Indian Jounaal of CbemlstryVol. 16A, Nonmber 1978, pp. 9~-914

Salt Sieving by Kaolinite & Bentonite Clay MembranesR. C. SRIVASTAVA & SARO] YADAV

Chemistry Department, Birla Institute of Technology & Science, Pilani 333031

Received 6 February 1978; revised and accepted 7 June 1978

The data on simultaneous transport of salt and water through kaolinite and bentonite claymembranes have been analysed in the lil1ht of nonequUibrium thermodynamics of hyperftltra-tion, to throw lil1ht on the salt slevtng behaviour of these clays. Frictional coefficients betweensalt and water, water and membrane and salt and membrane have been evaluated. The valuesof the frictional coefficients thus obtained reveal that both kaolinite and bentonite clay mem-branes only partially satisfy the criteria for efficient hyperftltration membranes, developed bySpiegler and Kedem on the basis of Spie~ler's frictional model.

REVERSE osmosis has by now been acceptedto be one of the most important methods forwater-desalination. Consequently quite a bit

of effort has been invested in search for suitablemembranes for reverse osmosis operation. Sinceclays are known! to possess salt rejecting propertieswhen aqueous solutions of salts are forced throughthem, it is worthwhile to assess the performanceand efficiency of clay membranes in an hyper-filtration operation. With this objective in viewthe data on simultaneous transport of salt and waterthrough kaolinite and bentonite clay membraneshave been ana lysed in the light of the formalismdeveloped by Johnson et al.2 and the criteria deve-loped by Spiegler and Kedem'' for efficient hyper-filtration membranes. The treatment of Johnsonet al.2 and Spiegler and Kedem" assumes reflectioncoefficient and salt permeability to be independentof salt concentrations. In order to conform to theseassumptions the experiments on the simultaneoustransport of salt and water described in this paperwere confined to low salt concentrations and concen-tration differences.

Although data on osmosis of electrolytic solutionsthrough both kaolinite and bentonite clays areavailable in literatures-s fresh experiments have beenperformed on the osmosis of sodium chloride solutionthrough kaolinite clay membrane to estimate thevalues of the parameters relevant to salt rejectionbeha viour. This became necessary because the dataof Abdel Aziz and Taylor+ on osmosis of electrolyticsolutions through kaolinite clay is not in a formconvenient for the analysis presented in this paper.In the case of bentonite clav, however, the dataobtained by Letey and Kemper+ for the osmosis ofsodium sulphate solution have been utilized.

Phenomenological RelationsThe linear phenomenological equations between

fluxes and forces for a system consisting of twocompartments containing the same binary aqueoussolutions of unequal concentrations and separated

920

by a membrane or a porous plug of thickness .!lx,can be written as6

Iv = LpVP+LpD V1t (1)I» = LpD VP+Lv V1t (2)with Lpn = LpD (3)on account of Onsager's theorem. In Eqs. (1) to (3)Iv represents the volume flux, ID represents thevelocity of the solute relative to that of the solvent,P and 1t stand for the pressure and osmotic pressurerespectively and Lp, LDP, Lpv and Lv arephenomenological coefficients. Following the proce-dure adopted by Kedem and Katchalskys-? thelinear phenomenological equations can be furthertransformed intoIv = Lp (VP-aV1t) ... (4)andIs = <UV1t+<;',(l-a)Iv ... (5)where Is stands for the solute flux. The quantitiesa and (,) in Eqs. (4) and (5) are called reflectioncoefficient and solute permeability respectively andare defined as

LpDa = - 't; ...(6)

and

I.' = (Is) = Cs(LpLD-L~D)~ I ···(7)V1t v=o Lp

where Cs is the average of the solute concentrationsin the two compartments. The value of the reflec-tion coefficient a lies between zero and unity.When a = 1 the membrane is said to be an idealsemipermeable membrane.

Eqs. (4) and (5) which were first deduced byKedem and Katchalskys-? because of their ope-rational form are more appropriate than the Eqs.(1) and (2) for the evaluation of L», a and (,)- thethree parameters which adequately describe the saltrejection properties of a membrane system. It

SRIVASTAVA & YADAV: SALT SIEVING BY COMPACTED CLAYS

TO K2 K, LZPRESSURE~ ==============~

~(1T,

b'"824 C824-"-,",--oJ...,

A ~ 1T3

o 824-

S A BT MZ

4-

should be borne in mind that in the deduction ofEqs, (4) and (5) validity of the linear phenomeno-logical relations and Onsager's reciprocal relationhas been supposed.

