Articles In d ian Jo urn al of Che mi cal T echn o logy Vo l. 10, May 2003, pp. 3 11 -320 Mass transfer analysis of the extraction of Nickel(II) by emulsion liquid membrane Mousumi Chakraborty*", Chiranj ib Bhattacharyah& Siddhartha Dattab " De partme nt of C he mi cal Eng ineerin g, S V Reg io nal Co llege of Eng in ee ri ng &Tec hn o logy, Sura t 395 007 . Ind ia hDe partm e nt o f C he mica l Eng inee ring, Jada vpu r Uni ve rsity. Ko lk a ta 700 032 , India Received 15 Julv 2002; revised received 17 January 2003; accepted 20 February 2003 A mathematical model for batch extraction of Nickei(II) with emulsion liquid membrane (ELM) from a dilute sulphate solution and from industrial wastewater, using di-(2-ethylhexyl) phosphoric acid (D2EHPA) as extractant and hydrochloric acid as stripping agent is reported. The model considers a reaction front within the emulsion globule and assumes an instantaneous and irreversible reaction between the solute and the internal reagent at the membrane internal droplet interface. Batch experiments are performed for separation of Nickei(II) from aqueous sulphate solution of initial concentration in the range of 100-75 mgJL. The influence of Nickei(II) concentration on the distribution coefficient at pH 3.5 is co-related by a semiempirical model, which has been used for simulation of the extraction process. The simulated curves are found to be in good agreement with the experimental data. A vari ety of separati on probl e ms have been in vesti gated over the last three decades by usmg e mul sion liquid me mbrane (ELM ) processes . Compared to co nventi onal processes, ELM processes have certainly so me attracti ve features e.g. simpl e operati on, hi gh effic iency, ex tracti on and stripping in one stage, larger interfac ial area, scope of co ntinuou s operati on, etc. The applicati o ns include 16 hydrometallurgical recovery o f metal io ns - , re moval of weak ac ids and bases from wastewater7- 11 , and applicati on in bi ochemi cal and bi omedi cal fi elds 12- 14 • ELM s are usuall y fo rmed first by makin g an e mul sion of two immi sc ibl e phases and the n di spe rsing the emul sion in a third phase (continuous phase). The liquid me mbra ne ph ase refers to th e ph ase whi ch separates the e ncapsul ated ph ase in the emul sion and the ex tern al continu ous phase whi ch are, in general, compl etely mi sc ibl e. Th ere are two types of tra nsport mechani sms. In the first mechani sm , call ed carri er-facilitated transport mech ani sm, a carri er is incorporated in the me mbrane phase to increase the mass tran sfer rates 5 . In th e seco nd mechani sm, th e so lute firs t dissolves in the me mbrane ph ase near th e ex ternal interface and th en diffuses through it to the in ward reg ion of e mul sion dro p in the di sso lved state and is released in to th e intern al phase by reversin g the so luti o n process. Thus *Fo r corres po nde nce Fax: 026 1 3228394). (E- mail: mousumi_c ha kra @y ahoo.co m ; a concentrati o n gradi e nt is maintained across the me mbrane 7 . A number of mathem atical models have been de vel oped over the years to describe the mechani sm o f solute tra nsfer th rough e mul sio n liquid me mbranes . Based on the homogeneous di stribution of noncirculating intern al droplets w ithin the globule, Ho et 15 al. formul ated the advancing reactio n front model. The me mbrane so luble so lute di ffuses th rough the g lobul e to a reacti on front where it is re moved by an instantaneo us and irre versibl e reacti on with the internal reagent. As the reagent is consumed by reacti o n, thi s reacti on front advances into the g lobul e. 17 Stroeve and Yaranas i 16 and Fales