Collection of submicron particles in electro-flotation

Chemcul Engmerzng Pergamon Press Ltd

Sczence Vol 35 pp 1097-l 105 Prmted I” Great Brltam 1980

COLLECTION OF SUBMICRON IN ELECTRO-FLOTATION Y

FUKUI

PARTICLES

and S YUU

Research Establishment of Powder Technology, Kyushu Institute of Technology, Tobata, Kltakyushu 804, Japan (Receded for pubimztron

11 September

1979)

Abstract-A theoretical analysis IS presented to describe the deposltlon of Browman particles onto hydrogen bubbles under surface mteractlons Smgle collectlon efficiency has been numencally calculated for zeta potent&s, havmgassumed that theeffe&veHamaker constant ISequal to 3 0 x lo-l1 erg though our choice of Hamaker constant IS rather arbitrary From a mass balance, total collection efficiency or the rate of flotation has been determined In this way, electro-flotation process 1s quantltatlvely described Expenmentally, the eiectro-flotation of polystyrene latlces of mean diameter 0 6pm has been studred to examme the effect of the charge on both particles and bubbles on the total collection efficiency The bubbles were of mean diameter 20 pm The electrolyte was AlCI, To measure the charge on the bubbles, we directly sampled solution mcludmg very small bubbles with a glass tube from a flotatron vessel and poured mto a micro-electrophoresls cell The honzontal veloctty measured when the bubbles rose up a “stationary level” m the cell under the known potential gradrent gave the electromoblhty The charge on the latex particles were found to change Its sign from negative to posltlve as flotation time went on The theoretlcal total collection efficiency has been m Llose agreement with the expenmentally determmed one INTRODUCTION

In recent years, the practical apphcatlon of dispersed air flotation, as a process m which fine particles are removed from suspension m water by attachment onto rlslng bubbles, has become of interest from the environmental vlewpomt [l-3] Because many hquld effluents contam particles which are too small to be removed economically m sedlmentatlon tanks or by conventional filters Cleanmg of waste water 1s a concern for the protection of the environment, health and quality of life The removal of suspended particles from effluents by dispersed air flotation 1s obviously similar m many ways to the froth flotation process used m mineral dressing But, m contrast to mineral flotation which has a long history [4], the particles to be removed m effluent treatment are normally less than 20pm and close to neutral buoyancy, and the concentration 1s also very dilute as low as 20 p p m Emplrrcally, it has been found advantageous to use very small bubbles often less than 100 pm in diameter for the removal of fine particles One of the methods to accomplish this aim 1s electro-flotation, m which bubbles are generated by electrolysis One of the first apphcatlons of electro-flotation to pollution problems mvolved the treatment of domestrc sewage m 1911 m the Umted States This method, however, has not become general m the treatment of mdustrlal waste water mamly because the electrodes tended to scum [1 ] Recent development by Mltsul Metal Engineering Co has solved this problem by usmg an alloy of alummlum as electhodes [2,3] Among a large number of physical variables m the correct descrlptlon of the collection of particles by bubbles, the particle size and charge, the bubble size

and charge and the effective Hamaker constant which 1s a measure of “hydrophoblclty” of the surfaces of particle and bubble are probably most nnportant variables One of the first pubhcatlons on the effect of particle size on the rate of flotation was by Gaudm ef al [S] who found that the rate offlotatlon was independent of particle size for particles up to 4 pm m dia , but that It was proportional to the diameter m the range 4-20pm Flint and Howarth [6] calculated the collision efficlencles from grazmg trajectories for particles m the path of a spherical bubble rising m an mfimte pool ofhquld Reay and Ratchff [7,8] analyzed the collection of small particles by bubbles Their results showed that the collectlon efficiency had a mlmmum at a particle size around 1 pm m dla because below this diameter the efficiency increases by Browman dlffuslon and above this diameter so does by the hydrodynamic mteractlons Recently, Collms and Jameson [9, lo] have reported that the rate of flotation of polystyrene particles varied approxnnately as the 1 5 power of particle diameter, after the slmdar dependence for the glass sphere was found by Reay and Ratchff [8] They also measured the charge on both bubbles and particles, and a new techmque has been described for the measurement of the electromoblhty of small gas bubbles They modified a standard flat electrophoresls cell m order to generate bubbles by electrolysis m It The horizontal velocltles at a so called “stationary level” m the cell under the known potential gradient gave the electromoblhty The results have indicated that the charges are of the same sign and magmtude as those of polystyrene partlcles with the same electrolyte (Na,So,) and surfactant (CTAB) concentrations

