detailed treatment of the flotation of coarse particles
under turbulent conditions is the kinetic theory proposed by Schulze
in 1977 (l, 16). This theory assumes that bubble-particle attachment
has occurred and that the stability of the aggregate is controlled
directly by the energy required to cause the particle to detach and
the kinetic energy of the particle. The particle acquires a velocity
(the turbulent relative velocity) vt, due to stresses on the
bubble/particle aggregate in the turbulent field of the flotation
cell (e.g. by collisions with other bubbles or aggregates).
vt refers to the velocity of gas bubbles in the flotation cell
(1, 16, 17).
The energy of detachment, Edet• refers to the work done in causing
a particle to move from its equilibrium position at the water/vapour
surface to some critical point where detachment occurs. In order to
determine Edet• the forces acting upon the particle must be
considered. The sum of the gravitational, buoyancy, hydrostatic
pressure, capillary, capillary pressure and machine acceleration
contributions is zero at equilibrium. The sum of these forces is
related to Edet by
(6c)
where heq(w) defines the equilibrium position of the particle
at the surface as a function of the central angle w and
hcrit(w) represents the position at which the particle is
detached from the surface and moves into the liquid phase. h is
88.
obtained by numerical integration of the Laplace equation.
The detachment process takes place when the·kinetic energy of the
particle equals the detachment energy, giving the maximum floatable
particle diameter based on the kinetic theory, dp max v as ' '
hcrit(w)
d { ' 2 2 I 0�Rp
3pfg { 1 2p . p
cos3w p,max,v 2�ppvt
3h +
2Rp
�<� sin
3 sin2w -
a2R 2
w) -2 { 2� Rb
p
Pf heq(w)
sin w sin (w + e) }
)�] 1
2Rbpfg } 3
where Rp and Rb are particle and bubble radii, Pf and
Pp are the fluid and particle densities and a is the capillary
or Laplac_e constant.
(6d)
Equation (6d) may be solved nume�ically or by plotting each of the
kinetic and detachment energies as a function of Rp at constant
� and Pp at specified vt. The latter technique was
chosen here. Schulze (1) provides partial solutions to allow the
calculation of Ekinetic and Edet·
Energy of detachment is given as a function of contact angle for
various particle radii in Appendix 9 . The kinetic energy of bubbles
rising at 20, 25 and 30 em s-1 (the bubble velocity range embraced
by 90% of the bubbles in this study) were calculated and are given in
Appendix 10. A plot of the detachment and kinetic energies against
particle size allows the limiting particle radius (Rp,max,v) to be
obtained from the points of intersection of these energies. These
points are given in Appendix 11.
89.
The 8 in equation (6d) refers to the advancing water contact angle because attachment has occurred. During detachment the liquid
·advances over the solid surface.
The kinetic approach of Schulze (1, 16) is more comprehensive than the thermodynamic method proposed by Scheludko et al (17), however the two theories show similar trends in their dependence of dp max v on 8
. ' '
The experimental results obtained from this study are shown in Figure 6.2. The dependence of dp,max,g on 8 obtained from equation (6a) predicts the flotation of much larger particles (for a given 8) than is observed experimentally.
The dependence of dp,max v on 8 from equation (6d) is shown for vt � 20 and 30 em s·i, corresponding to the predominant range of bubble sizes and velocities in the current study. (pp was taken as 2.5 x 103 g m·3 and"' was measured as 72 mNm-1).
For particles between 45 and 125pm in'diameter there is quite good agreement between experimental results and those predicted through equation (6d). Within experimental error, the flotation recovery of the angular methylated quartz particles (whose advancing water contact angles have been measured independently) agrees with that predicted by Schulze for smooth spheres. Microscopic events associated with surface roughness and particle shape (60, 62) are evidently of insufficient magnitude to detectably influence the dp max v versus 8 threshold behaviour under turbulent flotation
' '
conditions.
The current study could have focussed on the behaviour of single spherical particles at interfaces, however the theory represented by equation (6d) has .already been substantiated (16). Similarly, the flotation behaviour of spherical glass ballotini could have been studied, but it has been previously sh01m (10) that smooth spheres
90.
and angular particles display quite different short range
hydrodynamic flotation behaviour and collection efficiencies. Angular particles were chosen to enable direct correlation with
flotation practice. The current results indicate that the behaviour of coarse, angular particles typically encountered in flotation pulps may be predicted reasonably well by equation (6d) provided the
relevant parameters are known.
6.2.2 Fine Particles
The sole theoretical treatment of the limits of flotation of fine
particles has been performed by Scheludko et al (17). The
critical work of expansion of a three phase contact was equated with the kinetic energy of the particles yielding a minimum
particle diameter·for flotation given by equation (6e).
d . p,min,v 0) l
l
/
3 (6e)
where � is the line tension, opposing expansion of the three phase contact and vb is the bubble velocity. (All other terms are as previously defined.)
The value and importance of the line tension.is uncertain. It
was first proposed by Gibbs (21) and later analysed by others
(24, 25, 105). Experimental data are scarce and of doubtful
reliability (106) so that reliable calculations involving line tension cannot be performed.
Nevertheless using the extreme values of 2.8 x lo-10N and
5.6 x lo-10N determined by Scheludko et al (17), values of . -1 dp,min,v were calculated >lith vb at 20 and 30 em s .
p was taken as 1.6 kg m-3 and-y measured as
72.0 mNm-1. Receding >Tater contact angles (the liquid front
recedes as the three phase contact expands) calculated from the
Cassie equation '\•Jere used in this calculation because receding
contact angles could not be measured on the methylated particles
91.
with the \vashburn technique. Close agreement between calculated
and measured contact angles on plates suggests that the use of
these calculated angles involves little error.
Values of dp,min,v are given as a function of contact angle in
Table (6b) and displayed in Figure 6.2.
Contact Angle I (degrees) I
I I
vb !
I I
I i 10 I
20 I
I I
I 30 I
I
I 40
I 50 !
i 60 I
'
I I
Table (6b)
d . p,rn1n,v (Jim)
X: - 2.8 X lo-10N
20 cms-1 30 cms-1
I
3.1 I 2.3
1.9 1.5
1.5 1.1
1.2 0.9
1.1 0.8
1.0 ' 0.7 I I I
" - 5.6 X 10 -10N
20 cms-1 30 cms-1
4.9 3.7
3.1 2.3
2.4 1.8
2.0 1.5
1.7 1.3
1.5 1.2
I
92.
Figure 6.2 Experimental threshold values showing flotation domain
compared with theoretical prediction.
a:
b:
c: e:
f:
a
. ,, .
