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8
CHAPTER-2
LITERATURE REVIEW
PREAMBLE
This chapter is the discussion of the previous work by other researchers. At the
beginning of the chapter earlier studies on the effects of solids concentration and wall
effects on the settling behaviour of suspensions are discussed. The drag- coefficient
particles Reynolds number relationships proposed by earlier workers are presented
and their recommendations are discussed.
Next part of the chapter includes discussion on rheological properties of the
suspensions, the rheological behaviours and different rheological models. Further
effects of system parameters like solids concentration, particle size and temperature
on suspension viscosity are discussed. Different dispersants are also discussed. The
chapter concludes with the discussion on applications of artificial neural networks in
various fields of chemical engineering.
2.1 Effect of Solids concentration on suspension settling
When the concentration of solids is high, the distance between particles becomes so
small that the particles come into contact with one another. As a result, the settling
process occurs differently and Stokes law fails to describe the settling of particles
beyond infinite dilution. Hindered settling is a term used to describe behavior at
higher concentrations where sedimentation rates are largely related to concentration
rather than to particle size [1]. In hindered settling particles are crowded and surrounding
particles interfere with the motion of individual particles, typically creating a slower-
moving mixture than would normally be expected. Upward displacement of the liquid is
also more prominent under hindered settling conditions. Settling rates in multiparticle
systems are influenced by particle interaction effects, which consist of collision
among particles and non-hydrodynamic interactions.
In the concentrated suspensions of significant solid volume fraction (f), as the
suspension settles, it replaces equivalent volume of liquid. If suspensions settle with
their settling velocity (um) under the action of gravity, the displaced liquid moves
9
upward. The liquid velocity (uw) depends on the settling velocity of solids. According
to continuity, the relative motion between solid particles and liquid can be presented
as follows (Equation 2.1):
m wu (1 ) u 0f f+ - = (2.1)
m wu u u= - (2.2)
Where, u is the relative velocity between solids particles and the dispersing medium
and is the pertinent settling velocity as given below in Equation 2.3:
mu
(1 )u
f=
- (2.3)
For sedimentation phenomena, dimensional analysis suggests that,
u[(1 ), (Re )]
u pf f¥
= - (2.4)
Where, u∞ is the free falling velocity of the particle alone in the same fluid and the
container as the sedimentation of uniform spheres and Rep is the particle Reynolds
number. Richardson and Zaki [2] extensively studied sedimentation of solid-liquid
suspensions of spherical particles; they investigated the dependency of the settling
velocity on the solids volume fraction. Their results were summarized with the
relationship known worldwide as the Richardson-Zaki equation. Their relationship
(Equation 2.5) is a power law of the void ratio (1-f).
(1 )nu u f¥= - (2.5)
The parameter n was found to be a function of the flow regime, expressed by the
particle Reynolds number Rep, and of the particle to column diameter ratio.
Richardson and Zaki [2] have given the following relationships (Equations 2.6 to 2.9)
for the exponent; n as a function of particle diameter (dp) to cylinder diameter (D)
ratio and particle Reynolds number Rep:
4.65 19.5( ) Re 0.2pp
dn for
D= + < (2.6)
0.034.36 17.6( ) 0.2 Re 1pp
dn for
D-= + < < (2.7)
0.14.45 Re 1 Re 500p pn for-= + < < (2.8)
2.39 500 Re 7000pn = < < (2.9)
10
When the ratio of the particle to the container diameter is small, n has a value of about
4.6 [3], value of n between 4.65 and 5.1 was reported by Barnea and Mizrahi [4], Capes
[5] obtained the reduced values of n between 3 and 3.5. Turian et al [6] have suggested
the alternative scheme of maintaining the value of n to be near to 4.68. Recently Koo
[7] reported the value of n as 5.5 for settling of mono-dispersed suspensions. When
Particles of mixed sizes settle, inter-particle interactions are further compounded as
the faster settling, larger particle approach and overtake the slower, smaller particles
leaving then in their wake of trailing displaced liquid. Garside and Al Dibouni [8],
Cheng [9] and Baldock [10] confirmed the decreasing behaviour of n with the particle
Reynolds number.
2.2 Wall Effects on suspension settling
When particles settle in a quiescent liquid in a given container, the presence of the
container wall at a finite distance from the settling particle exerts retarding effect on
it. This phenomenon due to presence of solid boundary at a finite distance is known as
wall effect. Wall effect is commonly reported as a function of particle to container
diameter ratio (dp/D). The wall effect becomes significant at higher values of dp/D.
Garside and Al-Dibouni [8] and Selim et al [11] examined wall effects on sedimentation
particles. Settling of single spherical particle and multisized particle mixture in
Newtonian fluid was exhaustively investigated. It was found that the correction for
wall effects gives measurably better correlation of free falling velocity. For single
particle terminal velocity Garside and Al-Dibouni [8] recommended the following wall
effect correlations:
4u
1 0.475 1 Re 0.2 p pp
d dfor
u D D¥
é ùæ öæ ö= - - <ê úç ÷ç ÷
è øè øë û (2.10)
3u1 2.35 0.2 Re 10 p
p
dfor
u D¥ æ ö
= - < <ç ÷è ø
(2.11)
3 38/2
u 1 10 Re 3 10
1p
p
foru d
D
¥
é ùê úê ú= < < ´ê úæ öê ú- ç ÷ê úè øë û
(2.12)
11
Lali et al [12] studied settling of spherical particles of glass and stainless steel in
aqueous solution of CMC in the concentration range of 0.2 to 2 weight %, the settling
velocities were measured in nine different cylinders in the range of 9 - 200 mm
diameter. It was found that the wall effect factor is function of both the particle to
container diameter ratio and the particle Reynolds number. Di Felice and Parodi [13]
have demonstrated that the container wall diameter influences the falling velocity
only for dilute systems, which is in contrast with a widely used, established empirical
relationships. In creeping flow regime Francis [14] proposed the following relationship
for the wall effects:
4
1
0.4751
p
p
du D
du
D¥
é ù-ê ú
ê ú=ê ú-ê úë û
(2.13)
This relationship is simpler than those proposed by Clift et al [15]. Di Felis [16]
proposed the following equations (2.14) and (2.15) for wall effects correction for the
terminal settling velocity in viscous and inertial flow regimes respectively:
2.7
1
0.331
p
t
p
dV D
dU
D¥
é ù-ê ú
ê ú=ê ú-ê úë û
(2.14)
0.85
1
0.331
p
p
du D
du
D¥
é ù-ê ú
ê ú=ê ú-ê úë û
(2.15)
2.3 Drag coefficient particle Reynolds number relationship
The CD-Rep relationship (Equation 2.16) was first proposed by Stokes [18]; he obtained
the solution to a general equation of motion for a single sphere settling in a fluid by
assuming the total drag as viscous drag. The relationship is the well known Stokes
law, applicable for Rep < 1.
24ReD
p
C = (2.16)
12
Gilbert et al [19] proposed a three parameter equation (Equation 2.3.2) to correlate the
drag coefficient and the particle Reynolds number. They introduced a third parameter
in addition to the two parameters given by Stokes.
ReYD pC X Z= + (2.17)
A five parameter model (Equation 2.18) suggested by Clift and Gauvin [15]
incorporated the corrections to the Stokes law; these additional parameters were
obtained as a function of particle Reynolds number.
24
(1 Re )Re 1 Re
BD p E
p p
CC A
D= + +
+ (2.18)
Tourton and Levenspiel [20] introduced two equations (Equations 2.19 and 2.20) to
correlate the drag coefficient and particle Reynolds number for falling spheres. These
two equations are similar to the original three parameter model by Gilbert et al [19],
and five parameter model by Clift and Gauvin [15].