1097

1098

Y FUKUI

They have concluded that the rate of flotation strongly depends on the charge on both the bubbles and the particles and they presented the experimental equation - ln(k,/di

5, = 3 9 + 0 116 U,U,

Smce the flmd 1s incompressible and reaction does not occur, the dlffuslon equation m spherlcal coordmates becomes

g

(1)

where k, IS the rate constant (mm- ’), d, IS the particle diameter (urn) and U,, CJ, are the electromoblhtles (pm/s/V/&) of the pa%& and bubble respectively Other expernnental work on the effect of particle charge includes that of Derjargum and Shukakldse [ 111; Devlvo and Kager [12], and Jaycock and Ottewill [13] However, most of published researches m effluent treatment by bubbles have not dealt with submicron particles Moreover, it should be recognized that the results gwen m the common laboratory practice of generating small bubbles at a porous fret with the addition of up to 0 5~01 “/, of an alcohol to the solution cannot be extrapolated to commercial units where such alcohol addition 1s lmpractlcal and the small bubbles have to be generated electrolytically [S] Our previous work [14] has studied the electroflotation of submicron particles and has presented the smgle collection efficiency The results seemed reasonable even though the interaction potential between particles and bubbles was assumed to be neghglble The charge of the particles has been proved to be zero by the measurement later In this paper, we extend our previous work to include the effect of the charge on both the particles and the bubbles By calculating the single collection efficiency under the interaction potential, the electro-flotation process IS quantltatlvely evaluated to some extent THEORY

A rlgld sphere of radms a IS fixed m a uniform creeping flow with the velocity equal to the mean velocity of rlsmg bubbles V. as our model The Stokes expression for the creeping motion of a viscous flmd around a rigid sphere can be used as follows

(2) Q=

and S Yuu

-

+

vvc = v

[DVC + DCVdq

(3)

where mkT

DE---

a& c is the particle concentration at time t, D 1sthe Brownian dlffuslon coefficient of particle, k IS the Boltzman constant, m 1s the mob&y of particle, and T IS the absolute temperature ct, denotes the sum of potential energies such as the unretarded London-Van der Waals attraction energy @‘a between a sphere and a plate, and the double layer repulsion energy aR cp=cp,+m,,

(4)

where

(5) and QR = ca,ti1$,2 ln(1 + e-Kh)t161

(6)

E 1s the dlelectrlc constant, I,+, 1s the electrostatic potential of surface I and K is the reciprocal doubIe layet thickness Equation (6) IS derived under the assumption as follows [ 173 (1) The sphere and the plate are composed of similar material (2) This holds only m the region 1$11x 11//21 < 50mV and KaP > 5 (3) $, 1s mdependent of rch It IS well known [ 181 that the dlffuswlty depends on the posrtlon slgmficantly when the particle 1svery near to a solid wall, such as the surface of the collector The dlffuslvlty or mobility decreases as a result of frlctlon between the fluid and the particle The correction factor by Waklya [19] IS used as follows

where 1

(7)

m=m a IS the radms of sphere, r 1s the radial coordmate measured from the center of the sphere, 0 1sthe angle of devlatlon from the forward mcldence of flow v, 1s the mean velocity of rising bubbles and V, and V, are the components of V, m r and f3 direction, respectively

where

F=lO+%+$

-2ii;

+ Tii;

+

1099

CollectIon of submlcron Dartlclesm electro-flotation

Though F IS, III fact, mfimte series, the three terms of them are used at present stage This IS dlscussed later Consldermg a steady state and axlsymmetry, and

a2c -

assuming

that

~ rZ do2

compared

with za?’ ar

IS negligible

for

bubbles generated m dt 1sderived by dlvldmg dv by the volume of a bubble

collection

eqn (3) IS snnphfied as follows

dn

=$

= 3RgT1 dt &a3 F,P

Total collection efficiency IS, then, determined a mass balance for dt as

- l&4, dc = (tpca2CVo) dn

(12) from

(13)

