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Colloids and Surfaces, 8 (1983) 121-136Elsevier Science Publishers B. V., Amsterdam

121Printed in The Netherlands

A STUDY OF THE INTERAcrIONS BETWEE~CL~S ANDBUBBLES IN SURFACTANT SOLUTION~

P. SOMASUNDt\RAN, P. CHANDAR, and K. CHARI

Henry Krumb School of Mines, Columbia University, New York. N. Y. 10027 (U.S.A.,

(Received 20 July 1983; accepted 27 July 1983)~

ABSTRACT

-;;:~~~~:;,:;::.~

~L~.~~~~~Attachment of particles to bubbles involves various interactions resulti..- from electrical

double layer forces between the particle and the bubble (with adsorbed surfactant on both).van der Waals forces. the energy change due to the transfer of the hydrocarbon chains ad-sorbed on the particle to the gaseous phase. and steric repulsion between .-orbed sur-factant layers on the two interacting surfaces. The energies of these interactions for thealumina-dodecylsulfonate system are calculated using data for the zeta potential of themineral. the surface tension of the solutions and the surfactant adsorptioa density.Estimated total interaction energy is correlated with the results of bubble ~-up experi-ments. Like flotation. mineral pick-up by the bubble goes through a maxiD81D as a func-tion of surfactant concentration and this behavior is satisfactorily accouDt..J (or by thepresent treatment.

INTRODUCriON

'~Flotation is a complex process that is the result of many chemiCal and

hydrodynamic phenomena in a system that contains solid partides, liquid, andgas bubbles in a state of varying turbulence. While certain indiYdlal phenomenasuch as adsorption are fairly well understood, the manner in wbr.h thesevarious phenomena interact to yield flotation of a mineral has DOt been fullyestablished. Also, although the effects of most of the system ~erties onflotation are known, the mechanisms by which they control flotation have notbeen fully developed. Flotation of minerals has been shown in tile past to ex-hibit a surfactant concentration dependence sometimes characterized by amaximum [1-4]. This is illustrated in Fig. 1 for the quartz~cylaminesystem [1]. While the increase in flotation evidently is due to. hydro-phobicity imparted to the mineral surface by surfactant adsorpCi!>n, the de-crease at higher surfactant concentrations can be due to surfactat adsorptionin this range with a reverse orientation as well as to mutual re~ion betweenthe bubble and the particle, which will be similarly charged uIDr tJ1ese condi-tions. Excessive aggregation between particles, making them t8O coarse forlevitation, or a decrease in bubble size in this concentration rmJle also can lead

0166-6622/83/$03.00 e 1983 Elsevier Science Publishers B. V.

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DCA - HCI CONCENTRATION. kmol/m3FiC. 1. Flotation of quartz in a Hallimond Cell uling dodecylamine hydrocl8ride ascollector [1].

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to a reduction in flotation. In this stucjy, an attempt is made to ~titativelyaccount for the above flotation behavior in terms of various inteiations be-tween the bubble and the particle. In order to accomplish this, 1fIe, bubble-particle attachment process is treated as a heterocoagulation pr~. Whilesome models have been developed for coagulation between solid )8rticles, nomodel taking all the interactions into account exists for aggregatDt between asolid particle and a bubble. Aggregation between particles and ldbles underflotation conditions is complicated by the presence of significant hydrophobicinteractions between the bubble and the surfactant ions adsorbed on theparticle.

The bubble-particle at~hment process is treated here essentilily in termsof DL VO theory [5,6], modified to include both the hydropho18 attractiveinteraction arising from the transfer of surfactant chains from tile solid-liquidinterface to the liquid-air interface and the repulsive interactioo due to pos.-sible steric hindrance between adsorbed surfactant layers on the mteractingbubble and on the particle.

As indicated above, hydrodynamic forces also significantly affect the over.all flotation process [7-10]. In order to isolate such effects, tbe"flotation"behavior was studied here using a bubble pick-up technique unlk quiescent

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conditions. In addition, tJ1e bub~le:::::particl~ !!-l~tioIIS~y zed at a:iii~il~~~~~Ce...Q!; 5 A-;- where hy~odynamic iDi::enctiona ~.fI'iJ.i

The system selected for the present study was alumina (O.3..-)-dodecylsulfonate about which considerable information already ~1tIie literature[11-13]. Also, most importantly, in this work all the plO~ftJ1e systemrequired for tJ1e estimation of various intera:tion e~~ mctlt>eorrelationwith flotation were measured for the system using the 8me ~les.