0.827 527.2Re 0.427 Re 2 10D p pC for= + < ´ (2.19)
0.6571.09
24 0.413(1 0.173Re )
Re 1 16300ReD pp p
C -= + ++
6Re 2.6 10pfor < ´ (2.20)
Another five parameter equation obtained by Khan and Richardson [21] is as given
below:
( )3.450.31 0.06 52.25Re 0.36Re Re 3 10D p p pC for- -= + < ´ (2.21)
Turton and Levenspiel [20] tested their experimental data with three parameter
equation (Equation 2.19) and five parameter equation (Equation 2.20), as shown in
the following Figures 2.1 and 2.2. The results show that the three parameter equation
predict the drag coefficients value well for low particle Reynolds number where as the
predictions show significant error for the higher value of particle Reynolds number.
The five-parameter equation, on the other hand, is capable of showing a minimum CD
value, and it can be seen from Figure 2.2 that this equation correlates the data
extremely well throughout the whole particle Reynolds number range. Equation 2.20
has the added advantage of converging to the Stokes equation at low particle
Reynolds number; it is a better correlation for prediction of the drag coefficient values
in the sub critical regime (Rep < 2 x 105).
13
Figure 2.1: Comparison between experimental and predicted values of
drag coefficient of spheres using three parameter model [20]
A four parameter general drag coefficient-Reynolds number relationship proposed by
Haider and Levenspiel [22] is given below (Equation 2.22)
24( Re )
Re 1Re
BD p
p
p
CC A
D= + +
+ (2.22)
The experimental data used to find the best values of the four parameters was same as
used by Turton and Levenspiel [20]. The final equation obtained for the drag
coefficient is as given below (Equation 2.23):
0.645924 0.4251(0.1806 Re )
6880.95Re 1Re
D pp
p
C = + ++
(2.23)
The drag coefficient values predicted by this equation were compared with the
experimental values and earlier predictions by Turton and Levenspiel [20] with the
three parameter equation (Equation 2.21) and five parameter equation (Equation 2.22)
as discussed earlier. The drag coefficient values calculated by four parameter model
as depicted in Figure 2.3 were found more accurate.
14
Figure 2.2: Comparison between experimental and predicted values of
drag coefficient of spheres using five parameter model [20]
An explicit equation for particle settling velocities in solid-liquid systems was
presented by Zigrang and Sylvester [23]. This equation can be used to predict the
settling velocity of particles in liquid-solid suspensions; this correlation gives the
terminal velocity of a single spherical particle in a liquid as given below (Equation
2.24):
3/2 2
**
*
( 14.51 1.83 3.81)du
d
+ -= (2.24)
Where, d* and u* are dimensionless diameter and dimensionless terminal velocity of
sphere respectively.
13
2*
3Re
4 D pd Cæ ö= ç ÷è ø
(2.25)
13
*
Re43
p
D
uC
æ ö= ç ÷
è ø (2.26)
15
Figure 2.3: Comparison between experimental and predicted values of drag coefficient of spheres using four parameter model [22]
Turton and Clark [24] proposed the following correlation (Equation 2.27) to represent a
very simple and accurate way to evaluate the terminal velocity of a sphere of known
dimensions and density in a known fluid.
1.214
* 0.824 1.214
2* *
1
18 0.321u
d d
é ùê úê ú= ê úæ ö æ öê ú+ç ÷ ç ÷ê úè ø è øë û
(2.27)
This correlation cannot predict the velocity of a particle driven through a fluid by a
force other than its own weight without further manipulation. There are number
relationships available in the literature for the drag coefficient as a function of particle
Reynolds number; some of them are reported in the following Table 2.1
16
Table 2. 1: Drag coefficient- Reynolds number relationships
Author(s) Equation Range of Applicability
24ReD
p
C = Rep < 0.3
0.6
18.5ReD
p
C = 0.3 < Rep < <1000
Perry and Chilton [25]
0.44DC = 1000 < Rep < 20000
Cheng [9] ( )0.43 0.38241 0.27 Re 0.47(1 exp( 0.04Re )
ReD p pp
C = + + - - Rep < 100
Flemmer and Banks [26]
2410
ReE
Dp
C =
Where, 0.369 0.431
210
0.1240.261Re 0.105Re
1 (log Re )p pp
E = - -+
Rep < 3 x 105
Saha et al [27] 0.75
18.5ReD
p
C = 1 < Rep < 1000
Choncha and Almendra [28]
2
0.5
9.060.28 1
ReDp
Cæ ö
= +ç ÷ç ÷è ø
1 < Rep < 1000
Madhav and Chhabra [29]
( )0.529241 0.0604Re
ReD pp
C = + 0.095 < Rep < 400
Brown and Lawler [30]
( )0.681
1
24 0.4071 0.15Re )
Re 1 8710ReD pp p
C -= + ++
Rep < 2 x 105
2.4 Flow curve modeling
In order to describe the flow curves mathematically, several rheological models have
been developed. Mechanistic approaches are, however, difficult to apply because of
the diversity of the properties responsible for the rheological behaviour. More
commonly, empirical models have been used to describe the characteristics of the
flow behaviour. Several empirical equations relating shear stress to the shear rate have
been developed to model the basic flow curve shapes. The criteria for the suitability
of the model are:
i. It should be simple with minimum number of independent constants
17
ii. Its’ constants should be easily determined and
iii. The constants should have some physical significance
Regression methods can be used to fit the equations to the rheological data. The fit of
these equations can be then compared using statistical methods. Models with smallest
number of coefficients are preferred because they are usually simple to use. The
following sections describe some of the models commonly used to represent the
rheological properties of the suspensions. Included are Newton’s law of viscosity,
three models can be used to describe the shear thinning behaviour and three models
that describe plastic behaviour. The shear thinning properties are often characterized
by the power law model, the Cross model and the Cerreau model. Models that
describe plastic flow properties must have yield stress term such as the Bingham
plastic model, the Herschel Bulkley model and the Casson Model.
2.4.1 Newton’s law of viscosity
The flow behaviour of Newtonian fluids can be described by Newton’s Law of
Viscosity (Equation 2.28)
dudr
t m æ ö= ç ÷è ø
(2.28)
Where, m is the Newtonian viscosity of the fluid. It has been used to describe the
rheology of non-interacting spheres in Newtonian liquids [18, 31]. Above a critical
solids concentration, suspensions exhibit non-Newtonian properties.
2.4.2 The power law model
ndu
kdr
t æ ö= ç ÷è ø
(2.29)
This model (Equation 2.29) is also referred as Ostwld-De Waele model. This equation
can be used to model all three basic viscous flow behaviours. The coefficients k and n
are referred to as the fluid consistency index and flow index, respectively [32]. A high
k value implies that the suspensions have a high viscosity. The deviation of n from
unity is a measure of the non-Newtonian behaviour. Clearly, at n equal to unity, the
equation becomes Newton’s law of viscosity and k becomes m. For n is less than
unity, the model describes pseudoplastic flow and, for n greater than one it describes
the dilatant flow. This model has been used to describe many solid-liquid suspensions [6].
18
2.4.3 The Cross model
The Cross model (Equation 2.30) was developed base on the assumption that the
pseudoplastic flow is due to the process of formation and rupture of linkages in chains
of particles. This process is believed to occur in aggregated systems where links
between particles result in the formation of chain-like aggregates which rupture due to
Brownian motion and shearing [33-34].
mdudr
m m a-
¥æ ö= + ç ÷è ø
(2.30)
Where, m¥ is the apparent viscosity at infinite shear rate. A value of m equal to 2/3
was found to be suitable for many pseudoplastic systems which reduce the number of
coefficients in the equation to 2 [33]. The Cross model has been applied to suspensions
that exhibit pseudoplastic behaviour [35].