and Stroeve ex te nded th e approach of Ho et a/. by including an additi onal mass transfer res istance in the continuous 18 ph ase. Kim et al. assumed an additi onal thin liqu id me mbra ne layer, which contained no inte rnal dro pl ets. An alte rn ate a pproach has been take n by Te ra mo to 19 20 et al. and Bunge a nd Nobl e . They incorporated reacti on revers ibility in describing the transport process in the e mul sio n g lobule. C han and Lee 11 assumed reacti on equilibrium to ex its in both th e inte rnal and extern al continuous ph ases. They also incorporated th e overall mass tra nsfer res istance in their model. The reversibl e model was later extended 21 to predi ct the ex trac tion rate fo r by Braid et a/. multi co mpo ne nt systems. Articles Nickel, copper and chromium are the three most commonly used metals for electroplating. The wastewater of electroplating industries contains 22 Nickel(II) ions. Ku lkarni et al. have used ELM application for the recovery of Nickel(II) using D2EHPA as a carrier. Katsushi et al. 23 have show n that the use of a mixture of co mme rcial extractant LIX63-DOLPA has a hi gh synergistic effect o n the ex tracti on of Nickei(II) in the ELM system compared 24 to the LIX63-D2EHPA mixture. Serga et al. found that app li cation of direct current to ex trac ti o n system contributes to the complete extractio n of Nickei(II) using D2 E HPA as carri er. Recentl y Kulkarni et al. 25 have studi ed the recovery of Nickci(II) usi ng methane sulphonic ac id (MSA) as a strippant. There still exists so me scope for better insight into Nickei(II) recovery by ELM process. In thi s pape r the effects of initial so lute (N ickel) concentrati on in feed phase, internal reagent concentration, treat ratio and volume fracti o n of internal phase on the extraction of Nickei(II) are sys te maticall y in vestigated usi ng D2EHPA as a ex tractant. In view of this, applicatio n of thi s technique is investi gated for re mova l o f Nickei(II), from wastewater using di-(2-ethylhexyl) phosphoric acid (D2E HPA) as ex tractant, Sorbitan mono-oleate (Span 80) as surfactant, kerosene as me mbrane phase and hydrochl ori c ac id as stripping so luti on. Here, di-(2-ethylhexyl) phosphoric acid (D2E HPA ) faci litates the transport o f Nickei(IT) and Nickei(II) ion is simultaneo usly changed by intern al reagent, hydroc hl oric ac id, to ni ckel chl oride which has a low so lubility in membra ne phase, so that concentration grad ient of Ni ckei(II) between two aqueous ph ases is mai ntain ed. Experimental Procedure Simulated feed For the study of transport of Nickei(II) ions through e mul sion liquid membrane, ni c kel sulphate (99.99 % pure, Merck make) is used. Industrial feed characteristics Local electropl ating company supp lied the industrial feed. The feed contains large concentration of Nickel(II) and trace a mount of copper(II), chromium(III) a nd iron(II). Indu stri al feed composition is summ arized in Table I. Commercial kerosene of specific gravity 0.798 and boiling poi nt range 145-250°C is used as me mbra ne phase. The extractant used is D2E HPA [CAS No. 298-07-7] hav in g 98.5% purity, Span 80 (Sorbitan 312 Indian J. Chem. Tec hno !., May 2003 Table !