.... --
60° contact Angle
Maximum particle diameter for flotation-under static, gravitational conditions. Maximum particle diameter for flotation under turbulent conditions assuming bubble velo.city of 20 em s·1. As for (b) with assumed bubble velocity of 30 em s - 1 Minimum particle diameter for flotation under turbulent conditi��s taking K - 5.6 x lo-10N and bubble velocity 20 ern s •
As for fe) ·with K 2.8 x 10·10 N and bubble velocity 30 ems- .
There is a qualitative agreement between the predictions of
equation (6e) and the experimental data. For smaller particles
with less kinetic energy, a larger contact angle is required
before they will float. For the experimental data and theory to
more closely agree, the values of K would need to be at least
an order of magnitude larger than those determined to date.
93.
� should also depend on contact angle as well as on the
geometry of the three phase contact line (1, 104). A much
clearer interpretation of � is required before it can be used
in calculations with any confidence. The evidence to date
indicates that the concept of line tension� in its present form,
is inapplicable to flotation studies.
It is significant to note that the kinetic theories of flotation
limits for coarse and fine particles together predict both the
existence of a flotation domain and a minimum contact angle and
an optimum particle size for flotation under special conditions
(i.e. the intersection of the dp,max,v and dp,min,v curves).
The reasons for the changeover in mechanism from coarse to fine
particle behaviour are unclear, however it may be proposed that
for the finer particles the hydrodynamic resistance of the thin
liquid film between the particle and bubble andjor some delay in
the rate of formation of the wetting perimeter may contribute to
the difference between the theoretical predictions and the
experimental results of the present study.
Further insight into the differences between the flotation
behaviour of various particle sizes may be obtained from
consideration of flotation rate constants and induction times.
6.3 Induction Time
For a bubble and a particle to adhere during contact in a flotation
cell, two main events must take place:
(i) thinning and rupture of the film of liquid between a
particle and a bubble, and
(ii) expansion of the three phase line of contact to form a
wetting perimeter.
94.
The sum of the time taken for these two events to take place is the
induction time (A) and must be less than the contact time (tc)
if flotation is to occur. tc embraces both the collision time
(tc*) as well as the sliding times (tsl) (1).
It is possible to calculate (to a first approximation) A from the
kinetic theory proposed by Sutherland (107, 108). The Sutherland
model is based on potential flow. Dobby and Finch (109) corrected
the original derivation to principally account for an overestimation
of the induction and sliding times.
The concentration, C, of mineral floated at time t is related to its
initial concentration C0 by the recovery, R.
c R-
v1here bubble radius
Rp particle radius
vt bubble/particle relative velocity
NB number of bubbles per unit volume
(6h)
& fraction of particles retained in the froth
following bubble-particle attachment (stability
efficiency of bubble-particle union)
The Sutherland treatment is restricted to long range hydrodynamic
interactions and describes experimental particle trajectories quite
,.,ell except when particles come very close to the bubble surface,
(within two or three particle diameters) where the inertial forces of
the particle cause deviations from the fluid streamlines.
95.
This theory yields results which are in good agreement with
experimental determinations of bubble trajectories, touching
angles and collision efficiencies despite the absence of
allowance for bubble deformation and film thinning mechanisms,
deficiencies which were recognised by Sutherland (108).
Current alternative experimental and theoretical methods for
determining induction times are generally based on either
pressing a bubble against a smooth mineral surface or against a
bed of particles. The disadvantages of all current methods for
determining A include insufficient:
(i) understanding of the process of bubble deformation and
energy dissipation during bubble-particle collision.
(ii) information on the attractive hydrophobic forces during
bubble-particle interaction (e.g. how the thin film of
liquid evolves with time).
(iii) data on tfilm (e.g. the influence of surfactant type and
concentration on thin film drainage rate mechanisms).
(iv) data.available on ttpl (time of formation of the three
phase line) as. a function of hydrophobicity, surface
roughness and surfactant type.
One of the most appropriate methods for determining induction
�imes is probably through observation of bubble-particle
interactions in a flotation cell under well defined conditions
similar to those used in this study. For the present, the
Sutherland approach may be used to determine A from the
experimental flotation data generated in this study.
96.
A values were calculated from the flotation data shown in
Figure 6.3 for three particle sizes. Vt was taken as
25 em s-1, 0 as unity as no detachment was assumed after
successful attachment, RB taken as 6 x 10-4
m and NB as
5 x 106 bubbles;m3 (see Appendix 12 for calculation of NB).
To enable a reliable calculation of A, the recovery data was
required to be large due to the fact that the particles used
this study, although tightly sized, were of a narrow
distribution. Using large recoveries ensures that A
in
represents a reliable average of the particles in the size range
as RB, Rp and vt are all average values. Wherever
possible, recovery values of greater than 70% were used to
calculate A. Lower recovery values result in an
underestimate of A and are clearly shown (Figure 6.4).
Calculated A values range from 3.5 to 6.5 milliseconds.
These values fall within the range of experimental t0* and
tsl values presented by Schulze (1) and are an order of
magnitude less than the A data reported at ionic strengths of
10"1M KGl and less by Laskowski and Iskra (39) for coarse
(-200 + 150 pm) methylated quartz particles.
Figure 6.3 Flotation recovery as a function of time for various
surface coverages and advancing water contact angles.
�
tl 80 > ..... Ql > 0 � 60 "' c 0 � 40 b u:
20
�:�· � � Y://0
f; �= ( �0 'f �
------------· II �·
1�./· 2 4 8 10
Flotation Time CminJ
Figure 6. 3 (a}
-106+90/'m quartz
Surface coverages
/:,. 100%
... 70%
0 64%
• 41%
0 38%
• 26%
�
t; 80
i � 60 "'
.§ � 40 b u:
97.
2 4 6 8 10
Flotation Time cmln)
·---· 0
2 4 6 8
Flotation Time CmlnJ 10
Figure 6.3(b)
-45+40JLm quartz
Surface cover�ges
A 100%
� 60%
D 31%
• 27%
0 19%
• 14%
Figure 6.3(c)
-14+5JLm quartz
Surface coverages
A 100%
� 66%
D 45%
• 19%
0 18%
The induction times are shown in Figure 6.4. It can be seen that
(i) for a given particle size, A increases with decreasing
surface coverage and advancing water contact angle to a
limit controlled by the threshold values shown in Figure
6.1 and Figure 6.2. This may reflect a decrease in the
magnitude of the hydrophobic force with decreasing contact
angle (110), electrical double layer and Van der l'aals
forces remaining constant.
98.
(ii) for a given surface coverage and contact angle, above the
threshold values,
A-14+5pm > A-106+90pm > A-45+40pm
The variation in A with particle size indicates
differences in the bubble-particle attachment mechanism.