Materials and MethodsKaolinite clay (Mjs Impex Chemical Corp., Bom-

bay), sodium chloride (BDH, AR) and conductivitywater were used.

The osmosis cell used for the measurement offluxes is depicted in Fig. 1 and has been welllabelled to make it self explanatory. The kaoliniteclay plug was compacted on the sintered glass discS (porosity G-4) using the following procedure.A known amount (about 10 g) of the sodiumsaturated clay was put in a pyrex flask containingabout 250 ml of conductivity water and was allowedto stand for several days and shaken occasionally.The clay suspension was then transferred withstirring to the glass tube AB containing the G-4sintered glass disc S which was joined to a filteringflask connected to known vacuum (5 mm Hg).The arrangement is shown in Fig. 1a. The clayplug thus compacted on the sintered glass discsupport was stabilized further by making use ofrubber gasket on one side.

The volume flux was measured by noting therate of advancement of the liquid meniscus in thecapillary LIL2 (Fig. 1) using a cathetorneter readingup to 0·001 em and a stop-watch reading up to0·1 sec. For measurement of the salt flux, solutionon the two sides of the clay plug was analysed forsodium using a flame photometer (Elico, Hyderabad,model CL-22) reading up to 2 ppm.

All measurements were made at constant tem-perature by placing the osmosis cell in a thermostatset at 40° + 0·1°C.

Evaluati'On of L», a and co - Linear curves areexpected if ] v is plotted against VP in accordance

Fig. 1 - Osmosis cell [T1, Tz, T3 and T(are stopcocks; MI and M2' magnetic stirrers;K, kaolinite plug (thickness 1 cm and area10·9 cmZ); S, sintered glass disc of porosityG-4: LILI' capillary tube of (length 19 cmand diameter 0'0138 cm). Volumes of thecompartments C and D 288 and 372 ml res-pectively]. Fig. 1(a) gives the arrangementfor compaction of the clay on the sintered

glass support

with Eq. (4). From the slope and the interceptof the linear plots thus obtained, Lp and a can becalculated provided V1t is known and is more or lessconstant during the experiment. In the actualexperiments for the determination of Lp and (1

using Eq. (4), a solution of sodium chloride ofknown strength (O·00022N) was filled in the com-partment on the left hand side of the clay plugand distilled water filled in the compartment D(Fig. 1) on the right hand side of the clay plug.The system was allowed to stand for some time.As soon as recession in the capillary LIL2 due toosmosis was noticed, known pressure was appliedon the solution compartment by adjusting thepressure head and the rate of advancement of theliquid meniscus in the capillary was noted withtime. Since the back-flow of water in the solutioncompartment due to osmosis is quite small thevalue of V1t can be taken to be more or lessconstant during a particular run of the experiment.In order to maintain the condition V1t = constantin all such runs the electrolyte solution in theosmosis cell was replaced by the fresh stock solutionbefore the volume flux measurement correspondingto the next value of D,.p was made. The dataobtained in this manner have been plotted in Fig. 2for two different values of V1t.

Eq. (5) under the condition Jv equal to zerowas the basis for the determination of co. In theactual experiments for the determination of (,)a solution of sodium chloride of known concentration(O'00022N) was filled in the compartment C (Fig. 1)on the left hand side of the clay plug and distilledwater filled in the other compartment D on theright hand side of the clay plug. The conditionJv equal to zero was enforced on the system byadjusting the pressure head attached to the solutioncompartment. The solution in the two compart-ments was vigorously stirred with the help of

921

INDIAN J. CHEM., VOL. 16A,NOVEMBER 1978

magnetic stirrers Ml and M2 shown in Fig. 1. Aftera known period of time (t) which was several hoursthe solution from the two compartments werewithdrawn and analysed for sodium. The amountof sodium chloride lost by the solution compartmentor the amount of sodium chloride gained by thewater compartment divided by the time, gave thevalue of salt flux. Average of the values of V7tat the beginning and at the end of the experimentswere considered for the estimation of eo.