- S umm ary of expe rimental cond ition s for ELMs batc h tests Membrane phase (Oil) Vo lume Carrie r(D2EH P A) Diluent (11-hepta ne ) S urfac tan t (Span 80) Ke rose ne 25 mL 10 % V/V 5% V/V 5 % V/V 80% V/V Exterior phase (Water) Vo lume Ni c kel(ll) pH Buffer ( NaAc-HA c) 450 mL 100-200 ppm 1- 6 0.05 mo i/ L Interior phase (Water) Vo lume Ac idi ty 25mL IN (HC I) Industrial feed composition E le me nt s Co ne. (p pm ) Ni 900 Cr 45 Fe 40 Cu 50 Fo r preparati o n o f aqueo us soluti o ns do uble d istilled water has bee n used. monooleate containing 0 2 based mo ieties) as surfacta nt; 11-hepta ne as a diluent and stabi li zer for the membrane phase. Sodium acetate-Ace tic acid (NaAcHAc) is used as a buffer (to maintain pH) for ail the ex peri me nts. Method Emulsion IS prepared by emu lsifying aqueo us so luti on of ac id (s trip ph ase) with an organi c phase (membrane ph ase) . The membrane co nsists of varying proportio ns of surfactan t Span 80, extractant D2EHPA, and dilu e nt (n-heptane ). Th e mixer is st irred at 5000 rpm for 15 min using a homogenizer (s ix blade turbine impell er of 30 mm diameter) to form a uniform mixture. Then the internal strip phase is added . The contents are again stirred at 5000 rpm for 15 min. An exce ll e nt milky-white and stable e mul sio n is obtained. The emul si on is dispersed in feed phase CO!ltaining nickel ions from wh ich ni ckel is to be ex tracted. A six-blade paddle impell er of 50 mm diameter rotating at 500 rpm is used for stirring. For measuring speed o f the agitator and homogeni ser a hand tachometer hav in g a range of 0-10000 rpm has been used. Samples of about 5 mL are w ithdrawn from the extmc tor at different intervals of time and are filtered through a sintered glass plug to separate emulsion and aq ueous feed phase. At the e nd, the emul sio n phase is Articles Chakraborty et al.: Nickel(II) extraction by emulsion liquid membrane separated from feed phase by gravity separation in a separating funnel and finally the emulsion is broken down by heating to 80°C for the analysis of strip phase. 2 ex. phase org. phase in. phase 2(HR) 2 Analysis Samples of aqueous phase, containing nickel, have been analyzed by a spectrophotometer (CE1020, 1000 series manufactured by CECIL) according to the standard methods 26 . Results and Discussion Mechanism of Nickel(II) extraction process using ELM The equations given below show the extraction and stripping reactions of Nickel(ll) occurring in ELM process, where RH represents the protonated form of an extractant (D2EHPA, in this study). D2EHPA IS known to dimerize in nonpolar aliphatic solvents. Formation of the complex: Ni 2+ + 2 (HRh = NiRiHRh + 2 H+ ... (1) Stripping reaction: NiR2(HRh + 2H+ = Ni 2+ + 2(HRh ... (2) Eq. (1) represents the complexation reaction, which occurs at the membrane-external phase interface, while Eq. (2) shows stripping reaction at the membrane-internal aqueous phase interface. A schematic presentation of the liquid membrane globule and simultaneous extraction and stripping mechanism in ELMs is exhibited in Fig. 1. Mathematical description In the present study, an unsteady-state mathematical model is proposed for the separation and concentration of Nickei(II) ions using liquid surfactant membranes based on the advancing front model developed by Ho et al. 15 • According to this mathematical formulation, at the outer interface of the emulsion globules, solutes (Nickel ions) from the external phase reacts with the carrier contained in the membrane phase, thus forming a complex. The complex diffuses through the membrane phase until it is removed by an instantaneous and irreversible chemical reaction with the reagent (HCl solution) contained in the internal droplets . The solute cannot penetrate into the globule beyond those droplets , NiR2(HR) 2 (HR)l: dimer of carrier Fig. !