6·0
,... (./) E 5·5 u Q) E i=s·o c 0.
B -5 4·5 £
4·0
Advancing Water Contact Angle
35· s2· 6s· 77" sa·
3· sL---=-2�o---=4"""o---=6�o---=a"="o---..,1 o�o surface coverage C%)
Figure 6.4 Calculated induction times as a function of
particle size and surface coverage. (t indicates
overestimate) e-106+90jim, o-45+40pm, o-14+5 pm
In the current study, the shortest A values occur at or near
to the minimum. in the flotation domain curve of Figures 6.1 and
6.2.
99.
Particles with contact angles belm• the threshold values as shown
in Figures 6.1 and 6.2 do become attached to a captive air
bubble. This suggests .that a longer bubble-particle contact time
(and a lower vt) would be advantageous in obtaining a greater
flotation recovery of weakly hydrophobic particles.
The induction times calculated for the three particle sizes at
ionic strengths of 10-3M KN03 and 10-1M KN03 (Table 6(c))
show that an increase in ionic strength leads to a decrease in
). and an inc.reased flotation rate, together with a decrease
in the critical hydrophobicity required to initiate flotation
(Figure 6. 5).
The decrease in ). and increase in flotation rate at constant
contact angle is seen in the >lOrk of Laskowski and Iskra (39).
It is. usually linked to a reduction in electrostatic repulsion
between a bubble and a particle (35, 111, 112), however.the
influences of ionic strength of tfilm and ttpl are not known
precisely. It can be seen that an increased ionic strength is
Table 6(c)
Influence of Ionic Strength on Induction Time (.X)
Particle Average Actual Advancing Water >. (mS) Size Range Particle Size Contact Angle
(I'm) (I'm) 10"3M I � I
-106 + 90 99 as· 4.0
65° 4.2
-45 + 40 46 gg• 3.6 . .
65° 3.9
-14 + 5 15 as· 4.7
65° 5.2
- 10-lM
3.9
4.1
3.5
3.8
4.6
4.9
100.
advantageous in recovering weakly hydrophobic particles.
100 n
E :J... u 80 (J) .!::! "' (J) u 60 :e ro
0..
c 40 ro (J) ::2
20
Advancing Water Contact Angle 36' 52' 65' 77' 88'
5 10 15 20 25
Critical surface coverage C%)
Figure 6.5 Effect of ionic strength on critical surface coverage
required for initiation of flotation.
6.4 The Rate of Flotation
The relationship between rate constant, kf (for the fast floating
material) ·and advancing water contact angle, 08, is shown in
Figure 6. 6 for three particle sizes.
It can be seen that kf increases with contact angle, but for 8 values up to 90' there is no evidence of the plateau seen in the
S-shaped curves of Imaizumi and Inoue (96) or those of Barlett and
Mular (98).
101.
Using the information shown in Table 4(1) and extrapolating bett<een
known data points ·where appropriate, it is possible to obtain
informatiOD on the dependence of rate constant on particle size.
Theoretical studies, such as those performed by Flint and Hot<arth (6)
and Reay and Ratcliff (9) suggest that
t<here dp is the particle diameter and n lies bet�<een 1.5 and 2.
Sutherland (107) in earlier work predicted that the value of n would
be 1. Experimental trials performed by Reay and Ratcliff (93)
suggest that n would fall between 1.5 and 2 for spheres. The data
from a large number of batch flotation trials indicates that n is
unity (11).
The various sets of n values may well be attributed to different
attachment mechanisms for smooth spheres and angular particles
(4, 10).
In the present study, for particles with advancing water contact
angles bet>;een. so· to 88° it can be seen that t<ithin
experimental error, n- 1.0 ± 0.1 or 0.2 over the range of particle
sizes studied. Thus, the behaviour of the angular quartz particles
used in this study is in agreement with the results of flotation
studies performed with particles produced by crushing and grinding
rather than with smooth spheres. A value of unity for n is
consistent with Sutherland's model (107) however the data is not
suff�ciently accurate to reveal any influences of variations in
induction time1 A, on the rate constant.
It was previously shown (Chapter 4) that the fastest floating
material t<ithin a narrot< size distribution consists of coarser
particles, despite the fact that the particles t<ere all previously
shown to be equally hydrophobic. This ,,ould indicate that the
observed behaviour does not reflect enhanced methylation of larger
particles, for example. This enrichment process was remarked upon by
Sutherland and Hark in 1955 (108).
102.
The variations in flotation behaviour of particles of slightly
different particle size (i.e. within the one particle size range)
becomes more pronounced at low contact angles, as shown in Table
4(1). Ff changes with 8 even for a narrow size range.
t:
� c 0
u
Q) +' ro
n::
+'
Kl 1 u..
Figure 6.6
f
20" 40 60 . 80 100
Advancing water contact Angle
Fast rate constant as a function of advancing '\'later
contact angle for three particle size ranges. e -106+90 }'ill,
0 -45+40 }'ill, • -14+5 }.till
103.
The curves shown in figure 6.6 can be used to display the dependence
of rate constant on particle size. This is shmm in figure 6. 7. It
can be seen that the dependence is essentially linear.
,.... 10° ' c
E \.J
� 9 c
� � Vl
c 0 u
Q)
10-1 � ro
0:::
Mean Particle Size CiJm)
Figure 6.7: log10(fast rate constant) as a function of
loglO(particle diameter) at various surface coverages
and advancing water contact angles .
• 100% surface coverage, oa 88'
0 52% surface coverage, oa (:)0'
b. 37% surface coverage, oa 50'
(88 ° predicted from Cassie equation)
SUMMARY
Quartz particles of various discrete particle size ranges have been
methylated to varying known amounts using trimethylchlorosilane and
their flotation behaviour has been assessed in a modification of the
Hallimond tube. For each particle size there is a definite degree of.
surface coverage below which the particles do not float·. A
'flotation domain' is identified which shows that both coarse
(-lOOpm) and fine (-lOpm) particles require a greater degree
of surface coverage to initiate flotation than do intermediate
(-40pm) particles.
Hater contact angles have been measured on quartz plates and powders
which have been methylated (under the same conditions) with
trimethylchlorosilane. Both advancing and receding water contact
angles measured on quartz plates as a function of degree of surface
methylation,are in good agreement with the angles predicted by the
Cassie equation. Advancing water contact angles measured on quartz
particles as a function of degree of surface methylation are also in
good agreement with angles predicted by the Cassie equation up to
surface coverages of'about 70%. The angles measured at higher
surface coverages are less than those anticipated by the Cassie
equation.
The flotation behaviour of the particles has been compared ••ith that
predicted by existing flotation theories. It has been shown that
coarse particle behaviour is predicted by the kinetic theory of
flot�tion proposed by Schulze. Fine particle behaviour, however,
only qualitatively agrees with Scheludko's theory of fine particle
behaviour.