2.4.4 The Carreau model
The Carreau model (Equation 2.31) was developed to describe the pseudoplastic
properties of polymer solutions and melts.
2
1
s
duA
drm m
-
¥
æ öæ ö= +ç ÷ç ÷ç ÷è øè ø (2.31)
It is based on molecular network theory which describes the non-Newtonian flow with
respect to the creation and loss of segments. The rate of creation and loss of these
segments is function of shear rate which results in the non-Newtonian response to
shear [36-38].
2.4.5 The Bingham plastic model
The Bingham plastic model (Equation 2.32) describes the simplest type of
viscoplastic flow. The model characterizes the ideal case in which a complete
structure breakdown occurs once a yield stress has been exceeded. Once the yield
stress is exceeded a linear relationship exists between the shear stress and shear rate [39].
0
dudr
t t h æ ö= + ç ÷è ø
(2.32)
Where, t0 is the yield stress and h is the plastic viscosity. The Bingham model is
widely used because of its simplicity. Many suspensions including red mud, kaolinite,
clays, drilling mud and yeast suspensions have been modeled with equation [6, 35, 40-41].
19
2.4.6 The Herschel Bulkley Model
The Herschel Bulkley model (Equation 2.33) is the combination of the Oswald-De
Waele power law model and the Bingham plastic model. As the yield stress becomes
small the equation takes form of the power law model and as the index, n, approaches
unity, it becomes Bingham plastic model.
0
ndu
kdr
t t æ ö= + ç ÷è ø
(2.33)
This simple, versatile and practical model has been widely used to characterize both
dilute and concentrated suspensions [6, 35].
2.4.7 The Casson model
1/21/2o
dudr
t t hæ ö= + ç ÷è ø
(2.34)
The Casson model (Equation 2.34) is a simple two parameter model that has a
physical basis and is derived from structural arguments. This model is capable of
fitting low shear rate curvature and therefore it estimates the yield stress compare well
to the values obtained experimentally [6].
2.5 Effect of Solids Concentration on Suspension Viscosity Several studies have shown that the viscosity of suspensions increase in an
exponential manner with solids concentration and becomes infinite at the maximum
packing fraction. It is well known that the earliest theoretical work on the effective
viscosity was due to Einstein [18] whose derivation led to the effective viscosity to be
linearly related to the particle concentration as follows (Equation 2.35):
1 2.5rh f= + (2.35)
Where,
hr = µm/µf = relative viscosity of the suspension
µm = effective viscosity of the particle-fluid mixture
µf = viscosity of fluid, and
f = solid volume fraction of the suspension
This expression is exact when the viscous effect is dominant so that the creeping flow
equations can be applied at the particle level. This equation is based on the viscous
20
energy dissipated by the flow around the sphere, relating the relative viscosity of the
solids content. With increasing solids concentration, there are a greater number of
particle interactions: these are responsible for the exponential increase in viscosity.
These interactions result in energy dissipation that can be described in terms
hydrodynamic, and aggregation effects. These effects are also responsible for the
increase in non-Newtonian nature of the suspensions that is found at higher
concentrations.
Following Einstein’s work, numerous expressions have been proposed to extend the
range of validity to higher concentrations. They are either theoretical expansions of
Einstein formula to higher order in f, or empirical expressions that were obtained
based on experimental data [42-44]. The theoretical expansions are usually expressed in
the form of a power series as given below (Equation 2.36):
2 31 2 31 .....r k k kh f f f= + + + + (2.36)
Where k1, k2, k3 are the coefficients. Evaluation of these coefficients other than k1
requires the formulation of particle interactions, which is rather difficult. This is one
of the reasons that only the theoretical values of the coefficients related to lower order
in f, like k2 and k3, can be found in the literature so far. Even for these lower order
coefficients, the calculations are available only for idealized cases when the particle
arrangement or its statistic properties are simple.
An example for determining the k2-value was presented by Batchelor and Green [45]
who reported that the coefficient k2 was equal to 7.6 for a suspension undergoing a
pure straining motion. It should be noted however that Batchelor and Green
introduced a rough interpolation in their derivation, which led to an inaccuracy in the
k2-value obtained. A re-calculation under the same condition was conducted by Kim
and Karrila [46], leading to the k2-value to be changed to 6.95. Other k2-values have
been reviewed by Elic and Phan-Thien [47]. Furthermore, Thomas and Muthukumar [48]
found the third order coefficient, k3, to be 6.40 by applying the multiple scattering
theories to the evaluation of the hydrodynamic interaction of three spheres.
Following these theoretical attempts, it can be expected that more complicated
configurations of the particle arrangements will lead to further difficulties in the
mathematical formulation. On the other hand, particles suspended in fluid should in
fact be distributed in a random manner so that their arrangement cannot be fitted to a
21
simple configuration or described by a simple distribution function. Therefore,
although an idealized particle arrangement may enable a theoretical evaluation of the
k-coefficients in higher order, the applicability of the effective viscosity so derived is
limited in practice.
When aggregation effects exist, the aggregates may be considered to be the suspended
units in the suspension. This result in an increase in effective solids content as the
aggregate will trap liquid [49]. The size of aggregates depends on the type of attractive
forces, the shearing conditions and solids concentration in the suspensions [50]. Many
of these effects have been considered in the evaluation of the coefficients of the
general power formula [51]. This model, which is extension of the Einstein’s equation
applies only to moderately concentrated suspensions and does not cover the entire
solids concentration range [43, 51].
In addition to the theoretical expressions, various empirical relationships have been
proposed to evaluate the effective viscosity of a suspension with higher concentration.
An early survey of such relationships made by Rutgers [51] showed that large
discrepancies exist among the different relationships. Table 2.2 shows some typical
examples of the existing empirical formulas, where fm is the maximum particle
concentration and h is the intrinsic viscosity. It is noted that for those relationships
where the so-called maximum concentration is included as a parameter, the effective
viscosity approaches infinity when the concentration is equal to the maximum value.
This may not be physically reasonable. Strictly speaking, there are only two extreme
conditions that are meaningful for the effective viscosity. The first condition is a
suspension without particles, implying that the effective viscosity is the same as the
fluid viscosity. The other is a suspension without fluid, which would then
theoretically behave as a solid with infinite viscosity. On the other hand, only for
particles with regular shapes can the maximum concentration be mathematically
determined for a given packing arrangement. For example, the maximum
concentration can reach 1.0 for cubes packed face-to-face and 0.74 for spheres with
the closest hexagonal packing arrangement. With irregular particles, the maximum
value varies markedly even though the particle size is uniform. As a matter of fact, the
maximum concentration and intrinsic viscosity were often used as two empirical
parameters in fitting experimental data to an empirical formula [52-53].
22
Eilers [18] used the maximum solids content as an upper limit in relating relative
viscosity to the solids fraction for bitumen emulsions. Chong et al [54] modified Eiler’s
equation to correlate the relative viscosity to the solids content for poly-disperse
suspensions. Mooney [55] considered the crowding effects of mono-disperse sphere to
obtain his equation. He also showed how his approach could be extended to bimodal
and poly-disperse suspensions. Krieger and Dougherty [56] also used particle
crowding, in similar manner to derive their equation. Ting and Luebber [57] considered
the effects of liquid-solid density ratio, particle size distribution and particle shape on
packing arrangement to derive an empirical relation between the relative viscosity and
some function of these parameters for varying solids contents.