-Simultaneous extraction and st ripping mechanism m ELMs which are completely depleted of internal reagent, because the solutes are immediately removed by reaction with the internal reagent. Hence, there exists a sharp boundary or a reaction front separating the inner region containing internal reagent and no solute from the outer region where the internal reagent has been totally used up by reaction with the complex. As time progresses, more and more reagent is used up and the radius of the unreacted inner core shrinks. The concentration of solutes at the surface of the reacted core is zero. The following assumptions have been made in developing the present model. The size distribution of emulsion globules is uniform. No coalescence or redispersion occurs between the globules in which the encapsulated droplets are uniformly distributed. (ii) There is no internal circulation within all emulsion globules due to the presence of surfactants and the small dimension of the globules. (iii) The solute reacts with the internal reagent irreversibly and instantaneously at the reaction front. As the reaction proceeds, the reaction front shrinks towards the core of the globules. (iv) Both the important effects of resistance in the external boundary layer and the membrane are taken into account in the model. (v) The breakage and the swelling of the emulsions are neglected. (i) 313 Articles Indian J. Chern . Techno!., May 2003 A diagram of the model showing the above assumptions is given in Fig. 2. The rate of the solute diffusion in emulsion globules can be described by the following equations: The material balance for the solute in the membrane phase External phase Ex(emol botrldary layer ............/ ; .- - --- ' I I Memtnne~ Rea<.iion frort ... (3) / where (RJ(t)< r < R, t>o) (4) (r..:;,R) (5) Fig. 2-Schematic diagram of the model C=O, t=O, Then the diffusion equation becomes: r=RJ(t), C=O, (t~O) (6) a8 = _ At r=R, C=CoCe, (t~O) (7) The material balance for the solute in the extemal phase is -v dCe e dt t=O, acl =lvD R e ar r = R Ce =Ceo ... (8) ... (9) The material balance of the solute at the reaction front is (4 3 ) =4n RJ2 Deacl ar r=RJ(t) a CTJ2 ag ) o7J at (X <TJ < 1, r =0, g =0, TJ = x, g =0, oTJ ... (13) r > 0) (TJ..:;, I) (14) (r~O) TJ = 1 then g = Coh at ( r (15) ~ 0) (16) The material balance equation in the external phase is: dh dr d -n RJ ¢C -- 1 (1-¢)TJ 2 or = _ Ea8 aT/ TJ =I . .. (17) h= 1 . . . (18) dt 3 t = 0, Rr =R The above equations can be dimensionless form by defining transformed (10) r = 0, (II) The material balance equation at the reaction front is as follows : into dx -1- -ag= dr ¢ m aTJ TJ =x r TJ=R' Del RJ x=- r = - 2 - , R' R c Ce c g=-, h=-, m=-, Ceo Ceo Ceo 314 r=O, ... (12) X =I . .. (19) . . . (20) The coupled Eqs (13), (17) and (19) have been solved by numerical computation using an implicit finite difference technique. A central difference scheme has been used for integration along the d imensionless Articles Chakraborty eta/.: Nickel(II) extraction by emulsion liquid membrane radial distance. The grid sizes in r and X directions have been chosen by trial and error to obtain good convergence. As none of the three equations can be solved independently, an iterative process has been adopted for each time step. The computational steps for each time step are as follows: (i) Values of hand X have been assumed to be equal to those in the previous time step. (ii) The assumed values of h and X have been substituted in Eq. (13). Simultaneous linear algebraic equations having a tridiagonal matrix of coefficients obtained by representing Eq. (13) in finite difference form have been solved by matrix inversion and multiplication method to obtain g as a function of X. The solvent assoctat10n factor 1Jf has been taken as 1.0. The viscosity of the membrane phase is determined to be 0 .0025 kg/ms and the molar volume of the complex is estimated by additive volume principle29 to be 0.5125m 3/kg .mol. The molecular