It may be mentioned here that SmitS and Smitet al» have stressed that it is appropriate todetermine a, Lp and eo in this way, i.e, using

4·0 CURVE I-VTI=11'7gemem-1CURVEII -VTI 15·15 em em-I

3·5

3-0

2·5

2·0

1·5IU 1·0"1/1

Eu 0·5In0)(

> 0-. 15 20 25 30 35-0'5 V P em em-I

-1'5-2·O,I------ ~

Fig. 2 - Determination of Lp and a using Eq. (4)

Eqs. (4) and (5) rather than a and LI! in an ult~afiltration experiment and (j) separately m an osmoticexperiment.

Results and DiscussionThe values of Lp, a and co for the kaolinite

clay membrane, for two different concentrations ofsodium chloride are given in Table 1. The valueof Lp, a and w for bentonite clay membrane ascalculated using Eqs. (6) and (7), from the. valuesof the phenomenological coefficients determined byLetey and Kemper", are also given .in Tabl~ 1.The data for bentonite clay membrane IS for sodiumsulphate solution.

With the data of Lp, a and eo at hand (Table 1)the salt rejection performance of both kaoli~ite andbentonite clay membranes, in a hyperfiltration pro-cess can be assessed using the formalism developedby Johnson et ai». Defining salt rejection para-meter, r as

C"r = 1 - ~ ... ( )- Cswhere cg is the salt concentration in the hyper-filtrate and Cs is the concentration of the feedsolution, Johnson et al.2 have obtai~ed Eq. (9)describing the salt rejection, r, at different flowrates

a-1'F = a(I-1')The flow parameter F inF = eJvA

and A in the relation (10) for the present case canbe written asA = (l-a)Ax

nRTwwhere n is the number of ions given by onemolecule electrolyte on complete dissoc~ation, e.g. forsodium chloride n = 2 and for sodium su.lphaten = 3, R is the usual gas constant, T IS. theabsolute temperature. Eq. (9) can now be rewnttenas

Jv _ 2·303 W 100" a(I-1') ... (12}nRT - Ax(l-a) 0 (a-1')At high flow rate F-+O and hence the reflection

... (9}

Eq. (9) is defined as... (10)

... (ll}

TABLE 1- VALUES OF Lp , a, co A~D VARIOUS FRICTIONAL COEFFICIENTS FOR KAOLINITE/SODIUM CHLORIDE SOLUTIONAND BENTONITE/SODIUM SULPHATE SOLUTION SYSTEMS

(The values for the bentonite/sodium sulphate solution system have been calculated from the data of Letey and Kemper-)

System a co X 1016 t» X 10-7 iSM X 10-1 Isw X 10-11 iWM X 10mole cm-2 see? em see'? cm2 mole'? see em> mole+ see em" mole? see

Kaolinite/sodiumchloride soln 0'53* 5825·00t 20·00 0·1682

Kaolinite/sodiumchloride soln 0'59t 5774·00" 20·00 0·0545

Bentonite/sodium 996.00sulphate soln 0·824 4·291 0·00233

*'i77t= 11'79 em cm<: taverage 'i77t= 11'50 em crrr+; t'i77t= 15·15 em em-I;

1·2696

1·3961

1394·00

0·9035

0·9035

7754·93

922

.*average 'i77t= 11·60 em cm'".

SRIVASTAVA & YADAV: SALT SIEVING BY COMPACTED CLAYS

I.O~---------------------------------------------------'0.8

0.6

0.4

0.2

(j=0.824

(j=0.560

016.0 18.0 20.00 2.0 4.0

lY.. X 10'5 MOLE see' cm3 ( FOR CURVE I)3RT ~KXI012 MOLE Ste' cm3 (FOR CURVE II)2RT

Fig. 3 - Variation of salt rejection parameter r with volume flux as predicted by Eq. (12) [The curve II is for kaolinitemembrane/sodium chloride solution system. For this average of the values of a and «) given in Table 1 have been

considered. The curve I is for bentonite membrane/sodium sulphate solution system]

coefficient is the limiting value of r when filtrationflow overtakes diffusion.Jv-+oo; r-+a ... (13)By means of equation t12) it is possible to predictthe expected salt rejection curve using the valueof a and 6) determined from suitable experi-ments. The r versus ] • curves for the kaolinitemembrane/sodium chloride solution and bentonitemembrane/sodium sulphate solution, calculated fromEq. (12) using the values of a and 6) given inTable 1, are shown in Fig. 3.