The term m parentheses mchcates the number of particles removed by a bubble m time dt Substitution of eqn (12) into eqn (13) yields the rate (8) A numerical calculation may be carried out under the associated boundary condltlons as follows (The numerical procedure IS precisely described m the previous paper [15] ) C=lO

at

F=co

1?=00

at

r=lO+$

(9)

equation (14) where the term m parentheses denotes the rate constant Accordmgly, integration yields the total collection efficiency 3R,TI -rlFFpg

E = lo-exp

b The latter expresses the assumption that contact between particle and bubble IS estabhshed when the thickness of the liquid film between them goes to zero, and provldmg the bubble does not deform and there 1s no posslblhty of detachment of the particles, the boundary condltlon IS a reasonable one This calculation yields a concentration dlstrlbutlon around a bubble The collection efficiency q of a smgle bubble 1s defined as the fraction of particles m the bubble path which are actually plcked up by the bubble Consequently.

(10)

EXPERIMENTAL

(15)

PROCEDURE

The flotation experiments were carried out batchwise In a electrolysis vessel as schematically shown m Fig 1 Hydrogen bubbles of mean diameter 20,um

8z

P where

R=lO+%

The volume time dt IS

of generated

&j

=

RT 1 P

a

hydrogen

I Rdt

!7 L

bubbles

do m

(11)

where R, 1s gas constant, F, IS Faraday’s constant, P 1s the atmosphenc pressure Hence, the number of

e’

Fag 1 The arrangement of the apparatus Hydrogen bubbles are generated and rise up to collect particles Oxygen bubbles are captured m another part LIof the vessel Electric current LS controlled with a reostat b, and IS measured -with an

anemometerc d ISa samplinghole e and e’are carbon-black electrodes

1100

Y

FUKUI and S Yuu

were generated from carbon black anode The particles were of polystyrene latlces of mean dmmeter 0 6 m on a number basis The concentration of polystyrene particles m dlsttlled water were 5 cc/l The electrolyte was AlCl, whose concentration was 5 x lop4 M Before a run, the solution was mrxed well wth an ordmary kitchen electric Juicer to let the particles disperse well Samples taken with a syringe from a sampling hole before and durmg a run were analyzed for particle concentration with a spectrophotometer (JASCOUV-50) The change of total collectlon efficiency with time can be known The diameter and the rising velocity of bubbles were determmed m the same way as previously reported [ 141 The particles were dried on the glass and were photographed through a microscope m order to measure the particle diameter (a) Average bubble concentration vessel of smaller electrolysis The 20 x 20 x 1000 mm3 was used to Increase the he&t of the solution caused by the generation of the bubbles for the measurement of average bubble concentration When a steady state was reached, a photograph of the surface of aqueous solution together with a standard measure was taken Secondly, after the electric current was put off and all bubbles rose up and disappeared from the solution, another photograph was taken m the same way The difference between the two heights of the solution gave the average bubble concentration E, = (b)

the mcrease of solution the solution

height by bubbles

height wlthout

bubbles

Electromobhty of partzcle and bubble The eqmpment used was a Mltamura mlcroelectrophoresls cell of cross sectlon 1 x 23 mm A sample of the suspension was placed m a Pyrex glass cell to the contents of which a longltudmal potential gradient can be reposed via calomel electrodes A microscope system IS focussed on the so called “stationary level” m the cell (0 2036mm from the inner wall m our case [201), and usmg dark-ground lllumlnatton charged particles or bubbles can be observed moving toward one or other of the electrodes, depending on the sign of the charge The eyepiece of the microscope has a cahbrated gratlcule, and by noting the time t reqmred for them to traverse a set distance 1 (say SOpm), then velocltles can be measured Polarity can be changed by a normal-reverse switch, and the error caused by the devlatlon of the cell from the level IS cancelled out by averaging the values obtained m each polarity A filter IS mcorporated m the lllummatlon system to mmlmlze heating of the cell The aqueous solution of electrolyte was electrolyzed for a while, and then the electric current was put off After larger bubbles had risen up and dlsappeared from the sampled solution mcludmg very small solution, bubbles with a glass tube were poured mto the electrophoresls cell

The zeta potentials of the bubbles and the particles were calculated as follows

where c IS the zeta potential (mv), E IS the dlelectrlc constant (- ), 1 1s the set distance (cm), S IS the cross sectional area of the cell (cm2), I 1sthe current (mA), t IS the time (set) and R, IS the specific resistance (ncm) which was measured with a conduct meter (Model CM-lF, TDA Co ) At the temperature 25”C, for example, < = 12 82 U, The coagulation of particles was observed when the of electrolyte AlCl, was above concentration 1 0 x 10e3 M The generation of bubbles was too little to conduct an experiment when the concentration was below 10 x 10e4 M RESULTS AND DISCUSSION