weight of kerosene is determined by obtaining distillation data, and the average molecular weight of the membrane phase is calculated to be 142.2. The value of diffusivity of the complex in the membrane phase thus obtained is 3.17 X 10- IO m2/s. The effective diffusivity of the complex in the emulsion is obtained by the Jefferson- Witzell-Sibbitt correlation 30 , which in the present study becomes -n]cm2/s D . =104 D [4(1+2p) 2 e[f m 4(l+2p) 2 ... (23) (iii) Whether the values of X and g thus obtained satisfy Eq. (19) was checked. If they did not, a new estimate for X was made and the process from step 2 onward was repeated until the matching was satisfactory. (iv) h has been calculated from Eq. ( 17) and th e calculated and assumed values of h have been matched by an iterative process similar to that adopted in step 3 for solving X. Estimation of model parameters Emulsion globule size The emulsion globule size (Sauter mean) ts calculated by using the following correlation of 27 Ohtake et al. ... (21) The value of the interfacial tension between membrane and external phase is determined by a tensiometer and found to be 23.5 dyne/em. The value of d 32 was calculated to be 0.1 em. Effective diffusivity The value of the Effective diffusivity of D2EHPAMetal complex in the membran e phase is deter mined by the correlation of Wilke and Chang 28 : (117.3xi0 -' 8 )(!J! M ) D ill 05 T _:______. . :. . _-,- ____ m /s 2 0 .6 J.lm V c ... (22) where, p=0.403(¢) I 3 -0.5 ... (24) From the above equation effective diffusivity of the complex is found tO be 0.7832 X 10- IO m 2/s. Distribution coefficient Values of the distribution coefficient are calculated from the experimental data at pH 3.5. The logarithm of the distribution coefficient is correlated with the logarithm of the aqueous phase equilibrium solute concentration by the linear regression method. The equation obtained is, co= 56.23 c ~ l.ll ... (25 ) where C 0 = di stribution coefficient of the solute (Nickel) between membrane and external phase, C5 = equilibrium solute concentration in the aqueous ph ase, mg/L. The logarithmic values of the distribution coefficient are plotted aga inst logarithmic values of the equilibrium aqueous phase concentration, C5 , as shown in Fig. 4. It can be observed from the figure that at low concentration in the aqueous phase (< 5 mg/L), the curves slightly deviate from linearity. Howeve r, under the present experimental conditions the concentration range in the aqueous phase is always much hi gher than this limit value and the 315 Articles distribution coefficients of Ni(ll) ions throughout the extraction run can be considered to fo llow Eq. (25). The variables for the numerical calcul ations are initial solute [Nickel(II)] concentration in feed phase, internal reagent concentration, treat ratio and volume fraction of internal phase. The experimental data obtai ned for different values of the above variables are compared with the simulated curves as shown in Figs 5 to I 0. The operating conditions of the extraction runs and the calculated values of the different dimensionless variables are shown in Table 2. The parameters, De. R0 and C 0 used in the simulation are calculated as mentioned above. Indian J. Chern. Techno!., May 2003 0.9 2 0 0.8 i= u 0.7 ~ !<w 0.6 ;/!. 