I

THEORY

~

The energy changes associated wiUl Ule attachment of a pat*! to a bubblein Ule flotation process arise from Ule overlap of Ule electricalick'ble layers ofthe particle and the bubble. from van der Waals forces, from ~fer ofsurfactant adsorbed on the particle to the gaseous p~, and~dition.from steric hindrance or volume restriction of the 8urfactant:~es on theinteracting surfaces [7.14-16]. Expressions developed to estiate'the magni-tude of these interactions are discussed below.

Hydrophobic interactiom

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The free energy, VH, involved in the transfer of dodecyl eiiairof the sur-factant adsorbed on the solid surface to the gaseous phase ~attachmentof the bubble to the particle can be estimated as

V = rS/L",S/L-L/G X 12A \ .,." , ..~ 01'" df:>:t° II )H "'CH. ~ co: 6.~'j ( ~'" ~."~\)rS/L is adsorption density at the solid-liquid interface, ~G is the

tzansfer energy per mole of CH2 groups from the solid-liq\i1~the liquid-gas interface and Ac is the area of contact between bubble aD~cle. A1112hydrocarbon groups including the end group are consideredctbel identical inthis treatment.

.S/L-L/G can be estimated to be .L-L/G - .L-S/L (2)CHI CH. CHI

where superscripts L-L/G and L-8/L represent the transf~z groupsfrom bulk liquid to liquid:-gas and solid-liquid interfaces ~ely. Frompast studies [17], .~L/G - -:-1.08RT. ,~/L can be estim88tusing thefollowing adsOrption iAotherm of dodecylsulfonate on alUm811{ 18 J :

rS/L/(rS/L - raIL) ~ (C /55.5) exp [- ( .!!. L-S/L + ~ J (3) max R RT CHI RTwhere CR is the equilibrium concentration of sulfonate in kdliD3 and r isthe zeta potential of alumina, which is assumed to be the Sta~tential.rS/L is the maximum adsorption density and is estimated~4.5 X 10-6m~m 2 from surface tension studies and packing consider.- [19]. Using

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these expressions, V H can be calculated from data for adsorption density andzeta potential.

,IElectrical double layer interactions

Expressions for the interaction energy of the overlap of double layers[20-26] differ essentially in the choice of boundary conditions, l8nely, con-stant charge or constant potential of the interacting surfaces during theirmutual approach. For the case of constant potential at both surf~, the fol-lowing equation derived by Hogg et al. [21] is appropriate:

~-w = eala2(1/Ij + 1/1~) 21/111/12 In '1 + exp (-KHo) \E

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+(1/1 I +I/I~) 1":: up (-.«Ho)

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In (1- exp (-2"Ho» .",..-," '"-:- (4)

If, on Ute other hand, Ute charge densities at boUt interfaces is a-.med to re-main constant, Ute equation derived by Weise and Healy [22] usiug the proce-dure suggested by Frens and Overbeek [27] applies:

VF,-o = ~-111 - Eala2(1/1~ + 1/1~) In (1- exp (-2"Ho» (5)

2(al +a2)Several publications have dealt with Ute choice of boundary conditions[27-30]. The constant potential condition prevails if electroch~ equi-librium of the potential determining ions and adsorbing species between thebulk solution and the interface is maintained during the interac1D [30,31].Alternatively the constant charge condition would be more appr.."jate if theadsorption density of Ute species that are responsible for the ch~ develop-ment at the interface is not regulated rapidly enough during the ~roach ofthe surfaces [30,32]. In a real system, both the charge and the potential canchange, particularly if the adsorbed surfactant species "also contrilutes to thedevelopment of the surface potential. Under such conditions, the tEe ofneither the constant potential nor the constant charge condition will be valid,and an intermediate condition between these two extremes will .. more ap-propriate [33]. Accordingly, for Ute present treatment, the val~ C)f the doublelayer interaction energy is taken as the arithmetic average of the gues cal-culated usin:g equations 4 and 5.