23
Table 2.2: Formulas for effective viscosity
Einstein’s Equation [18]
Eiler Equation [18]
2
rm
1fhf
-æ ö
= -ç ÷è ø
Leighton and Acrivos’s Equation [52]
2
r
m
0.5 1
1
hfhff
æ öç ÷ç ÷= +ç ÷-ç ÷è ø
Chong et al’s Equation [54]
2
1 0.751
mr
m
ff
hff
æ öç ÷ç ÷= +ç ÷-ç ÷è ø
Mooney’s Equation [55]
r
m
2.5 exp
1
fhff
æ öç ÷ç ÷=ç ÷-ç ÷è ø
Krieger Dowarty’s Equation [56] m
rm
[1- ] hffhf
-=
Liu’s Equation [58]
nr m [a( )]h f f= -
Metzner’s Equation [59]
2
1 1.251
r
m
fhff
æ öç ÷ç ÷= +ç ÷-ç ÷è ø
Quemada’s Equation [60]
m2r
m
[1- ] ffhf
-=
2.6 Effect of Temperature on Suspension Viscosity
Liquid viscosity decreases with the increase in temperature. The trend of decreasing
viscosity at elevated temperatures occurs due to increased kinetic energy of the
particles promoting the breakage of intermolecular bond between adjacent layers
which results in decrease in viscosity of the suspension. For the limestone slurry of 70
weight % solids concentration, He et al [61] investigated influence of temperature on
the viscosity. They found that, the slurry viscosity decreases with increase in the
temperature from 13 to 55 0C. Reduction in the viscosity from the range of 0.0215 to
(1 2.5 )rh f= +
24
0.0365 Pas to the range of 0.01 to 0.019 Pas as for the increase in temperature from 13
to 55 0C was reported.
Mikulasek et al [62] shown the decrease in viscosity of the titanium oxide suspensions
of 10 to 30 volume % concentration over the range of temperature from 20 to 50 0C.
Similar results were observed by Roh et al [63] for coal water suspensions for the
temperature range of 15 to 50 0C and Senapati et al [64] for limestone suspensions in
the temperature range of 30 to 60 0C. The decrease in the suspension viscosity may be
the result of decrease in the interparticle forces between particles with temperature.
The decreased value of the viscosity with increased temperature confirms to
fundamental properties of any viscous materials as for all normal liquids [65]. Work of
different researchers [66-69] shown that the suspension viscosity also decreases with the
increase in temperature.
Senapati et al [64] presented a simple Arhenious type equation for the temperature
dependence of suspension viscosity. An identical relationship was confirmed by Li et
al [70] for temperature dependence of silicon carbide suspensions, they observed
increase in viscosity as temperature of the slurries increased from 20 to 60 0C. The
increase in the viscosity was observed because the suspensions induce flocculation
trend, which might be enhanced at higher temperature.
2.7 Effect of Particle Size on Suspension Viscosity
It is expected that the effects of particle size on suspension viscosity varies depending
on the range of particle size where these effects are studied because the actual inter-
particle forces will vary with the size of particles. Renehan et al [71] found that
suspensions of coal particles in a non-Newtonian suspension of bentonite clay
exhibited both increase and decrease in viscosity with increasing particle size.
Experimental results from Hasan et al [72] show that for high concentrations there is a
decrease in viscosity with increasing particle size, whereas at lower concentrations
there is an increase with increasing particle size. The size of particles in a suspension
has been shown strong influence on its rheological properties. In particular it has been
shown that suspensions with very large (higher than 100 mm) or very small (less than
10 mm) particles have a higher viscosity than suspension containing immediately
sized particles i.e.-100+10 mm [71]. These differences in the viscosities can be
25
explained by contributions of the hydrodynamic and aggregation effects. These
effects contribute to the viscosity to a greater or lesser degree depending on the size of
the particles.
It is difficult to determine the effect of particle size on the viscosity of suspensions
since parameters like shape and charge, which characterize the system may vary with
particle size. Most authors do not specify precisely the accuracy of the size
distribution, or provide much detail as to experimental conditions. Therefore the
disparity in observed results is not unexpected.
Some investigators have reported an increase in viscosity with the decrease in the
particle size [73-76]. This increase in viscosity has been attributed to the aggregation
effects that dominate fine particle behaviour [43, 70, 76-79]. Inter-particle forces of
attraction and repulsion are responsible for these effects which dominate the
movement of colloidal size particles [43, 71]. The magnitude of these factors may be
large enough to influence the movement of course particles. Rehenan et al [71] showed
that the movement of coal particles as course as 200 mm were influenced by surface
charge related effects, that were large enough to contribute to the rheological
properties. Sweeney and Geckler [74] suggested that the contribution from
electroviscous effects to the rheological properties of fine particle suspension can be
very significant. They showed that the viscosity of a suspension of glass spheres in
anionic suspending fluid, where electroviscous effects should be large, was greater
than the viscosity of the same sphere suspension in non-ionic fluid, in which
electroviscous effects should be small.
For suspensions of glass and polystyrene spheres, Parkinson et al [73] Saunders [78]
explained the increase in non-Newtonian behaviour with decreasing particle size, by
contribution of aggregation effects. Inter-particle forces of attraction dominate over
inertial forces for small particles which make them more susceptible to aggregation
than course ones. With increasing shear rate the attachments break resulting in more
dispersed suspension. As the particle becomes dispersed the apparent viscosity
decreased resulting in the shear thinning behaviour [75]. Since this dispersion with
shearing is not instantaneous, at a given shear rate the apparent viscosity will decay
with time resulting in the thixotropic characteristics of such suspensions. The
structure that forms as a result of the aggregation of the fine particle contributes to the
yield stress. Below a critical solids concentration the structure may not be continuous
26
and therefore no yield stress may be present [80]. The effects of particle size are more
pronounced at high solids concentrations than at low ones.
The magnitude of the hydrodynamic effects is proportional to specific surface area of
the particles. Since the specific surface area increases with decreasing particle size,
the contribution of the hydrodynamic effects also increases. Therefore the increase in
viscosity of suspensions resulting from decreasing particle sizes can be explained by
the greater amount of hydrodynamic energy dissipation [78]. According to Hasan et al. [72] increased particle interaction for smaller particles leads to increase in the
suspension viscosity. The formation of aggregates or flocks with decreasing particle
size due to the increasing significance of inter-particle forces at smaller particle sizes
increases the suspension viscosity. Kawatra and Eisele [81] observed an increase in
viscosity with reduction in particle size for constant solids concentration. This is due
to increased surface area, which binds up water molecules and thus increases the
effective solids concentration.
The results of several investigations [71, 75, 77] have shown that the increase in viscosity
occurs as particle size increases. This result has been explained by the energy
dissipated due to physical particle interactions. Since coarse particles have greater
inertia than fine ones they will collide rather than slip past each other. The physical
collisions dissipate energy through friction and loss of translational and rotational
momentum. Thomas [43] and Hasan et al [72] suggest that at low concentrations particle
interactions are minimal and viscosity may increase with particle size. Mangesana at
al [82] shown that viscosity increases with particle size at a fixed concentration for any
given shear rate. The reason suggested for this increase was that particles of greater
size possess greater inertia such that on interaction, the particles are momentarily
retarded and then accelerated. In both these stages their inertia affects the amount of
energy required. This dissipation of energy is what may appear as extra viscosity. The
contributions of the hydrodynamic, aggregation and electroviscous effects clearly
depend on the size of the particles. In order to minimize the viscosity, it seems that an
optimum particle size exists that is not too large and not too small.
27
2.8 Dispersing Agents
Dispersing agent can be classified into: (i) Inorganic compounds, and (ii) polymeric
dispersants [83]. While inorganic dispersants are primarily to control the charge density
at the solid/liquid interface, the polymeric compounds also provide steric hindrance.