0.5 0.4 0.3 0 2 6 4 pH Fig. }--Extraction profile of nickel (II) from a pure salt solution Effect offeed phase Nickel (II) concentration It is found from Fig.5 that the fraction of sol ute [Nickel (II)] extracted is higher with a lower initial external phase solute concentration. This is due to a hi gher distribution coefficient for a lower initial external phase solutes concentration. However, it has been found that the time taken by the complex to reach the center of the emulsion globule remains almost unaffected and is only marginally higher with a lower initial external phase solute concentration. Effect of internal reagent concentration From Fig. 6, it is ev ident that a variation in the concentrations of stripping phase acid (0.5-1.0 N) does not effect the removal of Nickel(II) at the beginning of the process. However, towards the end of the process, extraction is more effective when a more concentrated stripping acid is used. This is because at the beginning of the process, extraction into the membrane phase is independent of the composition of the stripping phase and is mainly controlled by the continuous phase resistance. But at the later stage owing to high H+ concentration in the stri pping phase, reaction rate in stripping phase is more than the reaction in membrane phase and the capacity of the internal phase as a sink for metal io n increases and, therefore, the solute penetrates at a faster rate inside the emulsion globu les. This increases the diffusional distance necessary for the complex to reach the reaction front inside the emulsion globule. It thus increases the mass transfer resistance, thereby decreasing the extraction rate. The reaction front movement is shown in Fig. 7. Fig. 4-Distribution coefficients as a function of equilibrium aqueous phase solute concentration .c;; c.i z 1.2 • • 0 u w en Ellj>Oriment.ai.Ceo-100 fnlj/1 Ellj>Oriment.ai.Ceo-150 fnlj/1 -Thecrobcai.Ceo=100fnlj/1 < ::1: -Theoreticai.Ceo=150fnlj/1 a.. ..J z< w Ill: 0.8 ~ en en ~ z Q en z w ::E i5 • • • • 0.6 • • • • 0.-4 0 0 .05 0.1 0 .15 0 .2 DIMENSIONLESS TIME, "t 1:.1fect of treat ratio The treat ratio is defined as ratio of emul sion phase vol ume (Ve) to aqueous feed phase vol ume (V) . The 3 16 Fig . .5--Yariation of external phase nicke l ion concentration with initia l external phase nickel concentration Articles Chakraborty et a!. : Nickel(Il) ex tracti on by emulsion liquid membrane Table 2-0perating co nditions and parameters for the extraction runs (Ro=0.05 em, D, = 0.7832 x 10' 10 m2/s, C0 =56.23 C ~ 111 ) Sample Figure C,, (mg /L) E q> Ci (N) 2 3 4 5 6&7 8 9& 10 100,150 100 100 100 0.33 0.33 0.33, 0.25 0.33 0.5 0.5 0.5 0.5, 0.3 1.0 1.0, 0.5 1.0 1.0 .c 1.2 • . , _ _,Ci• Ul(N) E>cperirnerUI,Ci=0.5(N) -Theoreticoi,CF1 .0 (N) -Theoreticol,CP0.5(N) u z 0.9 A 0 u w )( c( :::l J: c.. z w .. 0.8 0: t<w (/) (/) .. 0 0.7 !z0 0.8 ~ .. 0.6 "...z 0 .5 ;:: u 0 .4 " 0 .3 :i • • • • z 0 :::E Ci=O .SN 0 ~ iii zw - ..; (/) ...J c( - Ci=1 .0N 0 .8 0 .4 0.2 0 0.05 0.1 0 .15 0.2 0.1 i5 DIMENSIONLESS TIME, 't 0 .000 0.018 Fig. 6-Variation of ex ternal phase nickel concentration with internal reagent concentration treat ratio is varied by changing the amount of emulsion added to the feed phase and keeping the volume of the later constant. Fig. 8 exhibits the time profile of the feed phase concentration of Nickel(II) at different treat ratios. The treat ratio is varied from 1:12 (£ = 0.25) to 1:9 (£ = 0.33). With increase in treat ratio (E) the volumes of both the carrier and the stripping agent increases. Therefore, the surface areas for mass transfer owing to the formation of a larger number of emulsion globules increases. Hence, a hi gher degree of extraction is obtained. However, it has been fo und that the reaction front movement is not affected. This is because in each emu lsion globule, the quantity of solute reacti ng with the carrier at the globule surface and the amount of internal reagent remains unaltered with a change in the value of E. Effect of volume fraction of internal phase With a decrease in the volume fractio n of the internal phase ( ¢ ), the amount of internal reagent with the globule decreases, resulting in the consumption of most of the reagents in the early stage. This causes a faster advancement of the reaction front towards the centre of the globu les 0.036 0.054 0 .090 0.072 0.108 OIM::NSIONLESS TIME, 't Fig. ?