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van der Wool's interactions

Since the present system is comprised of three different media fsolid, airand intervening solution), there will be an energy change assoc~ with vander Waal's forces when the bubble and particle are brought togelier [7]. Forthe case of a fiat plate and a sphere (ap « ab), this free energy dange is givenby [34],Vy = -Aap/6Ho (6)

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I" where A is the Hamaker constant for the system, ap and ab ~1tl~ radii of theparticle and bubble respectively, and Ho is the distance of ~on. TheHamaker constant for the system is given by [35].A = (~ - ~)(VA'PP - VAll) (7)

The values listed by Visser [35] of the Hamaker constants f«~na (App)and water (All) are 15.5 X 10-20 J and 4.38 X 10-20 J, r~tJ\I'ely. Thevalue for air (Abb) is considered to be negligibly small. The Y8lItefor A is there-fore -3.86 X 10-20 J. Interestingly. the Hamaker constantilffjfind to be nega-tive. suggesting that in this case the van der Waals interactim1!isr~wsive. Theconcept of a negative Hamaker constant and correspondingly;~ repulsivevan der Waals interaction has been discussed by Visser [36).~8 Vv for theabove value of A is. -=~ .. "'o!

Vv = 9.65 X 10-28/Ho (8)- ---=--~ -=--

,

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When the interacting spheres (bubble and particle in thjs aNt bontain ad-sorbed layers, their adhesion will be sterically hindered, ~y due to thephysical size of the molecules. Therefore the treatment of tb~egationphenomenon has to be modified to include a volume rest~tteim in the ex-pression for overall interaction energy [15,16]. Mackor [37]huestimatedthis interaction energy by considering the loss in entropy dvtt&(fue restrictionof the molecules during the attachment. The expression derlt-dcby Mackor is,

Vs=8N_RT(1-Ho/~) (9)

where N - is the maximum number of sites available for adJqJ't1on; 8 is thefractional surface coverage; and ~ is the adsorbed layer thickM'.' Thesteric repulsion has therefore been calculated using the foBcwtrig expressionwith ~ = 20 A.

vs = raIL R7'(l- Ho /20)X Ac

It should be noted that Mackor's derivation is only valid atO.~dsorptiondensities when there is negligible lateral interaction betw--.

..

126

EXPERIMENTAL

I Materials

(i) AluminaLinde grade alumina of 0.3 ~ size purchased from Union Carbide Corpora-

tion had a BET surface area of 15 m2/g and an isoelectric point of 8.7 as deter-mined by electrophoresis.

I

~ (ii) SurfactantSodium dodecylsulfonate (> 98% pure) purchased from Aldrich Chemicals

was used as received.

(iii) Inorganic reagentsSodium chloride (> 99% pure) (Aldrich Chemicals), hydrochloric acid and

sodium hydroxide (Fisher Scientific Company) used were of reagent grade.

Sample preparation

The alumina was conditioned in sodium dodecylsulfonate solutions using amagnetic stirrer. After conditioning for 6 h. a small amount of the sample wasremoved for the measurement of zeta potential. The remaining sampled wascentrifuged at 4000 rpm for 10 min and the residue was used for the bubblepick-up experiments and aggregation tests. The supernatant was centrifugedagain at 5000 rpm for 10 min and divided into five portions and a portion wasused to determine adsorption. a second portion to measure surface tension. athird portion for zeta potential sample preparation and the remaining portionsw.ere used for bubble pick-up and aggregation tests.

'",

Experiments

(i) Surface tensionSurface tension measurements were made using the Wilhelmy Plate method

and a sandblasted platinum sensor. Readings were taken at equilibrium.

(ii) Zeta potentialThe zeta potentials were measured using a Lazer Zee-Meter manufactured

by Pen Kern, Inc.

(iii) AdsorptionThe residual concentration of sulfonate was detennined by a two-phase

titration technique [38] and therefrom the adsorption was obtained.

(iv) Bubble pick-up(a) Equipment: A sketch of the equipment used is shown in Fig. 2. The sur-

factant solution was held in a beaker (D). The alumina particles were con-

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127

BUBBLUI_CK UP APPARATU~

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A STANDB GLASS SPOUTC HAMILTON MICRO BURET SYRINGE

D GLASS BEAKER (50ml)E NARSHIGHE ML - B MICROMANIPULATOR

Fig. 2. Schematic diagram of bubble pick-up apparatus.

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tained in a spout (B). Air bubbles were produced by means of a micro buretsyringe (C) which was attached to a micromanipulator (E) so that the syringecould be moved in vertical and horizontal directions as desired.

(b) Procedure: An air bubble of given volume was conditioned in the sur-factant solution for 30 s, and then contacted with the equilitmated aluminafor 30 s. The microsyringe with the bubble was then moved away from thespout and the bubble was released. The procedure was repeated 100 times andthe weight of the transferred particles was obtained after centzifUging and dry-ing the contents of the beaker.