Calculated induction times, in conjunction with observed flotation
behaviour, indicate that the bubble-particle attachment process is
most efficient for particles of about 38pm in diameter ander the
set experimental conditions used in this study.
Flotation rate trials were performed for three particle size ranges
and rate constants were evaluated for the various degrees of surface
coverage. It was found that the dependence of rate constant on
particle size is essentially linear.
Appendix 1
Sample Calculation of the uptake of TMCS by quartz
Quartz: 7.00g of -45 + 40pm material
Initial Concentration of Methylating solution
(determined by the pH difference technique)
pHaq,initial- 5.70(0) pHaq,final
[TMCSJoriginal 6.44 x 10-5 M
4.17(5), 4.18(1)
:. molesoriginal in 100 cm3 - 6.44 x 10-6 moles
Final Concentration of Methylating solution (after reaction)
pHaq,initial 5,70(0)
[TMCSlremaining - 3·61
pHaq,final
X 10-5 M
4.41(6), 4.42(3)
:. molesremaining in 100 cm3 3.61 x 10-6 moles
:. moles of TMCS reacted with quartz surface
6.44 X 10-6 - 3.61 X 10-6
2.83 x 10-6 moles
2.83 X 10-6
7.00 4.04 x 10-7 mole g-1
Appendix 2
Complete uptake of TMCS
Particle size : -30 +
21.01
23pm, 15 gram charge
x 10-7 mole g-l rmax
rmax 3.15 x 10-5 moles in 15 g
Initial Concentration of Methylating solution
(determined by the pH difference technique)
pHaq,initial 5·7°(0) pHa6,final [TMCSlremaining - 2.85 x 10- M �moles in 100 cm3 2.85 x 10-5
5.31(2). 5.31(7)
Final Concentration of Hethylating solution (after reaction)
pHaq,initial 5·7°CO) pHaq,final [TMCSlremaining 0 moles
moles in 100 cm3 0 moles
5.70(0), 5.70(0)
moles of TMCS reacted with quartz surface
- 2.85 x 10-5 moles
Hence, after reaction, no detectable amount of HCl from the methylation reaction was present in the cyclohexane.
Appendix 3
Contact Angle as a function of surface coverage for quartz po,.ders
Particle Size Percentage eadv. Mean Range Surface Gov. Cassie Equation eadv (±20)
(±2%) Heasured
22 38° 38°
23 39° 43°
-40 + 30Jlm 29 44° 43°
36 so· 54°
47 57° 51°
65 68° 63°
0 o· 10
14 30° 30°
20 36° 38°
-45 + 401'm 29 44° 45°
39 52° 56°
63 67" 66°
100 88· n·
Pm·1ders exposed to vapours
21 37" 35°
29 44° 40°
-40 + 30Jlm 34 48° 46°
35 49° so•
39 52° 52°
40 52° so·
43 54° 52°
50 59° 56°
56 63° 63°
34. 48° 48°
38 51° 51°
-45 + L,OI'm 39 52° 52°
44 ss· ss·
Appendix 4
Table of Gradients of rate of penetration trials 1'/ashburn method
Particle Surface Cyclohexane Toluene \'later
Size Covet age Gradient Gradient Gradient
1%)
22 0.100 0.177 0.210
23 0.077 0.165 0,180
23 0.091 0.172 0.184
-40 + 30pm 29 0,110 0.191 0.230
36 0.107 0.225 0.191
47 0.108 0.201 0.194
65 0.123 0.189 0.112
"' ).< Q)
0 0.103 0.199 0.299 <0
� 14 0.101 0.196 0.255 P<
� 15 0.102 0.213 0.238 A
-45 + 40pm 20 0.106 0.244 0. 244
29 0.112 0.222 0.234
39 0.085 0.178 0.140
63 0.105 0.171 0.112
100 0.102 0.096
21 0.107 0.255
29 0.089 0.150 0.185
34 0.086 0.195 0.209
).< -40 + 30pm 35 0.080 0.145 0.145
g 39 0.087 0.160 0.153
� :> 40 0.092 0.179 0.177 0 ..... 43 0.098 0.186 0.177 <0 '" 50 0.089 0.160 0.140 "'
· 0
� 56 0.106 0.192 0.133 [>.]
"' ).< '" 34 0.091 0.175 <0
� -45 + 40pm 38 0.091 0.170 0.168 P<
39 0.092 0.204 0.164
44 0.091 0.165 0.146
Appendix 5
Sample Calculation (Washburn Method)
e.g. -45 + 40pm, 29% surface coverage, DRY powder
Cyclohexane Gradient 0.112
Toluene Gradient 0.222
Water Gradient 0.234 �
-1 { ( ,,.,,..,..�. ) 0 "'·'] 8 cos · gradient cyc1ohexane
-1 ( 0.234 0.344�
= cos 0.112
44'
� cos-1 {( '""'" "'"' ) 0 ""] 8 gradient toluene
cos-1 ( 0.234 0. 6653)
0.222
� 45'
Appendix 6
Contact Angle as a function of surface coverage for quartz plates
Surface %
0
13
18
19
21
22
23
29
34
35
36
37
38
39
40
42
43
44
50
53
56
77
100
Coverage Cassie e Measured
'
*0 A *0 R ')'(OA
0 0 0
29 25
34 29
36 30
37 32 40
38 33 45
39 33
44 37 45
48 40 49
49 41 49
50 41
50 42 53
51 42 51
52 43 52
52 44 57
54 44 58
54 45 54
55 45 55
59 49 59
61 50 . 62
63 52 63
75 62 73
88 72 88
� Advancing contact angle with respect to water
� Receding contact angle with respect to water
e (±2 o)
*OR
0
29
30
30
31
31
35
37
38
40
39
42
41
42
44
44
43
48
46
53
65
71
16
12
N 10
�
�-m I 6
16
14
12
«1<1
� "-
..
" ill I 6
'
16
14
12
� 10
"-
'lc 0 "' I 6
10
M o
10
40 60 eo
• •
.II II
• •
f 40 60 80
;· ..
I
!/' i/
10 40 60 80
"'
TIME, t IS€C.)
100 120
TIME, t IS€C.l
•
100 120
TIME, t csec.J
Dry Powder
SURFACE COVERAGE !i'.l• 0
PARTIClE SIZE• -45+40f-1
•Cyclol1exane
•Water
140 16<J
"Toluene
1BG 200
Dry Powder
SURFACE COVERAGE t'l.l•1ll
PARTICLE SIZE• -45+ 40f-1
• Cyctollexane
•Water
140 160 180 200
Dry Powder
SURFACE COVERAGE 11.1•20
PARTIClE SIZE• -45+ 40jJ
"'Toluene
• Cyc!ot1exane
•Water
140 160 180 100
16
14
11
N 10
� '!..