Suspensions of aggregated particles can exhibit yield stress and typically have shear
thinning flow properties [84]. Dispersing the particles results in more Newtonian flow
behaviour and reduced apparent viscosity. It should be noted, however, that by
increasing electrostatic repulsion, electroviscous forces can also become important
resulting in greater apparent viscosities. Organic reagents typically used in iron ore
processing are polysaccharides such as starch, guar gum and carboxyl methyl
cellulose which are used to flocculate iron ore [85-86].
The effectiveness of these regents depends on the nature of the reagents, the particle
surface chemistry, the type of dissolved ions and the pH. Typical inorganic dispersing
agents are sodium polyphosphates and sodium silicates [84]. These dispersing agents
are widely used in processing of iron ores.
2.9 Artificial Neural Networks (ANN)
ANNs are massively connected parallel distributed processor made up of simple
processing units, which has a ability for storing experimental knowledge and making
it available for use. ANNs are well known for their utility as universal approximator
of complex nonlinear relationships between process variables and product quality
properties. ANNs have the ability to learn from input data and are very useful for the
prediction of complex high-dimensional data. ANN methods have a broad range of
applications in agriculture [87], weather forecasting [88], water resources engineering [89-
90] finance, medicine, robotics, etc. As in other fields of science, ANN methods have
become popular in chemical engineering too, soon after their development.
Artificial neural networks have been successfully used for dynamic modeling and
control of chemical processes and fault diagnosis [91], in the catalytic reactor modeling
and design of solid catalysts [92] and for modeling the kinetics of a chemical reaction [93]. The applicability of ANN modeling in emulsion liquid membranes [94] and in the
prediction/estimation of the vapor–liquid equilibrium data [95-96] has also been
investigated. Melkon Tatlier et al [97] used ANN model for the prediction of the molar
28
composition of the zeolitess. They estimated the quantities of Si and H2O in the
zeolites by using ANN. They reported the amounts of deviation from the experimental
results for the Si and H2O contents to be equal to about 10 and 20%, respectively.
Bhat and McAvoy [98] applied ANN to dynamic modelling for a pH-controlled CSTR.
The predicted pH values when compared to two other approaches demonstrated that
ANN could predict more accurately than conventional method. Willis et al [99]
discussed the application of ANN as both inferential estimator and predictive
controller. The results demonstrated that ANN could accurately predict the process
output and significantly improved the control scheme. Pollard et al [100] utilized
backpropagation trained ANN for process identification. They concluded that ANN
was particularly useful when the input-output mapping was unknown since ANN was
able to accurately represent nonlinear behaviour in a black box manner. Rajasimman
et al [101] used ANN for modeling of an inverse fluidized bed bioreactor. Initial
substrate concentration and the chemical oxygen demand (COD) values for a given
retention time were predicted by using ANN. Predictions of these parameters were
obtained with desired accuracy.
Shaikh and Al-Dahhan [102] compared the selected literature correlation and the ANN
model for the prediction of gas holdup in bubble column reactor. The standard
deviation of the ANN results for different column parameters was within 14% which
was still less than the other models. They further suggested the use of ANN for scale
up of he bubble column reactors. Sablani et al [103] developed ANN model capable of
explicitly calculating the friction factor for a non Newtonian fluid over a wide range
of Reynolds number. Among different architectures studies they found the maximum
average mean error to be about 3% for the laminar and turbulent regions. Fadare and
Ofidhe [104] developed artificial neural network for the prediction of friction factor in
pipe flow. The proposed model found accurate for prediction of factor using relative
roughness and Reynolds number as input parameters.
ANNs are good at pattern recognition, trend prediction, modeling, control, signal
filtering, noise reduction, image analysis, classification, and evaluation. In fact, the
uses for neural networks are so numerous and diverse that these applications may
seem to have nothing in common. However, they all share the ability to make
associations between known inputs and outputs by observing a large number of
examples. ANNs have been successfully applied in various fields of chemical
29
engineering which include, modeling of multiphase reactors [105], Process control [91,
106-109], Catalysis [110], Estimation of concentration of components in a mixture [108-113],
calculation of heat transfer coefficient [114], modeling of pump-mixer characteristics [114], Membrane separations [110], Reactor modeling [105, 116], waste water treatment [117].
The success of the ANN depends on the selection of the process variables, the quality
of the data and the type of algorithm used. The backpropagation [118-120] is the most
well known and widely among all types of ANN algorithms. The back propagation is
the multilayer feed forward network with different transfer functions in an artificial
neuron and a powerful learning rule. The learning rule is known as backpropagation,
which is kind of error minimization technique with backward error propagation.
ANN is attractive due to its information processing characteristic such as nonlinearity,
high parallelism, fault tolerance as well as capability to generalize and handle
imprecise information [118, 120]. These characteristics have made ANN suitable for
solving a variety of problems.
2.10 Critical Appraisal
The two phase systems of solid-liquid suspensions are inherently unstable. Sufficient
amount of literature is available on settling behaviours of different types of
suspensions for different ranges of particle Reynolds numbers. Among the
relationships for the single particle terminal settling velocity in concentrated
suspensions, Richardson and Zaki’s equation is confirmed and recommended by
several theoretical and experimental studies. From the available literature it is well
understood that, the hindered settling coefficient ‘n’ varies from suspension to
suspension. No unique value of ‘n’ is available for all suspensions. It varies from 3 to
5.1 for the suspensions of different types of solids. In the literature various drag
coefficient- particle Reynolds number (CD-Rep) relationships are available. The
available relationships contain two to five constants.
No settling data for the hindered settling coefficient ‘n’ of magnetite ore suspensions
is available in the literature. Because of the unstable nature of these two phase
systems the, available CD-Rep relationships are erroneous if applied to all types of
suspensions. Hence there is good scope for studying settling behaviour of magnetite
ore suspensions and to obtain the useful data on the ‘n’ values. From the experimental
30
data it would be possible to develop experimental CD-Rep relationship for magnetite
ore suspensions.
Rheological characteristics of the suspensions depend on various parameters. Particle
size and concentration of solids significantly influence the shear stress-shear rate
relationship and the relative viscosity of the suspensions. The effect of solids
concentration on the suspension rheology is not the same for all types of suspensions.
It depends on the nature and type of the solid particles and their surface
characteristics. Studies by Some suspensions show the increase in non Newtonian
behaviour with the increase in solids concentration, whereas the decrease in non
Newtonian behaviour of the suspensions also has been presented in some studies.
Same suspension also can show different rheological behaviours at different solids
concentrations and shear rates. Particle size effect on suspension rheology and relative
viscosity was studies by many workers. The earlier studies show increase in non
Newtonian behaviour and relative viscosity with the increase in particle size of the
solids in suspensions as well as decrease in non Newtonian behaviour and relative
viscosity with increased particle size.
Well established empirical equations are available in the literature to describe the flow
curves of the suspensions, but the suspensions of different types of solids particles can
not be presented by a same equation. Even for same suspensions different equations
were suggested by a few workers. For magnetite ore suspensions, to describe the
shear stress- shear rate relationship, equations such as power law, Bingham plastic
and Casson equation were proposed by earlier workers. For very dilute suspensions,
the relative viscosity can be predicted by Einstein’s formula. For concentrated
suspensions, numbers of equation are available in literature, but any of these
equations is not suitable for all types of suspensions. Different equations are suitable
for different type of suspensions. No such relationship for magnetite ore suspensions
was found in the literature.
Hence there is good scope studying rheological behaviour of the magnetite ore
suspensions, to investigate the effects of particle size and solids concentration on the
suspensions rheology and to find out a suitable equation to describe the flow curves. It
would be worth to know the effect of particle size on relative viscosity of magnetite
ore suspensions and to find out a suitable better fitting equation for the dependence of
relative viscosity on the solids concentration in the suspension. Further there is good
31
potential to develop artificial neural network models to describe the flow curves for
magnetite ore suspensions and the relative viscosity-solids volume fraction
relationships for the same.