(u) Aggregation testsAbout 0.2 g of the residue was redispersed in the surfactaat by stirring for

15 min, after which the light transmission at a given position in the suspensionwas measured as a function of time using a Brinkman probe.

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RESULTS AND DISCUSSION

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The bubble pick-up behavior of the alumina-dodecylsulfonate system is il-lustrated in Fig. 3. Interestingly, tlle shape of the curve is similar to that of tlleHallimond cell flotation of quartz using dodecylamine shown in Fig. 1. A max-imum is obtained for the alumina "flotation" at. approximately 4 X 10-4kmol/m3 sulfonate.

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NaDDS/ALUM1NAT = 2SoC .To 1° CpH = 6.2 .To 0.1I = 1 X10-2 kmol/m3

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RESIOUAL SULFONATE, kmol/m3 ;'

Fig. 3. Weight of particles picked up by 100 bubbles as a function of dod~lfonateconcentration.~~

)

Results for the sulfonate adsorption density, zeta potential aJMt aggregationof alumina particles are given in Figs. 4, 5 and 6 respectively.

To determine the interactions responsible for bubble--particle Blhesion, thebubble and the attached particle are assumed to be 5 A apart. ~ area of con-tact between the bubble and particle is estimated to be 10-14 .2 ~based ongeometrical considerations for a 0.3 J.Lm spherical particle with a 20 Athick adsorbed layer interacting with a flat surface).

The free energy change resulting from tJ1e transfer of the dolie.:yl chainfrom the solid-liquid to tJ1e liquid-air interface, VH (calculated1lsing Eq. (1)and the data for adsorption density and zeta potential) is given.. Fig. 7.This attractive interaction goes through a maximum as a result- a reductionin t/J~:l-L/G with increase in surfactant concentration. This reStion re-sults from the fact that the lateral association of adsorbed surf.-ant species

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r.258C:t18CpH s 6.2:t 0.1I . 1X10-21 0.lx10-2 kmol/m3 ,.;p.

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0 10-6 10-5 10-4 10-3 , .'RESIDUAL SULFONATE, kmol/m3

Fig. 5. Zeta potential of alumina particles at pH 6.2 and ionic strength 1 X 10-2 kmol/m:NaCl.

~jc~10-2

NoDDS/ALUMINA1 . 25.C t 1.CpH . 6.2 t. O. 1I . 1 x 10-2 kmol/m3

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10-5 10-4 10-3 10-1-RESIDUAL SULFONATE, kmol/m3

Fig. 7. Interaction energy due to transfer of adsorbed surfactant moleculea fnnn the solid-liquid interface to the liquid-air interface and interaction energy due to staii: repulsion.

this interaction requires values for the potential of both surfaceL The poten-tial on the particle surface is assumed to be equal to the zeta potatial, whichin turn was calculated from electrophoretic mobility data. The iNMential onthe bubble surface can be estimated from the surface tension data for the sys-tem (see Fig. 8) by fllSt calculating the adsorption densities at the liquid-airinterface using the Gibbs equation [39],

~rL/G = -(1/2o303RT)(d'Yid log CR)

and inserting th'",se in the Gouy-chapman equa~on, t18],

rLl9 = -(1/F)(8 X 103 'NaekTC)1/2 sinh (ZFl/lbIRT]

The bubble potential, 1/Ib, calculed in this manner is given in ~ 9. Values for~ - 1/1 ~d VE-o calculated using Eqs. (4) and (5) respectively.e given in

~ig. 10. ..YE, the average value for the double layer interaction ~rgy, andVEV (= VE + Vv where Vv = 1.93 X 10-18 J) are also shown. VEV thus rep-resents the repulsive energy barrier that must be overcome befJB the particlecan attach to the bubble.

The overall interaction energy VT, i.e., Vs + VE + Vv + VH .given in

Fig. 6. Light transmission through alumina suspension as a measure of a88gation ofalumina in dodecylsulfonate solutions.

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100

HoODS/ALUMINAT z 25.C .t. 1. CpH a 6.2 .t. 0.1I = 1x10-2 kmol/m'

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30..,;'1'1111111111",,1 Iltllllll '11'11,,1'1'1"'1'0 10-5 10-5 10-4 10-3 lor2

RESIDUAL SULFONATE. kmol/m3Fig. 8. Surface tension of dodecylsulfonate solutions (supernatant from a_rption teats).