'1;o "
iji '
'
12·
16
14
12
�10 "-
'1;o " ill "' '
'
I. ./ •
I I /
.I/' �<Toluene // • Cyctohexane
0 •
20
•Water
40 60 60 10<1 120
TIME, t (SeC.)
II . .. ./
140 160
0
J.Toruene
Dry Powder
SURFACE COVERAGE r/.1• 29
PARTICLE SIZE•-Il5+40p
180 ,.,
Dry Powder
SURFACE COVERAGE 1%1 •39
PARTICLE SIZE• -4S+liOJ-1
I ./ • CycJoflexane
•Water
" 100 120 140 160 160 200
TIME, t !Sec.)
I 0 •
# . �·
Dry Powder
SURFACE COVERAGE rl.l• 63
"Toluene
• Cyclohexane PARTICLE SIZE• -45+40p
•• •Water
20 40 " 60 100 120 140 160 160 "'
TIME, t tsec.)
"
16
12
� m I 6
16
14
12
.. � 10
ll
7--6 m I 6
"
...
"
" 120
TIME, t tsec.J
Dry POWder
SURFACE COVERAGE l'l.J110Q
PARTICLE SIZE• -115+40p
• Cyclohexane
•Water
1<0 160 160 200
;;· / . ;· /"
•
Dry Powder
40 60 " 100
TIME, t tsec.)
40 60 BO 100 •120
TIME, t (58C)
•Toluene
SURFACE COVERAGE l'l.J• 22
PARTICLE SIZE•-40+30�
• Cydohexane
•Water
100 160 180 200
Dry Powder
SURFACE COVERAGE 11.1 •23
PARTIClE SIZE•-40+30j.J
... Toluene
•Cycfollexane
•Water
140 160 180 200
16
N 10
� "-
16
12
14
12
.. - 10-
�
4
'
;· / I/.
Dry Powder
SURFACE COVERAGE l'l.l• 23
PARTICLE SIZE• -ll0+30� // !/' ...
•Toluene
• Cyclohexane
" 60 100 1l0
TIME, t !sec.)
•Water
140 160
"Toluene
160 lOO
Dry Powder
SURFACE COVERAGE (i'J• 29
PARTIClE SIZE• -LI0+30fJ
• Cyclohexane
•Water
60 60 100 1l0 140 160
TIME, t !SeC)
I;· /. . . /" II .
160 200
Dry Powder
SURFACE COVERAGE 11.1•36
PARTIClE SIZE•-llO+ 30p II/ J. . • Toluene
• Cyc!ollexane • •Water
100 1<0 160 160 200
TIME, t tsec.J
"-
" .
� 6
2
.. 1//
II /. II /.
• • •
•Toluene
Dry PO\vder
SURFACE COVERAGE li'.l147
PARTIClE SIZE• -40+30Jl
• Cyclohexane
•Water
TIME, t IS€C.I
!//' 111·
1/ Dry Powder
SURFACE COVERAGE r1.1 • 65
PARTICLE SIZE•-40+ 30Jl
# .�o.ratuene
• Cyclohexane
•Water
" 80 100 140 16<l 180 200
TIME, t IS€C.l
I / ;· . . /
//' Powder In Equlllbrlum with vapour
SURFACE COVERAGE l'l-1•34
PARTICLE SIZE• -45+40JJ
.f/ • Cyctohexane
•water
" 80 100 120 140 1W 180 200
TIME, t csec.)
16
12
¥ !j! 6
12
'
20 60 so 100 120
TIME, t (SeC)
•Toluene
Powder In Equilibrium with Vapour
SURFACE COVERAGE If.)' 38
PARTICLE SIZE• -45+ 40p
• Cyclohexane
•Water
140 160 180 200
I /. I ./·
f/ Powder In Equ!Hbrtum with Vapour
SURFACE COVERAGE r/.l' 39
PARTIClE SIZE• -45+ 40p
1/ � .
•Toluene
• Cydol1exane
60
60
•Water
100 uo 1<0 160
TIME, t (sec.J
"Toluene
180 200
Powder In Equilibrium with Vapour
SURFACE COVERAGE l'l.l •44 PARTICLE SIZE• -45+ 40p
• Cyclohexane
•Water
100 uo 1<0 160 180 200
TIME, t lsec.J
16
"
12
"� 1<>
� "-" . I: D "' r 6
"�
�;;· D "' r
�
'
16
12
'
16
X 6
•
I •
I
//' • •
1/ • •
•
•
Powder In Equilibrium with Vapour
SURFACE COVERAGE IZJ •21
PARTICLE SIZE• -ll0+30p
• Cyclol1exane •Water
20 40 60 80 100 120 140 160 180 200 TIME, t {SeC.)
// .1 .. 1. •
II II/ . ' .
;; •
20 60
TIME, t ISeCI
00 100
TIME, t tsec.J
... Toluene
Powcter I n EQLIII!llrlum wlth Vapour
SURFACE COVERAGE l'l-"29
PARTICLE SIZE> -�0+30�
• cyclohexane
•Water
Powder In Equ!ilbrium Witll Vapour
SURFACE COVERAGE l'l.l•3ll
PARTICLE SIZE• -40+30j..l
•Toluene
• Cyclohexane
•Water
100 160 180 200
12
.. - 10
!l "-
"
12
" .
� m :c 6
� .Y 20 "
16
12
N- 10
§ ...
� "' :c 6
20
60 eo 100 120
TIME, t Jsec.J
... Toluene
Powder In Equlllbrfum with Vapour
SURFACE COVERAGE li'J•35
PARTICLE SIZE• -li0+30JJ
• Cyclohexane
•water
1<0 160 1BO 200
;f ./ ;�· ./ Powder In Equilibrium
with Vapour
" BO
" BO
100 120
TIME, t IS€C.l
SURFACE COVERAGE 11.1•39
PARTICLE SIZE• -ll0+30f1
"Toluene
• Cyc!ohexane
•Water
140 160
"Toluene
1BO 200
Powder In Equilibrium with Vapour
SURFACE COVERAGE 1/.l•liO
PARTICLE SIZE• -ll0+30f1
• Cyclohexane
•Water
120 140 160 180 200
TIME, t Jsec.J
"
"
"-
II/ . .
20
"
"
"
20 40
/.. /. " /'
• • •
60 80
,o 80
100 120
TIME, t.
(SeC)
100 "'
TIME, t !sec.)