The zeta potential of the particle and the bubble IS given m Fig 2 along with the data of Collms and Jameson [lo] Since it IS very difficult to measure the charge on small bubbles, It was, m fact, a great trouble to Introduce the captured bubbles mto the sultable posltlon of the electrophoresls cell for a microscope system After all, our method to measure the charge on small gas bubbles was rather prlmltlve, compared with the method by Collins and Jameson They modified a standard electrophoresls cell by sealing two platmum wires mto the upper and lower walls Oxygen bubbles of about 35 pm m diameter were generated by electrolysis The mobrllty of the oxygen bubbles was determined m the usual way, though the gas used m their flotation expertment was nitrogen Nevertheless, It seems to be one of the most suitable methods at present

50 1

*

( rnOl/l Fig 2

1

The effect of the conamtratlon of electrolyte on the zeta potential of bubbles and particles

Collection of submlcron particles m electro-flotation

Their results demonstrated that the bubble moblhty 1s of the same order as that of the particles under the same condltlons and that It follows the same general trend with sodmm sulfate addltlon Their method 1s precisely reported m the reference [21] Our results indicate that the bubbles were posltlvely charged as were their results (see Fig 2), but that the particle were negatively charged and changed its sign from negative to positive as flotation time went on as shown m Fig 3 However, pH in the solution kept about 4 5 with the devlatlon of 3 8% at maximum so that the change mrght be due to the change m the surface properties The smular phenomenon 1s reported by Wneck et al [22] To calculate the total collection efficiency, the single collection efficiency for each zeta potential of particles, corresponding to the respective period wrth the change of the zeta potential of the particle, was used The zeta potential of the bubbles was supposed unchangeable with time at this stage When particles 1 and 2 are m the medium 3, the effective Hamaker constant 1s expressed as follows

A(=A

12,~)=(A,,+

A,,) - (A,, + Az3)

(17)

If 2 IS a bubble the term Including the subscript 2 1s negligible and eqn (17) 1s slmphfied as

A=A,,-AA,,

(18)

denote the Hamaker constant of waterwater and water-particle m the vacuum, respectively estimated as [23 1 The value A,, 1s roughly 6 0 x IO- I3 erg DerJarguin and Shukakldse assumed that the value A,, is equal to 30 x lo-“erg, correspondmg to the ‘mean’ value of the ratio A,,IA,, = 0 5 [l 1 ] The value of A was assumed to be 3 0 x 10-14erg m our calculation though our choice of the value 1s rather arbitrary because It IS extraordmarlly difficult to calculate Hamaker con-

A33andA13

1101

stants for water Furthermore, even though the change of the surface properties unphes the change of Hamaker constant, we have a very great dficulty to explain it Therefore, the value of A was supposed to keep 3 x lo- 14erg at present stage Incidentally, the effective Hamaker constant m case of coagulation of latex particles was determmed to be about 8 x lo- l4 erg by Hlgashitani et al [24]which 1sm fair agreement with the result by Lyklema [25] Hence It 1s physically plausible that the effective Hamaker constant m hetero-coagulation between bubble and latex particle 1s less than the value However, It IS not easy to estimate Hamaker constant because the nature of the surface of particles or bubbles are altered by a various chemicals m an actual flotation process The surface potential energy for various values of cl x cZ IS plotted against F m Fig 4 Potential barrier by double layer repulsion energy forms as the product of cl and cZ increases Correspondmg to the presence of potential barrier, the stagnation point of concentration where there IS a considerable concentration mcrease m the direction of flux emerges as m Fig 5 The position of the extreme value of concentration which emerges when the produce ot c, and i, 1s above 800 corresponds to the posltlon of the extreme mmlmum ofmteractlon potential The fact that theconcentratlon becomes lower with the increase of attractlon potentgal 1s reasonable because we assume the perfect sink of particles at the surface of bubble The total flux, of course increases with the decrease of repulsion potential due to the increase of V Q even though V C decreases with the increase of repulsion potential The ratio of flux due to dlffuslon term and due to potential term IS about $ when the product of i, and i, 1s zero Numerical calculation of the single collection efficiency was carried out under double preclslon and the length of mesh m r direction was 24 25 A The efficiency was calculated at the separation 24 2.5?. between the bubble surface and the particle surface