-Variation of reacti on front progress with internal reagent concentration .c 0 1.2 z ..• 0 u w - (/) c( J: ~. E=O. :D E - -.E=0.2S Th<creticai,Eo<l.:D Th<creticai,E-D.25 c.. ...J c( z Ill: w t<w 0.8 .. .. .. .. (/) (/) ~ z 0 0 .6 iii • • • • zw :::E i5 0.4 0 0.05 0.1 0.15 0.2 DIMENSIONLESS TIME, T Fig. 8---Yariati on of ex ternal phase ni ckel co ncen trati on with volume ratio of em ul sion to ex ternal phase (Fig. 9). The higher penetration leads to a lower extraction rate because of the longer diffusion path needed by the solute to reach the reaction front as shown in Fig. 10. 317 Articles Indian J. Chem . Techno!., May 2003 0 .9 0 .8 - Theoretical, '=0.5 0 .7 - Theoretical. f=O.J .; . ::0 i5 0 .6 0: 1- z 0 0 .5 0: u. z 0 ;:: . u w 0: 0.4 0 .3 0 .2 0 .1 0.018 0 .000 0.036 0.054 0.072 0 .090 0 .108 DIMENSIONLESS TIME, T Fig. 9--Yariation of reaction front progress with volume fraction of internal aqueous phase ..u z 0 u w ., ------ "I •... - < using emulsion liquid membranes based on the 15 ad vancing front model developed by Ho et al. , neglects external phase mass transfer and the effect of membrane breakage, and has no adjustable parameter. The effects of variab les, such as initial solute concentration in the external phase, internal reagent concentration, treat ratio, vo lume fraction of interna l phase on external phase solute concentration as well as o n the reaction fro nt movement are studied. The so lute distributio n coefficient is fo und to be infl uenced by the ex ternal phase so lute concentration, and a semiempirical correlation between the distribution coefficient and the equi librium external phase Nickel(Il) concentratio n has been developed for use in the simul ation of mode l equations. The theoretical resu lts obtained by numerical solution of the model eq uations are found to be in good agreement with the experimental data. Coexisting ions (I ndustria l wastewater) copper(II), chro mium(III) and iron(II) hardly affect the separation. Nomenclature Elq)erimental . t~.5 Experimental, t -<>.3 Theoretical, +=0.5 Theoretical, t=0.3 c :r 0.. ..J < z a: w t)( .,.,w w ~ 0 .8 ~ ... ... • • • • 0 0 ... 0 .6 ..J z iii z w ... • 0.4 0 0.05 0.1 0.15 0.2 DIMENSIONLESS TIME, T Fig. LG-Yariation of external ph ~se nickel concentration with volume fraction of internal aqueous phase Comparison between experimental and computed results Tab le 3 shows the absolute deviatio n between experimental and theoretical values of the external phase solute concentration for each experi mental run . The average absolute deviation s were found to be between 0.024 and 0.048 for an initial dimension less solute concentration (h) of 1.0. This shows that the simulated curves are in good agreement with the experimental data. Conclusion An unsteady- state mathematica l model is proposed for the separation and concentration of Nicke l(! I) ions 3 18 r R Rr T v metal ion (nickel) concentration in saturated zone of emulsion globule, mol/L initial internal reagen t concentration in internal phase, moi!L internal reagent concentration in internal phase, mol/L metal ions concentration in external phase, moi/L initial metal ion concentration in external phase, moi/L effective diffusivity of metal ions in saturated zone of emu lsion globules, m2/s distribution coefficients of the solutes (nickel) between membrane and externa l phase equi librium