The data on a, Lp and 6) (Table 1) can befurther utilized to assess, how efficient these claymembranes would be for salt rejection, in a reverseosmosis operation, by using the criteria for efficientmembrane, developed by Spiegler and Kedems fromthe consideration of thermodynamics of hyper-filtration. The criteria developed by Spiegler andKedemf can be stated as follows:15M iJ>lwM ... (14)15M iJ>lsw ..• (15)where 1represents the coefficient of friction betweenthe species indicated by the subscripts. The sub-scripts 5, M, W in the present case stand for thesalt, the membrane and water respectively. Theinequality (14) expresses a kinetic selectivity co-efficient. The friction between salt and membranehas to be much higher than the friction betweenwater and membrane. This alone is not enough.If 15M is high, it would mean that the salt andwater are strongly coupled, which in turn wouldimply that one will drag the other along. Therefore,it is necessary to decouple the two fluxes. Theinequality tIS) in fact expresses this decouplingcondition.

In order to check whether the inequalities (14)and (15) hold good or not in the case of clay

membrane under study, the frictional coefficient,15M, fsw and lwM were calculated from the datagiven in Table 1. For this the equations ob-tainedtl,lO on the basis of Spiegler's frictional model'!connecting L», a and 6) with the various frictionalcoefficients were made use of. These equationsfor the present case are as follows:

Lp

= cpw fiwlwM

a = 1- Ks!sw(fsw +lsM)cpwKs

6)=(fSW+!SM)

In Eqs. (16) and (17) cpw and fiw represent thevolume fraction and the partial molar volume ofwater respectively and Ks represents the distributioncoefficient of the electrolyte between the membranephase and the aqueous phase. For determinationof the value of K«, known amount of the claywas taken in a pyrex flask and known volume ofthe electrolyte solution of known concentration wasadded to it and well stirred for several daysusing a magnetic stirrer. The supernatant liquidwas analysed for sodium using a flame photometer.The concentration of the electrolyte chosen werewithin the range of concentration used in theosmosis experiments. The electrolytes chosen weresodium chloride for kaolinite and sodium sulphatefor bentonite. The values of Ks for kaolinite andbentonite were found to be 0·8376 and 0·9778respectively. Using the value of Ks thus obtainedand the values of Lp, a and 6), the frictionalcoefficients 15M, Isw and lwM were calculat-ed using Eqs, (16) to (18) and are given inTable 1.

•.. (16)

•.. (17)

... (18)

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INDIAN J. CHEM., VOL. 16A, NOVEMBER 1978

It is evident from the values of the frictionalcoefficients in Table 1 that for both the systemsnamely kaolinite membrane/sodium chloride solutionand bentonite membrane/sodium sulphate solutionthe inequality (14) is satisfied while the inequality(15) is not, indicating a strong coupling betweensalt and water. Thus both kaolinite and bentonitemembranes only partially satisfy the criteria forefficient membranes for reverse osmosis, evolved bySpiegler and Kedem" from kinetic consideration ofthe membrane process.

AcknowledgementThis work forms a part of the programme

sponsored by the Indian Council of AgriculturalResearch, New Delhi. We are also grateful toDr Tulsi Ram and Mr A. K. Thukral for their helpwith the flame photometer.

924

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Sci. Hydrol., 14 (No.2) (1969), 17.2. JOHNSON, J. S., DRESNER, L. & KRAUS, K. A., cited in

Principle oj desalination (Academic Press, New York),1966, 345-439.

3. SPIEGLER, K. S. & KEDEM, 0., Desalination, 1 (1966), 311.4. ABD-EL-AzIZ, M. H. & TAYLOR, S. A., Soil Sci. Soc. Am.

Proc., 29 (1965), 141.5. LETEY, J. & KEMPER, W. D., SoilSci. Soc. Am. Pl'oc.,

33 (1969), 25.6. KATCHALSKY, A. & CURRAN, P. F., Non-equilibrium

thermodynamics in biophysics (Harvard UniversityPress, Boston), 1967, 113-132.

7. KEDEM, O. & KATCHALSKY, A., Biochim. Biophys. Acta,27 (1958), 229.

8. SMIT, J. A. M., Partition and friction in membranes,Ph.D. thesis, University of Leidon, 1970.

9. SMIT, J. A. M., EI]SERMANS, J. C. & STAVERMAN, A. J.,J. pbys. Chem., 79 (1975), 2168.

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