TI me (mln) Fig 3 The change of zeta potential of particles with flotation time

1102

Y

Fig 4 The effect of the product

FUKUI

of the zeta potential

andS

Yuu

of bubbles and particles

on the Inter surface potential

0 08 IV 0 06

10300

10302

10304

10306

10308

r Fig 5

Theeffectoftheproductofthezeta

potentlaiofbubblesandpartlcleson on the axls reCO

The smgle collectlon efficiency decreases with the mcreasmg product of ct and c2 as was expected (Fig 6) This shape IS sumlar to the data of Collins and Jameson m Fig 7, which may support out model The theoretical and experimental bubble concentratlon are m good agreement From a mass balance, the total collection efficlencles for different bubble concentration were obtained as m Fig 8, which are m close agreement with the experimental results The dlffuslon coefficient becomes vamsfingly small when the particle touches the surface (h = 0) by the hydrodynamic mterdctlon Homg ef al [26] found that the hydrodynamic interaction dlmmlshes the absolute rate of rapId coagulation by a factor of about 0 4-O 6, depending on the Hamaker constant An addltlonal reduction m the dlffuslon coefficient can be caused by the deviation of the vlscoslty from Its bulk value Nevertheless, we consider only first three terms of the Infinite series by Waklya Consequently, D IS regarded as nearly constant However, Lonsldermg the

theconcentratlondlstrrbutlon

fair agreement of theoretlcal and experunental results, the surface of the bubble and the particle might not be perfectly smooth, and London attractive force might predominate before the moblhty of the particle decreases slgmficantly Moreover, the solution by Brenner, Waklya, and others who introduced the correction factor of hydrodynamic interaction IS based on the Navler-Stokes equation by neglectmp the term This means that the medium IS lnertlal considered separation

as contmuum, but as short as the order ofA,

whether

in

the

the concept of the contmuum holds IS remained for future work The first assumption m eqn (6) IS not appropriate to apply the analysis of flotation process because particle and bubble are not composed of similar matenal However, the sultabke potential equation for the flotation process has not yet been derived CONCLUSION

The process of electro-flotation IS quantltatlvely evaluated by calculatmg single and total collection

Collection

of submrcron

A = 30 0 0025

-

0 0020

-

0 0015

-

1103

particles m electro-flotation

X

Id”

(1.39)

L 0 OOlO-

0 0005-

0

Fig 6

-800

-400

0

The effect of the product of the zeta potential

400

Theoret

0 L . 100

s iz

lcal

ExperImental

1200

of bubbles and particles on smgle collection

Fig 7 DataofColhnsand Jameson [lO]onflotatlonofmeandlameter6 Na2S03 and the surfactant IS CTAB The rate constant LSproportional 6

-

800

efficiency

6~mlatexpartlcles Theelectrolyters to the single coilectlon efficiency m Fig

curve result

I

I

I

10

20

30 Trme(

Al&=5

I

0x10-hoi/L

I=0 1OOA 1=0125A I =0 175A

I

I

I

50

60

70

50

W

0 Fig

8 Change

of total collectlon

efficiencies

40 mln)

for different bubble concentrations mass balance

with time evaluated

from

Y

1104

FIJKUI and S Yuu

efficiency for various values of the product of c, and cZ on a simple model which takes account of Interaction potential energy The results clearly demonstrate that the collection efficiency, or the rate of flotation strongly depends on the charge on both the particle and the bubble as concluded by Collms and Jameson, and that It decreases suddenly as the product of ii and cZ IS above a certam value, depending on the effectwe Hamaker constant Experimentally, such a phenomenon appears as that the rate offlotatlon IS very rapid for the while and gradually decreases, correspondmg to the tune when the zeta potential of the particle changes its sign from negative to posltlve and increases Its posltlve magnitude, until It becomes nearly zero In the dlstrlbutlon of concentration on r axis, a stagnation point of concentration, where there 1s a considerable concentration Increase m the dIrection of flux due to the presence of potential barrier, emerges as the product of cl and L2 increases The results unply that the maxnnum rate of flotation IS achieved when zeta potentials of bubbles and particles are opposite m sign If the fact 1s found to exist generally, because it 1s very difficult to measure the charge on the bubbles, so the change of the charge on the bubbles with tnne was not examined m this work Future work should be pomted at the precise measurement of the zeta potentials of bubbles with general appllcablhty Acknowledgements-The authors would like to express their gratitude to Mr Y Ito, Mr M Tanakaand Mr Y Fujimura who performed some of the calculation and the experimental work