References
1. Rushton, A. S. Ward and R. G. Holdich, “Solid-Liquid Filtration and Separation Technology”, Wiley-VCH Verlag GmbH, Weinheim, Germany, (1996)
2. J F Richardson and W N Zaki., “The Sedimentation of a Suspension of Uniform Spheres under Condition of Viscous Flow”, Chemical Engineering Science, 3, (1954), 66-73
3. S Mirza and J F Richardson, “Sedimentation of Suspensions of Particles of Two or More Sizes”, Chemical Engineering Science, 34, (1979), 447-454
4. E. Barnea, J. Mizrahi, “Generalized Approach to the Fluid Dynamics of Particulate Systems Part 1: General Correlation for Fluidization and Sedimentation in Solid Multiparticle Systems”, The Chemical Engineering Journal, 5, (1973), 171-189
5. E. Capes, “Particle Agglomeration and the Value of the Exponent n in the Richardson-Zaki Equation”, Powder Technology, 10, (1074), 303-306
6. R. M. Turian, T. W. Ma, F. L. G. Hsu and D. J. Sung, “Characterization, settling and rheology of concentrated fine particulate mineral slurries” Powder Technology, 93, (1997), 219-233
7 Sangkyun Koo, “Estimation of hindered settling velocity of suspensions”, Journal of Industrial and Engineering Chemistry, 15, (2009), 45–49
8 Garside and M.R. Al-Dibouni, “Velocity-voidage relationships for fluidization and sedimentation in solid-liquid systems”, Industrial and Engineering Chemistry Process Design and Development, 16, (1977), 206–214
9. Nian-Sheng Cheng , “Comparison of formulas for drag coefficient and settling velocity of spherical particles”, Powder Technology, 189, (2009), 395–398
10. T.E. Baldock,, M.R. Tomkinsa, P. Nielsena and M.G. Hughes, “Settling velocity of sediments at high concentrations”, Coastal Engineering, 51, (2004), 91–100
11. M.S. Selim, A.C. Kothari and R.M. Turian, “Sedimentation of multi-sized particles in concentrated suspensions”, A.I.Ch.E.Journal, 29, (1983), 1029–1038
32
12. M. Lali, A. S. Khare and J. B. Joshi, “Behaviour of Solid Particles in Viscous Non-Newtonian Solutions: Settling Velocity, Wall Effects and Bed Expansion in Solid-Liquid Fluidized Beds”, Powder Technology, 57, (1989), 39 – 50
13. Di Felice, R. and Parodi, E., “Wall effects on the sedimentation velocity of suspensions in viscous flow”, AIChE Journal, 42, (1996),. 927–931
14. Alfred W Francis, “Wall Effects in Falling Ball Method for Viscosity”, Journal of Applied Physics, 4, (1933),.403-406
15. Clift R, Grace J. R. and Weber M. E., “Bubbles, Drops and Particles”, Academic Press New York (1978)
16. R Di Felice, “A Relationship for the Wall Effect on the Settling Velocity of a Sphere at Any Flow Regime”, International Journal of Multiphase Flow, 22 (3), (1996), 527-533
17. Edward J. Wasp, John P Kenny and Ramesh Gandhi, “Solid-liquid Flow Slurry Pipeline Transportation-Bulk Materials Handling”, Trans Tech Publications¸ Cranfield, UK (1977)
18. Sumer M. Peker Serife S. Helvaci, “Solid–Liquid Two Phase Flow”, Elsevier Amsterdam, The Netherlands (2008)
19. M. Gilbert, L. Davis and D. “Altman, Velocity lag of particles in linearly accelerated combustion gases”, Jet Propulsion 25, (1955), 26-31
20. R. Turton and 0. Levenspiel, “A Short Note on the Drag Correlation for Spheres”, Powder Technology, 47, (1986), 83 – 86
21. A.R. Khan and J.F. Richardson, “The Resistance to Motion of a Solid Sphere in a Fluid” , Chemical Engineering Communications, 62(1– 6), pp.135 – 150 (1987)
22. Haider and 0. Levenspiel, “Drag Coefficient and Terminal Velocity of Spherical and Nonspherical Particles” Powder Technology, 58, (1989), 63 – 70
23. J. Zigrang and N. D. Sylvester , “An explicit equation for particle settling velocities in solid-liquid systems”, AIChE Journal, 27(6), (1981), 1043–1044
24. R. Turton and N. N. Clark, “An explicit relationship to predict spherical particle terminal velocity”, Powder Technology, 53, (1987), 127 – 129
25. R. H. Perry and C. H. Chilton, “Chemical engineers' handbook”, McGraw-Hill, New York, USA (1973)
26. R.L.C. Flemmer and C.L. Banks, “On the drag coefficient of a sphere”, Powder Technology, 48(3), (1986), 217-221
33
27. G. Saha, N.K. Purohit and A.K. Mitra, “Spherical particle terminal settling velocity and drag in Bingham liquids”, International Journal of Mineral Processing, 36 (3-4), (1992), 273-281
28. F. Concha and E. R. Almendra, “Settling velocities of particulate systems, 1. Settling velocities of individual spherical particles”, International Journal of Mineral Processing, 5 (4), (1979), 349-367
29. G. Venu Madhav and R. P. Chhabra, “Drag on non-spherical particles in viscous fluids”, International Journal of Mineral Processing, 43 (1-2), (1995), 15-29
30. P.P. Brown and D.F. Lawler, “Sphere drag and settling velocity revisited”, Journal of Environmental Engineering, 129 (3), (2003), 222–231
31. Harris J., “Rheology and non-Newtonian flow”, Longman, New York, USA (1977)
32. Bird, R.B., Stewart, W.E. and Lightfoot, E.N., “Transport Phenomena”, John Wiley & Sons, New York, USA (2001)
33. Malcom M Cross, “Rheology of non-Newtonian fluids: a new flow equation for pseudoplastic systems”, Journal of Colloid Science, 20, (1965), 417-437,
34. Malcom M Cross, “Rheology of viscoelastic fluids: elasticity determination from tangential stress management”, Journal of Colloid and Interface Science, 21, (1968), 84-90
35. Mewis J and Spaull A J B, “Rheology of concentrated dispersions”, Advances in Colloid l Interface Science, 6, (1976), 173-200
36. Carreau P. J., “Rheological equations from molecular network theories”, Transactions of Society of Rheology , 16(1), (1972), 99-127
37. Carreau P. J. and De Kee D., “ Review of some useful rheological equations”, Canadian Journal of Chemical Engineering, 57, (1979a), 3-15
38. Carreau P. J. and De Kee D., “Analysis of viscous behaviour of polymeric solutions”, Canadian Journal of Chemical Engineering, 57, (1979b), 135-140
39. Howard A Barnes, “A Handbook of Elementary Rheology”, Cambrian Printers, Llanbadarn Road, Aberystwyth, UK (2000)
40. Q.D. Nguyen and D.V. Boger, “Application of rheology to solving tailings disposal problems”, International Journal of Mineral Processing, 54, (1998), 217–233
41. S K Nicol and R J Hunter, “Some Rheological and electrokinetic properties of kaolinite suspensions”, Australian Journal of Chemistry, 23(11), (1970),
34
2177 – 2186
42. Cheng, N. S., and Law, A. W. K., “Exponential formula for computing effective viscosity”, Powder Technology, 129(1-3), (2003), 156– 160
43. Thomas D. G. "Transport characteristics of suspension: VIII. A note on the viscosity of Newtonian suspensions of uniform spherical particles." Journal of Colloid Science., 20, (1965), 267-277
44. G. S. Khodakov, “On suspension rheology”, Theoretical Foundations of Chemical Engineering, 38(4), (2004), 430–439
45. Batchelor, G. K., and Green, J. T., “The determination of the bulk stress in a suspension of spherical particles to order c2”, Journal of Fluid Mechanics., 56, (1972), 401-472
46. Kim, S., and Karrila, S. J., “Microhydrodynamics: principles and selected applications”, Butterworth-Heinemann, Boston, USA (1991)
47. V Ilic and N Phan-Thien, “Viscosity of concentrated suspensions of spheres, Rheological acta., 33, (1994), 283-281
48. Thomas, C. U., and Muthukumar, M., “Convergence of multiple scattering series for two-body hydrodynamic effects on shear viscosity of suspensions of spheres”, Journal of Chemical Physics, 94(6), (1991), 4557-4567.