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BUBBLEPICK-UP

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- .~go 11. Correlation of bubble pick-up with total interaction energy, VT - VB + Vs + VvVEo

'~ concentration conceivably could produce a decrease in aggregation, leading toreduced attachment of mineral to bubbles. However, in the pr~t case nosuch decrease was observed at high surfactant concentrations (~ Fig. 6).Evidently the sum of interactive forces between bubble and particle is themajor factor determining the extent of mineral pick-up by the oobbles.

SUMMARY f!

Mineral pick-up by bubbles was found for the alumina-dodecylsulfonatesystem to exhibit a maximum similar to that obtained often in the past forflotation. This behavior is quantitatively accounted for in this study in termsof the interaction energies involved in the attachment of a particle to a bubble.

The overall interaction energy is the sum of contributions from 1) the attrac.tive hydrophobic forces resulting from the partial transfer of dodecylsulfonatechains adsorbed at the solid-liquid interface to the liquid-ak interface;2) the net repulsive forces (throughout most of concentration range studied)resulting from the van der Waals interaction, the overlap of the electrical

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135

double layers of the particle and the bubble and the steric repulsion betweenthe surfactant layers adsorbed on the two surfaces. For tlle present systemthese forces are calculated from data obtained using some test samples forsulfonate adsorption density. electrophoretic mobility of alumina particlesand surface tension of sulfonate solutions. Homoaggregation of particles alsowas monitored by measuring the supernatant clarity of mineral suspensions insulfonate solutions. The overall interaction energy calculated in thW mannerwas found to-correlate with tlle results obtained for bubble pick-up for tllesame test solution; concentration corresponding to tlle maximum wbble pick-up correlated well with tllat for maximum interaction energy between bubblesand particles.

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ACKNOWLEDGMENTS

The authors wiSh to acknowledge the Chemical and Process EngineeringDivision of the National Science Foundation (ENG-78-25213) for supportingthis research, and Dr. K.P. Ananthapadmanabhan for helpful discussions.

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REFERENCES

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1 P. Sornasundaran and L.T. Lee, Separation Science and Technology, 16 (1981) 1475.2 P. Somasundaran and L. T. Lee, XIV International Mineral Processing Congress,

Toronto, 1982.3 K. L. Sutherland and I. W. Wark, Principles of Flotation, Australian Institate of Mining

and Metallurgy (Inc.) Melbourne (1955) 257.4 P. Somasundaran and B.M. Moudgil, J. Colloid Interface Sci., 47 (1974) 290.5 B. V. Derjaquin and L. Landau, Acta Physicochirn. U.R.S.S., 14 (1941) 633.6 E.J. W. Verwey and J. Th.G. Overbeek, Theory of Stability of Lyopho- Colloids,

Elsevier, Amsterdam, 1948.7 B. V. Derjaquin and S.S. Dukhin, Trans. lost. Min. Metall., -70 (1961) 221.8 K.L. Sutherland, J. Phys. Chem., 52 (1948) 394.9 L.R. Flint and W.J. Howarth, Chern. Eng. Sci., 26 (1971) 1155.

10 D. Reay and G.A. Ratcliff, Can. J. Chern. Eng., 51 (1973) 178.11 P. Somasundaran and D.W. Fuerstenau, J. Phys. Chern., 68 (1964) 3562-12 T. Wakamatsu and D.W. Fuerstenau, Adv. Chern. Ser., 79 (1968) 161.13 M.J. Rosen, Surfactants and Interfacial Phenomena, Wiley-lnterscience, New York,

1978.14 A. meier, E.D. Goddard and R.D. Kulkarni, Flotation, M.C. Fuerste~ (Ed.), Vol. I

(1976) 117.15 Th.F. Tadros, Adv. Colloid Interface Sci., 14 (1980) 144.16 J. Lyklerna. Adv. Colloid Interface Sci., 2 (1968) 65.17 I.J. Un and P. Somasundaran, J. Colloid Interface Sci., 37 (1971)18 G.A. Parks in Riley and Skirrow (Eds.), Chemical Oceanography, Acadelilic Press,

New York, 1975.19 J.F. Scarnerhorn, R.S. Schecter and W.H. Wade, J. Colloid Interface ti, 85 (1982)

494.20 B. V. Derjaquin, Disc. Faraday Soc., 18 (1954) 85.21 R. Hogg, T.W. Healy and D.W. Fuerstenau, Trans. Faraday Soc., 62 (1934) 155.22 G.R. Weise and T.W. Healy, Trans. Faraday Soc., 66 (1970) 490.

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