60 ao 100 120
TIME, t !S€C.I
1. Toluene
Powder rn Equllltxlurn wltll Vapour
SURFACE COVERAGE C/.)•tl3
PARTICLE SIZE• -40+30lJ
• Cyc/ollexane
•Water
1<0 160
... Toluene
180 100
Powder In Equilibrium w/tll Vapour
SURFACE COVERAGE f'l.I•SO
PARTICLE SIZE' -ll0+30p
• Cyc!of1exane
•Water
140 160 100 200
Powder In Equ!libr!um With Vapour
SURFACE COVERAGE r;.J•56
PARTICLE SIZE• -40+30)-1
�.Toluene
• Cyclohexane
•Water
140 160 180 100
APpendix 8
Calculation of �,max,g under various conditions
[Reference (l)]
(;
"( sin w* sin (w* + ·�'!' Rp, max, g !',pg + pp
bm
w* 180 e
+-2
Taking - 72 dyne -1 (or mNm-1) "( em
g 981 em s -1
2.5 -3 (quartz) Pp g em
"{(l •<n (n• ., D)j >/2
R 72.0 )sin w*
p, max, g 1.5 X 981
e w* w*+8 R d p,max,g p,max,g
(pm) (pm)
2. 179 181 47.3 94.6 5• 177.5 182.5 118.2 236.4
1o· 175 185 236.1 472.2 2o· 170 190 470.4 940.8 3o• 165 195 701.2 1402.8
'
40° 160 200 926.6 1853.2 so· 155 205 1145 2290 Go• 150 210 1355 3710 70° 145 215 1553 3106 so· 140 220 1741 3482 go• 135 225 1916 3832
Appendix 9
Calculation of Rp}rnax,v under various conditions
[Reference (1)]
f
hcrit(w)
Z F dh(w)
heqw
Taking
1 72 dyne cm-1 (mNm-1)
Pp 2.5 gem -3
Data obtained from Reference applied to particle sizes 50, 100, 500
pm of contact angles of 30', 50' and 70•. Other values of Edet were interpolated from these values, given in the figure below.
SOO!Jm
10-1
G 0:: w �
i5 10-2
100tJm 0:: w
· z SOtJm w
1-z
10-3 w :2 ::r:
� 1-w D 10-4
20' 40' so· so·
CONTACT ANGLE
The values of Edet for given particle sizes and contact angles is
given in the following table.
APpendix 9 (continued)
R p,maxj
v (pm
50
100
500
••
Contact angle (degrees)
20
25
30
32.5
35
37.5
40
45
50
70
20
25
30
32.5
35
37.5
40
45
50
70
20
25
30
32.5
35
37.5
40
45
50
70
Detachment energy (erg)
6.00 X 10"5
1.18 X 10·4
2.08 X 10·4
2.70 X 10·4
3.50 X 10"4
4.30 X 1o·4
5.40 X 10-4
8.40 X 10-4
1.21 X 10"3
4.14 X 10-3
1. 30 X 10-4
2.95 X 10·4
5.79 x 1o·4
8.00 X 10·4
1.08 X 10"3
1.42 X 10"3
1.85 X 10"3
3.00 X 10"3
4.70 X 10·3
1. 58 X 10·2
5.00 X 10-4
1.50 X 10"3
3.82.x 10"3
5.90 X 10"3
8. 80 X 10-3
1. 28 X 10"2
1.85 X 10-2
3.50 X 10-2
6.10 X 10-2
2.36 X 1o·1
Appendix 10
Calculation of the Kinetic Energy of a Rising Bubble
rs�:;"''' ) .
�
10 X 10-4
25 X 10-4
30 X 10·4
40 X 10·4
so X 10-4
60 X 10-4
70 X 10"4
80 X 10"4
90 X 10"4
100 X 10"4
110 X 10·4
120 X 10"4
130 X 10-4
140 X 10"4
150 X 10-4
2 2 3 Ek - 3 1rnpvt Rp
20
2.09 X 10-6 3.27
3.27 X 10·5 5.11
5,65 X 10-5 8.84 1.34 X 10-4 2.09
2.62 X 10-4 4.09
4.52 X 10-4 7.07
7.18 X 10·4 1.12
1.07 X 10-3 1.68
1.53 X 10"3 2.39
2.09 X 10"3 3.27
2.79 X 10"3 4. 36.
3.62 X 10"3 5.65
4.60 X 10·3 7.19
5.75 X 10·3 8.98
7.07 X 10·3 1.10
-��
Energy (erg)
25 30
X 10-6 4, 71 X 10-6
X 10-5 7.36 X 10-5
X 10-5 l. 27 X 10-4
X 10-4 3,01 X 10-4
X 10·4 5.89 X 10·4
X 10"4 1.02 X 10·3
X 10·3 l. 62 X 10"3
X 10·3 2.41 X 10�3
X 10"3 3.44 X 10"3
X 10·3 4. 71 X 10"3
X 10·3 6.27 X 10·3
X 10·3 8.14 X 10"3
X 10"3 1.04 X 10"2
X 10·3 l. 29 X 10·2
X 10"2 1.59 X 10"2
Appendix 11
Rising Bubble Velocity I ! -1) (em s '
20
25
30
RISING-2ocms·' BUBBLE
VELOCITY.,. \ 25cms·1
30cms·1
so'
,.
40'
37o5"
35'
32·5"
30'
25'
20'
I CONTACT
ANGLE
50 100 . 500
PARTICLE RADIUS (�ml
I Contact Angle R
I p,max,v '
(degrees) i (J.Lm) i '
25 ' 29 30 42 32.5 51 35 62 37.5 75 40 92 45 133 50 197
30 29 32.5 36 35 44 37.5 53 40 64 45 93 50 I 135
32.5 I 25 35 31 37.5 37 40 47 45 70 50 100
I
d I p,max,v i
I (J.Lm) I
I
I 58 84
102 ! 124
150 184 266 394
I 58 72
I 88 106 128 186 270
so
62 74 94
140 200
Appendix 12
Calculation of the number of bubbles present per cubic
centimetre in the flotation cell.
Gas flm• rate
RB (bubble radius)
vt (bubble velocity)
3 1 3 -1 60 em min- or 1 em sec
6 x 10-2 em
25 cms-1
Volume of bubble - � 1r(6 x l0-2)3 cm3
Therefore cell must pass it.
1100 bubbles s-). through
Internal diameter of cell 3. 3 em
Area of cell 4
34. 21 2 4
- 8. 55 em
Each 1 cm3 contains bubbles and water and each bubble
sweeps through vt em in ). second.