49. T. B. Lewis and L. E. Nielsen, “Viscosity of dispersed and aggregated Suspensions of spheres”, Journal of Rheology, 12, (1968), 421-442
50. Bruce A. Firth and Robert J. Hunter, “Flow properties of coagulated colloidal suspensions : I. Energy dissipation in the flow units”, Journal of Colloid and Interface Science, 57(2), (1976), 248-256
51. Rutgers, J. “Relative viscosity of suspensions of rigid spheres in Newtonian Liqiud”, Reologica Acta, 2, (1962), 202-212
52. David Leightont and Andreas Acrivos, “Viscous resuspension”, Chemical Engineering Science, 41(6), (1986), 1377-1384
53. Barnes, H. A., “Shear-Thickening (``Dilatancy'') in suspensions of non-aggregating solid particles dispersed in Newtonian liquids”, Journal of Rheology, 33(2), (1989), 329-366
54. Chong, J.S., Christiansen, E.B. & Baer, A.D., “Rheology of concentrated suspensions”, Journal of Applied Polymer Science, 15, (1971), 2007-2021
55. Mooney, M, “The viscosity of concentrated suspension of spherical particles”, Journal of Colloid Science, 6, (1951), 162-170
56. Irvin M. Krieger and Thomas J. Dougherty, “A mechanism for non-
35
Newtonian flow in suspensions of rigid spheres”, Transactions of the Society of Rheology, 3, (1959), 137-152
57. Andrew Pusheng Ting and Ralph H. Luebbers, “Viscosity of suspensions of spherical and other isodimensional particles in liquids”, AIChE Journal, l3, (1957), 111–116
58. Dean Mo Liu, “Particle packing and rheological property of highly-concentrated ceramic suspensions: An determination and viscosity prediction”, Journal of Material Science, 35, (2000), 5503 – 5507
59. Metzner, A. B., “Rheology of suspensions in polymeric liquids.” Journal of Rheology, 29, (1985), 729-735
60. Quemada, D., “Rheology of concentrated disperse systems and minimum energy dissipation principle”, Rheologica Acta, 16, (1977), 82-94
61. Mingzhao He , Yanmin Wang and Eric Forssberg, “Parameter studies on the rheology of limestone slurries”, International Journal of Mineral Processing, 78 (2006) 63– 77
62. Mikulasek, P., Wakeman, R.J., Marchant, J.Q., 1997. The influence of pH and temperature on the rheology and stability of aqueous titanium dioxide dispersions. Chem. Eng. J. 67, 97–102
63. Nam-Sun Roh, Dae-Hyun Shin, Dong-Chan Kim and Jong-Duk Kim, “Rheological behaviour of coal-water Mixtures- 2. Effect of surfactants and temperature”, Fuel, 74, (1995) 1313-1318
64. Pradipta Kumar Senapati, Dibakar Panda and Ashutosh Parida, “Predicting Viscosity of Limestone–Water Slurry”, Journal of Minerals & Materials Characterization & Engineering, 8(3), (2009), 203-221
65. Shenoy A. V., “Drag reduction with surfactants at elevated temperatures”, Rheologica Acta, 15(11-12), (1976), 658-664
66. Lu-Cun Guo, Yao Zhang, Nozomi Uchida and Keizo Uematsu, “Influence of temperature on stability of aqueous alumina slurry containing polyelectrolyte dispersant”, Journal of the European Ceramic Society, 17(2-3), (1997), 345-350
67. Mishra S. K., Senapati P. K. and D. Panda, “Rheological Behavior of Coal-Water Slurry” Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 24(2), (2002), 159 – 167
68. Naik H.K, Mishra M. K, and Rao Karanamet, “The effect of drag reducing additives on the Rheological properties of fly-ash water suspensions at varying temperature environment”, Coal Combustion and Gasification Products, 1 (2009), 25-31
69. Lu-Cun Guo, Yao Zhang, Nozomi Uchida and Keizo Uematsu, “Influence
36
of temperature on stability of aqueous alumina slurry containing polyelectrolyte dispersant”, Journal of the European Ceramic Society, 17(2-3), (1997), 345-350
70. Yang Hua-Gui Li, Chun-Zhong, Gu, Hong-chen, Fang, Tu-Nan, “Rheological behavior of titanium dioxide suspensions” Journal of Colloid and Interface Science 236, (2001)96– 103
71. Renehan M.J., Pullum L., Lambrianidis J. and Bhattacharya S.N., “Effects of coarse particle size fractions on rheology of coal suspensions containing fine particles”, Tenth International Congress on Rheology, 2, (1988), 207-213
72. Hasan, A.R., Baria, D.N. and Rao, A.V., , “Rheological behaviour of Low-rank coal-water slurries”, Chemical Engineering Communications, 46(4-6), (1986), 227-240
73. Parkinson, C., S. Matsumoto, and P. Sherman, “The influence of particle-size distribution on the apparent of non-Newtonian dispersed systems”, Journal of Colloid and Interface Science, 33, (1970), 150–160
74. Keith H. Sweeny and Richard D. Geckler, “The Rheology of Suspensions”, Journal of Applied Physics, 25( 9), (1954), 1135-1144
75. D. N. Saraf and S. D. Khullar, “Some studies on the viscosity of settling suspensions”, The Canadian Journal of Chemical Engineering, 53(4), (1975), 449–452
76. F. W. A. M. Schreuder, A. J. G. Van Diemen and H. N. Stein, “Viscoelastic properties of concentrated suspensions”, Journal of Colloid and Interface Science, 111(1), (1986), 35-43
77. Eveson G F, "Rheology of disperse systems”, Pergamon Press, London, UK, (1959)
78. Frank L. Saunders, “Rheological properties of monodisperse latex systems: Flow curves of thickened latexes”, Journal of Colloid and Interface Science, 23(2), (1967), 230-236
79. Irvin M.Krieger, “Rheology of monodisperse latices”, Advances in Colloid and Interface Science, 3(2), (1972), 111-136
80. Heikki R. Laapas and Ulla-Riitta Lahtinen, “Thedetermination of particle size distribution using combined gravitational and centrifugal sedimentation analysis”, Particle & Particle Systems Characterization, 1(1-4), (1984), 127–131
81. Kawatra and Т. C. Eisele, “Proceedings of the Sixteenth International Mineral Processing Congress”, Elsevier Science Publishers BV, Amsterdam, (1988), 195-207
37
82. N. Mangesana, R.S. Chikuku, A.N. Mainza, I. Govender, A.P. van der
Westhuizen, and M. Narashima, “The effect of particle sizes and solids concentration on the rheology of silica sand based suspensions”, The Journal of The Southern African Institute of Mining and Metallurgy, 108, (2008), 237-243
83. J.S. Laskowski and J. Ralston, “Colloid chemistry in mineral processing”, Elsiever Science, Amsterdam, The Netherlands (1992)
84. H. D. Chandler; R. L. Jones, “Flow kinetics in concentrated suspensions of silica-iron (III) oxide-water”, Philosophical Magazine A, 59(3), (1989), 645–660
85. S. A. Ravishankar, Pradip, and N. K. Khosla, “Selective flocculation of iron oxide from its synthetic mixtures with clays: a comparison of polyacrylic acid and starch polymers”, International Journal of Mineral Processing, 43(3-4), (1995), 235-247