NOTATION

A

4

a

2 C

e D

b

Db

DP E

F F, h 1, 1 k k, N” P R Rx

(effectwe) Hamaker constant cross sectional area of vessel radius of bubble radius of particle concx2ntration of particles far from collector local concentration of particles C/C, (dunensronless) dlffuslon coefficient D/a& (dunenslonless) diameter of bubble diameter of particle total collection efficiency correction factor Faraday constant mnmnum separation between collector and particle surface electric current Boltzman constant flotation rate constant moblhty radial flux of particles atmospheric pressure 1 0 + ada (dlmenslonless) gas constant

specific resistance component m spherical coordmate r/a (dlmenslonless) cross sectional area of electrophoresls cell time absolute temperature electrophoretlc moblhty of bubble, pm/s/V/cm electrophoretlc moblhty of particle, ,um/s/V/cm superficial flmd velocity component of local velocity field V, m r directIon component of local velocity field V, m 19directIon denotes a dnnenslonless value Greek

symbols

dlelectrlc constant bubble concentration zeta potential of bubble zeta potential of particle smgle collection efficiency component m spherlcal coordinate reciprocal Debye length fluld vlscoslty fluid density particle density component m spherical coordmate total mteractlon potentlal London-Van der Waals potential double-layer potential electrostatic potential of surface i

REFERENCES

[l] Slegerman H , Chem Tech 1971 (Nov ) 672 & Petroleum Ckem (In Japanese) [2] Ishu M, Petroleum 1972 16 87 [3] Ishu M , PPM (in Japanese) 1976 (Jan ) 52 [4] Sutherland K L and Wark J W , Prznczples ofFlotatzon Austrahan Institute of Mnung and Metallurgy, Melbourne 1955 [S] Gaudm A M , Schuhmann R and Schlechten A W , J Pkys Ckem 1942 46 901 [6] Flint L R and Howarth W J Chem Engng SC] 197126 1155 [7] Reay D and Rat&IT G A, Can J Ckem Engng 1973 51 178 [8] Reay D and Ratchff G A, Can J Ckem Engng 1975 53 481 c91 Collins G L and Jameson G J, Ckem Engng Scz 1976 31 985 [lOI Collins G L and Jameson G J , Ckem Engng SCI 1977 32 239 El11DerJargum B V and Shukakldse N D, Trans 1 M M 1961 70 569 DeVlvo D G and Karger B L, Sep Scz 1970 5 145 ;::3 Jaycock M J and Ottewlll R H , 7hzns I M M 1963 72 497 El41 Yuu S , Fukm Y and Jotakl T , C’kem Engng Scz 1977 32 239 Cl51 Verwey E J W and Overbeek J Th G, Theory of the Stabzlzty of Lyopkobzc Collozds Elsevrer, New York 1948 [I61 Splelman L A and Cukor P M , .I Collozd Scz 1973 43 51 Cl71 Ruckenstem E and Prleve D C , J Chem Sot Faraday 7fczns 1973 69 1522

Collectlon

of submxxon

[ 181 3renner H , Chem Engng SCI 1961 16 242 [19] Waklya S , Coil Engng Res Rep 1957 6 155 of the Electrotechnrcal [20] Komagata S , Researches 1933 348 Laboratory [2l] Collms G L, Motaqeml M and Jameson G J , J Colload Interjace Scz 1978 63 69 [22] Wneck W J , Gldaspow D and Wasan D T, Chem Engng Scz 1975 30 1035

particles m electro-flotation

1105

Eiectrrcal Surface [23] Kitahara F and Watanabe A, Phenomena (m Japanese) Kyorltsu Shuppan, Tokyo 1973 [24] Hlgashltam K , Tanaka T and Matsuno Y , J Collold Interface Scz 1978 63 551 Collard Inter&ace Scr 1968 2 65 [25] Lyklema J , Advan [26] Honing E P , Roebersen G J and Wlersema P H, J Collotd Interface Scr 1971 36 97