__Q_
cm3
b
X
X vt
1100
total volume swept out by bubbles in one second
cell cm3 X area s
1100 bubbles s-1
1100 bubbJ.es s-1
bubbles cm-3 25 X 8.55
5.15
Bubbles per cm3 - 5
REFERENCES
l. _ H.J. Schulze, 'Physico-Chemical Elementary Processes in
Flotation', Elsevier, Amsterdam (1984)
2. T.M. Morris, Amer. Inst. Metallurg. Eng. Trans.,� (1952) 794
3. P.G. Blake, MAppSci Thesis, Swinburne Institute of Technology,
Melbourne
4. P.G. Blake and J. Ralston, Colloids and Surfaces, 15 (1985) 101
Colloids and Surfaces, 16 (1985) 41
5. G.J. Jameson, S. Nam and M. Moo Young, Minerals Sci. Engng., 2
(1977) 3
6. L.R. Flint and H.J. Howarth, Chern. Engng. Sci., 26 (1971) 1155
7. B.V. Derjaguin and S.S. Dukhin, Trans. Instn. Min. Metall., 70
(1961) 221
8. A. Fonda and H. Herne, Mining Research Establishment, Rep. No.
2068, National Coal Board (U.K.) (1957)
9. D. Reay and G. Ratcliff, Can. J. Chern. Engng., 51 (1973) 178
10. J.F. Anfruns and J.A. Kitchener, Trans. Instn. Min. and
Metall., Section C, 86 (1977) C9
11. H.J. Trahar, Int. J. Miner. Process.,§. (1981) 289
12. D.B. Hough and L.R. White, Adv. in Colloid and Interface Sci.,
14 (1980) 3
13. J. Maharity and B.H. Ninham, 'Dispersion Forces', Academic
Press, London (1976)
14. A.B.D. Cassie, Disc. Faraday Soc., l (1948) 11
15. J. Lask01vski and J .A. Kitchener, J. Colloid Interface Sci., 29
(4) (1969) 670
16. H.J. Schulze, Int. J. Miner. Process.,� (1977) 241
17. A. Scheludko, B.V. Toschev and D. Bojadiev, J. Chern. Soc.
Faraday Trans.1, 72 (1976) 2815
18. T.M. Morris, Amer. Inst. Metallurg. Eng. Trans., 187 (1950) 91
19. H. Princen, 'Surface and Colloid Science'. Edit. E. Matjevic,
John Hiley and Sons, N.Y., .2. (1969) 1
20. C.IV. Nutt, Chern. Eng. Sci., 12 (1960) 133
21. J.l<. Gibbs, The Collected \Vorks, Longmans Green and Co. N.Y.
(1928)
22. IV.D. Harkins, J. Chern. Phys., 5(1937) 135
23. J.A. De Feijter and A. Vrij, J. Electroanalyt. Chern., 37 (1972)
9
24. J.E. Lane, J. Colloid Interface Sci., 52 (1975) 155
25. B.A. Pethica, J. Colloid Interface Sci., 62 (1977) 567
26. �!.IV. Biddulph, Can. J. Chern. Eng., 37, (1979) 268
27. M.\V. Biddulph, Conservation and Recycling, l (1980) 361
28. C. Orr and J.M. Dalla Valle, Fine Partic�e Measurement,
Macmillan, New York (1959)
29. M. W. Biddulph, A. I.Ch.E. J., 22 (6) (1983) 956
30. P. W. Atkins, 'Physical Chemistry' 2nd Edit., Oxford University
Press (1982) 883
31. A. F. Taggart, 'Handbook of Mineral Dressing', Wiley Handbook
Series (1954) Chapter 19
32. J. R. Vig, J.\v. LeBus and R.L. Filler, Proc. Ann. Freq. Control
Sym. , 29 (1975) 220
33. J. Leja, 'Surface Chemistry of Froth Flotation', Plenum, New
York, N.Y. (1982)
34. R.M. Pashley and J.A. Kitchener, J. Colloid Interface Sci., 71
(1979) 491
35. T.D. Blake and J.A. Kitchener, J. Chem. Soc. Faraday Trans. I,
68 (1972) 1435
36. R. N. Lamb and D. N. Furlong, J. Chem. Soc. Faraday Trans. I, 78
(1982) 61
37. A.D. Read and J. A. Kitchener, Soc. Chem. Ind. , Monograph 25,
'Wetting', London (1967)
38. P.F. Holt and D.T. King, J. Chem. Soc., 52 (1979) 379
39. J. Laskowski and J. Iskra, Trans. Inst. Min. Metall. C., 12
(1970) 6
40. D. ounstan, BSc(Hons) Thesis, University of Melbourne,
Melbourne
41. R. Iler, 'The Che1nistry of Silica - Solubility, Polymerisation,
Colloid and Surface Properties and
Biochemistry', Wiley�Interscience, New York,
Chapter 6 (1979)
42. Agla Syringe Information Handbook, li'ellcome Research
Laboratories, Beckenham, U.K. (1980)
43. Handbook of Chemistry and Physics, 6lst Edition, CRC Press,
Boca Raton, Fl. (1981)
44. H. Stephens and T. Stephens (Eds.) Solubilities of Inorganic
and Organic Compounds, Pergamon, London (1963)
45. A.F. Hallimond, Mining Magazine, 70 (1945) 87
46. A.F. Hallimond, Mining Magazine, 72 (1945) 201
47. J.B. Melville and E. Matijevic in R.J. Akers (Ed.) Foams,
Academic, London (1976)
48. Calibration Curve, Fischer and Porter Co., Hatboro P.A. Tube
FP 1/6-12-G-S Float 1/16-SS (1980)
49. R.J. Hunter, 'Zeta Potentials in Colloid Science' Academic
Press (1981)
50. A.F. Lee, J. South African Inst. Min. and Metall. (1969) 94
51. J.F. Anfruns and J.A. Kitchener, Trans. HIM, Section C., 86
(1977) 9
52. A.J. Lynch, N.li'. Johnson, E.V. Managig and C.G. Thorne, Mineral
and Coal Flotation Circuits, Volume 3 in
Developments in Mineral Processing, Elsevier,
Amsterdam (1981)
53. T. Young, Phil. Trans., 95 (1805) 65
54. L.R. White, J. Chern. Soc. Faraday Trans. I, 73 (1977) 390
55. R.J. Good, 'Surface and Colloid Science', Vol. II (eds. R.J.
Good and R.R. Stromberg) Plenum Press, N.Y.
(1979) Chapter 1.
56. P.C. Hiemenz, 'Principles of Colloid and Surface Chemistry',
Marcel Dekker Inc. N.Y. (1977)
57. F.M. Fowkes, Ind. Eng. Chern., 56 (1964) 40
58. R.E. Johnson Jr and R.H. Dettre, 'Surface and Colloid Science'
Vol. II (Ed. E. Matijevic) Hiley-Interscience,
N.Y. (1969)
59. T.D. Blake and J .�!. Haynes, Contac.t Angle Hysteresis from
'Surface and Membrane Science' edited by
Danielli1 Rosenberg and Cadenhead, Academic
Press (1976)
60.