86. Pawlik, M. and Laskowski J.S., “Stabilization of Mineral Suspensions by Guar Gum in Potash Ore Flotation Systems” Canadian Journal of Chemical Engineering, 84, (2006), 532-538
87. Ray, C .and Klindworth, K. K., “Neural networks for agrichemical vulnerability assessment of rural private wells”, Journal of Hydrologic Engineering, 5, (2000), pp.162-172
88. Silverman, D., & Dracup, J. A., “Artificial neural networks and long-range precipitation prediction in California”, Journal of Applied Meteorology, 39, (2000), 57-63
89. Cigizoglu, H. K., “Incorporation of ARMA models into flow forecasting by artificial neural networks”, Environmetrics, 14, pp.417-421 (2003)
90. Cigizoglu, H. K., “Estimation, forecasting and extrapolation of flow data by artificial neural networks”, Hydrological Sciences Journal, 48, (2003), 349-359
91. Hussain, M. A., “Review of the applications of neural networks in chemical process control-simulation and online implementation”, Artificial Intelligence in Engineering, 13, (1999), 55-63
92. Huang, K., Chen, F. and Lu, D., “Artificial neural network-aided design of a multi-component catalyst for methane oxidative coupling”, Applied Catalysis A, 219, (2001), 61-67
93. Serra, J. M., Corma, A., Chica, A., Argente, E. and Botti, V., “Can artificial neural networks help the experimentation in catalysis?”, Catalysis Today, 81, (2003), 393-399
38
94. Chakraborty, M., Bhattacharya, C. and Dutta, S., “Studies on the applicability of artificial neural network (ANN) in emulsion liquid membranes”, Journal of Membrane Science, 220, (2003), 155-161
95. Sharma, R., Singhal, D., Ghosh, R., and Dwivedi, A., “Potential applications of artificial neural networks to thermodynamics: Vapor–liquid equilibrium predictions”, Computers and Chemical Engineering, 23, (1999), 385-391
96. Mehmet B., “The use of neural networks on VLE data prediction” Journal of Scientific and Industrial Research, 63 (4), (2004), 203-312
97. Melkon Tatlier, H. Kerem Cigizoglu, and Ays¸Erdem-Senatalar, “Artificial neural network methods for the estimation of zeolite molar compositions that form different reaction mixtures”, Computers and Chemical Engineering, 30, (2005), 137–146
98. Bhat N and McAvoy T.J., “Use of neural nets for dynamic modelling and control of chemical process systems”, Computers and Chemical Engineering, 14(4-5), (1990), 573-583
99. Willis, M., Montague, G.A., Massimo, C.D., Tham, M.T. and Morris, A.J., “Artificial Neural Networks in Process Estimation and Control”, Automatica, 28(6), (1992), 1181-1187
100. Pollard J.F., Broussard M.R., Garrison D.B. and San K.Y., “Process Identification Using Neural Networks”, Computers and Chemical Engineering, 16(4), (1992), 253- 270
101. Rajasimman, M., Govindarajan, L. and Karthikeyan, C., “Artificial Neural Network Modeling of an Inverse Fluidized Bed Bioreactor”, International Journal of Environment Research, 3(4), (2009), 575-580
102. Ashfaq Shaikh and Muthanna Al-Dahhan, “A new methodology for hydrodynamic similarity in bubble columns”, The Canadian Journal of Chemical Engineering, 88(4), (2010), 503–517
103. Sablani S. S., “A neural network approach for non-iterative calculation of heat transfer coefficient in fluid-particle system”, Chemical Engineering and Processing, 40, (2001), 363-371
104. D.A. Fadare and U.I. Ofidhe, “Artificial Neural Network Model for Prediction of Friction Factor in Pipe Flow”, Journal of Applied Sciences Research, 5(6), (2009), 662- 670
105. Laurentiu A. Tarca, Bernard P.A. Grandjean and Faıcal Larachi, “Reinforcing the phenomenological consistency in artificial neural network modeling of multiphase reactors”, Chemical Engineering and Processing, 42, (2003), 653-676
39
106. Soundar Ramchandran and R Russel Rhinhart, “A very simple structure for neural network control of distillation”, Journal of Process Control, 5(2), (1995), 115-128
107. J. Fernandez de Canete, S. Gonzalez-Perez, and P. del Saz-Orozco, “Artificial Neural Networks for Identification and Control of a Lab-Scale Distillation Column using LABVIEW”, World Academy of Science, Engineering and Technology, 47, (2008), 64-69
108. Zeybek Z., Yuce S., Hapoglu H. and Alpbaz M., “Adaptive heuristic temperature control of a batch polymerization reactor”, Chemical Engineering and Processing, 43, (2004), 911-918
109. Ngu C. W. and Hussain M. A., “Hybrid neural network- prior knowledge model in temperature control of a semi batch polymerization process”, Chemical Engineering and Processing, 43, (2004), 559-567
110. Yan Liu Yang Liu Dazhuang Liu Tao Cao, Sen Han and Genhui Xu, “Design of CO2 hydrogenation catalyst by an artificial neural network”, Computers and Chemical Engineering, 25, (2001), 1711–1714
111. Robert R. Jensen, Shankar Karki, Hossein Salehfar, “Artificial neural network based estimation of mercury speciation in combustion flue gases”, Fuel Processing Technology, 85, (2004), 451– 462
112. Tzu-Ming Yeh, Ming-Chieh Huang, Chi-Tsung Huang , “Estimate of process composition and plant wide control from multiple secondary measurements using artificial neural networks”, Computers and Chemical Engineering, 27, (2003), 55-72
113. Obodeh O and Ajuwa, C. I., “Evaluation of artificial neural network performance in predicting diesel engine NOx emissions”, European Journal of Scientific Research, 43(4), (2009) , 642-653
114. Sing K. K., Shenoy K. T., Mahendra A. K. and Ghosh S. K., “Artificial neural network based modeling of head and power characteristics of pump-mixer”, Chemical Engineering Science, 59, (2004), 2937-2944
115. Bowen W.R., Jones W. R. and Yusef H. N., “Prediction of the rate of cross flow membrane ultrafiltration of colloids: a neural network approach”, Chemical Engineering Science, 53(22), (1998), 3793-3799
116. Saxen B. J. and Saxen H., “A neural network based model of bio-reaction kinetics”, Canadian Journal of Chemical Engineering, 74, (1996), 124-129
117. Gontaraski C. A., Rodrigues D. R., Mori M. and Prenem L. F., “Simulation of an industrial waste water treatment plant using artificial neural networks”, Computers and Chemical Engineering, 24, (2000), 1719-1728
40
118. Boughman D. R. and Liu Y. A., “Neural networks in bioprocessing and chemical engineering”, Academic Press, London, UK (1995)
119. Tambe S. S., Kulkarni B. D. and Deshpande P. B., “Elements of artificial neural network with selected applications in chemical engineering and chemical and biological sciences”, Simulation and Advanced control Inc. USA. (1996)
120. Lumin Fu, “Neural networks in computer intelligence”, McGraw Hill Inc. New York, USA (1996)