solutes concentrations in the aqueous phase, mg/L radial coord inate in emulsion globules, m radius of emu lsion globules, m reactio n fro nt position, m time, min total volume of emulsion phase, L volume of external phase , L avg. molecular wt. of the membrane phase Articles Chakraborty eta/.: Nickel(II) extraction by emulsion liquid membrane Table 3---Absolute deviation between experimental and computed values of ex tern al phase solute concentration Run 0.048 Maximum absolute deviation 0.088 0.040 0.015 0.010 0.017 0.045 0.060 0.052 0.060 0.037 0.060 0.018 0.036 0.054 0.072 0.090 0.108 0.126 0.144 0.090 0.037 0.035 0.047 0.070 0.070 0.070 0.058 0.044 0.090 0.018 0.036 0.054 0.072 0.090 0.108 0.1 26 0.144 0.010 0.025 0.045 0.020 0.010 0.030 0.022 0.030 0.024 0.045 0.018 0.036 0.054 0.072 0.090 0.108 0.126 0.144 0.010 0.035 0.015 0.010 0.010 0.030 0.040 0.050 0.025 0.050 C"' =IOO mg/L £= 0. 33 <p = 0.5 C; =I .O(N) 0.018 0.036 0.054 0.072 0.090 0.108 0.126 0.144 Absolute dev iation 0.088 0.069 0.037 0.028 0.037 0.032 0.046 0.050 2 C,., = 150mg/L £= 0. 33 <p = 0.5 C; =I.O(N) 0.018 0.036 0.054 0.072 0.090 0.108 0.126 0.144 3 C,., =100 mg/L T £= 0. 25 <p = 0.5 C; =l .O(N) 4 C,., =100 mg!L £= 0. 33 <p = 0.5 C; =0.5(N) 5 C,, =100 mg!L £= 0. 33 <p = 0.3 C;=I .O(N) c Ill = - ' C,o Greek Letters r T} =- R x=f\ R Average absolute deviation 'II= solvent association factor Jl rn= viscosity of the membrane phase Vc= molar volume of the complex ¢ =volume fracti on of internal aq ueous phase in the emulsion References I Reis M T A & Carvalho J M R, J Membr Sci, 84 (1993) 20 1. 2 Teramato M T, Sakai M, Ohsuga K & Miyake Y, Sep Sci Techno/, 18 ( 1983) 735. 3 Yang X J & Fane A G, J Membr Sci, 156 ( 1999) 25 1. 4 Sa fa vi A & Shams E, J Membr Sci, 144 ( 1998) 37. 5 Lee S C, AhnBS&Lee WK , JMembrSci, 11 4(1996) 171. 319 Articles Bhowal A & Dutta S, J Membr Sci, 188 (200 I) I. Fudu M, Xinpei L & Yuanqi Z, Desalination, 56 ( 1985) 355. Bhowal A & Dutta S, J Membr Sci, 139 (1998) 103. Takeshimal S, Wada S & Sakurai H, Sep Sci Techno!, 29 (1994) 2117. 10 Juangl R S, LeeS H & Huang R H P, Sep Sci Teclm ol, 33 (1998) 2379 . l l Chan C C & Lee C J, Chem Eng Sci, 42 ( 1987) 83. !2 Chan J H & Lee W K, Chem Eng Sci, 48 (1993) 2357. 13 Sahoo G C & Dutta N N, J Membr Sci, 145 (1998) 15. 14 Ghosh A C, Bo rthakur S, Roy M K & Dutta N N, Sep Teclm ol, 5 ( 1995) l 2 1. 15 HoW S, Hatton T A, Lightfoot EN & LiNN, AICHE J, 28 ( 1982) 662. 16 Stroeve P & Varanasi P P, AICHE J, 30 (1984) 1007. 17 Fales J L & Stroeve P, J Membr Sci, 21 ( 1984) 35. l 8 Kim K, Cho i S & lhm S, lnd Eng Chem Fundem, 22 ( 1983) 167. 19 Teramoto M, Takihana H, Shibutani M , Yuasa T & HaraN , Sep Sci Techno/, 18 (1983) 397 . 6 7 8 9 320 Indian J. Chern. Techno!., May 2003 20 21 22 23 24 25 26 27 28 29 30 Bunge A L & NobleR D, J Membr Sci, 2 1 ( 1984) 55. Braid R S, Bunge A L & Noble R D, AICH E J, 33 (1987) 43 . Kulkarni P S, Tiwari K K & Mahajani V V, Indian J Chem Techno/, 6 (1999) 329. Katsu shi Y, Takashiko K, Hiroshi K & Masahiro G, Sep Sci Techno!, 33 ( 1998) 369. Serga V E, Kulikova L D, Purin B A, Sep Sci Techno/, 35 (2000) 299. Kulkarni P S, Tiwari K K & Mahajani V V, Sep Sci Teclmol, 36 (2001) 639. Basset J, Danney R C, Jaffery G H & Mendham J, Vogel 's Text Book of Quantitative Inorganic Analysis (Longman, London), 1978, XVIII-26. Ohtake T, Hano T, Takagi K & Nakashio F, J Chem Eng Japan , 20 ( 1987) 443 . Wilke C R & Chang P, AICHE J, l (1955) 264. Reid R C, Prausnitz J M & Sherwood T K, The Properties of Gases and Liquids (McGrawHill Pub! , New York ), 1988. Jefferson T B, Witze l! 0 W & Sibbitt W L, lnd Eng Chem, 50 (1958) 1589.
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