61.
62.
' 63.
64.
65.
66.
67.
J.F. Oliver, C. Huh and S.G. Mason, J. Adhesion, � (1977) 223
J.A. Finch and G.W. Smith, Min. Sci. and Eng., Vol. II No. 1,
(1979)
C. Huh and S.G. Mason,�· Colloid Interface Sci., 60 (1977) 11
R.N. Henzel, Ind. Engng. Chern., 28 (1936) 988
1\T.J. Herzberg, J.E. Marian and T. Vermeulen, J. Colloid
Interface Sci., 33 (1970) 164
N.l\T.F. Kossen and P.M. Heertjes, Chern. Eng. Sci., 20 (1965) 593
J.T. Davies and E.K. Rideal, 'Interfacial Phenomena' (2nd
Edition) Academic Press, N.Y. (1963) Chapter 1
N.K. Adam, Adv. Chern. Ser., 43 (1964) 52
68. H.W. Fox and W.A. Zisman, J. Coll. Sci., 2 (1950) 514
69. E. Wolfram and R. Faust in J. F. Padday (Ed.) Wetting, Spreading
and Adhesion, Academic, London, (1979) 213
70. A.V. Kise.lev, Russ. J. Phys. Chern., (English Trans.) 38 (1964)
1108
71. H. Knozinger in P. Schuster, G. Zundel and C. Sandorf (Eds.)
'The Hydrogen Bond', Vol. III, North Holland,
Amsterdam (1976)
72. A. W. Neumann and R.J. Good, 'Surface and Colloid Science'
Editors R.J. Good and R.R. Stromberg, Plenum
Press, N.Y., Volume II (1979)
73. E.W. Washburn, Phy. Rev., 1Z (1921) 374
74. F.E. Bartell and H.J. Osterhof, Ind. Eng. Chern., 19 (1927) 1277
75. F.E. Bartell and H.J. Osterhof, J. Phys. Chern., 34 (1930) 544
J. Phys. Chern., 37 (1933) 543
76. F.E. Bartell and C.E. Whitney, J. Phys. Chern., 36 (1933) 3115
77. L.R. \fuite and D. Dunstan, J·. Coll. Int. Sci., in press
78. E.K. Rideal, Phil. Mag., 44 (1922) 1152
79. M.L. Studebaker and C.W. Snow, J. Phys. Chern., 59 (1955) 973
80. D.D. Eley and D.C. Pepper, Trans. Faraday Soc., 42 (1946) 697
81. V. T. Crowl ':'nd VI. D. S. Woolridge, 'A Method for the Measurement
of Adhesion Tension of Liquids in Contact with
Powders' in 'Wetting', Soc. Chern. Ind.,
Monograph 25 (1967) 200
82. J. Van Brakel and P .H. Heertj es, Pm1der Technology, 16 (1977)
75
83. J. Szekely .. A.H. Ne>nnan and Y.K. Chuang, J. Coll. Int. Sci., 35
(1971) 273
84. L.R. Fisher and P.D. Lark, J. Coll. Int. Sci., Q2. (1979) 46
76 (1980) 251
85. R.J. Good and N.J. Lin, 'Proceedings of the 50th Colloid and
Interface Science Symposium', Call. Int. Sci.,
Vol. 3, (1976) 277 Academic, N.Y.
86. R.J. Good and N.J. Lin, J. Call. Int. Sci., 54 (1976) 52
87. R.J. Good, J. Coll. Int. Sci., 42 (1973) 473
88. W.D. Harkins, 'The Physica:l Chemistry of Surface Films',
Reinhold, N.Y. (1952)
89, L.R. White, J. Coll. Int. Sci., 90 (1982) 2
90. L.C. Drake and H.L. Ritter, Ind. Eng. Chern. Anal. Ed., 17
(1945) 782
91. H.L. Ritter and L.C. Drake, Ind. Eng. Chern. Anal. Ed., 17
(1945) 787
92. L.C. Drake, Ind. Eng. Chern., 41 (1949) 780
93. D. Reay and G.A. Ratcliff, Can .. J. Chern. Eng., 21 (1975)
479
94. A. Patrick, Proc. of the Fourth Particle Analysis Conference,
Loughborough ·University of Technology, 45 (1981)
8
95. J, Van Brakel and P.M. Heertjes, Pm1der Technology, ·.2. (1974)
263
96. T. Imaizumi and T. Inoue, 6th Annual Mineral Processing
Congress (Ed. A. Roberts) Pergamon Press (1965)
581
97. K.W. Anderson, P.J. Scales and J, Ralston, Proc. Australasian
Inst, Min. Metall. No. 291 (1986) 73
98. D.R. Bartlett and A.L. Mular, Int. J. Min. Proc.I (1974)
277
99. D. Dunstan, University of Melbourne, Private Communication
100. G.L. Batton Jr., J, Call. Int. Sci., 102 (1984) 514
101. L.R. Fisher, J. Call. Int. Sci., 11 (1979) 200
102. F.E. Bartell and C.W. Walton, J. Phys. Chern., 38 (1934) 503
103. S. Garhsva, S, Contreras and J. Goldfarb, Colloid Polym. Sci.,
256 (1978) 241
104. L.R. White, University of Melbourne, Private Communication.
105. I.B Ivanov, B.V. Toshev and B.P. Radoev, 'The Thermodynamics of
Contact Angles, Line Tension and Wetting
Phenomena', Chapter l in J.F. Padday (Ed.)
'Wetting, Spreading and Adhesion' , Academic
Press, London (1978)
106. J.A. Mingins and A. Scheludko, J. Chern. Soc. Faraday Trans. I,
75 (1979)
107. K. L. Sutherland, J. Phys. Chern., 52 (1948) 394
108. K. L. Sutherland and I. W. 1\fark, 1 Principles of Flotation' ,
Australas. Inst, Min. Metall., Melbourne (1955)
109. G.S. Dobby and J.A. Finch, J. Co11. Int. Sci., 109 (1986) 493
110. J. Israe1achvi11i and R. Pashley, Nature, 300 (1982) 341
111. J. Israe1achvilli, 'Intermolecular and Surface Forces',
Academic Press, London
112. J, Laskowski, 'The Relationship Bet>Teen Floatability and
Hydrophobicity' Chapter 11 in Advances in
Mineral Processing (Editor P.
Somasundaran) SHE, Littleton, Colorado
113. C. Huh and S. G. Mason, J, Coll. Int. Sci., 47 (1974) 271