Pii: s0376-7388(01)00470-7

Journal of Membrane Science 191 (2001) 215–223 Modeling of the permeation swelling of emulsion during lactic acid extraction by liquid surfactant membranes Jiang Yuanli a,∗, Wang Fuan a, Kim Dong Hyun b, Lim Mee Sook b a College of Chemical Engineering, Zhengzhou University, Zhengzhou 450002, PR China b Department of Chemical Engineering, Kyungpook National University, Taegu 702-701, South Korea Received 18 September 2000; accepted 24 April 2001 Abstract
Based on the extraction mechanism by carriers in the membrane phase, the hydrophilic property of the carrier–solute complex formed at the interface of emulsion has been studied. By gas chromatograph the solubility of water in the membranephase was measured. Solubilization of water in the membrane phase is caused not only by surfactant but also by carrier–solutecomplex. Furthermore, water diffusion through the membrane goes on due to both the chemical potential of electrolytesand the chemical potential between reactants and reaction products. A mathematical model for estimating the permeationswelling rate during lactic acid extraction is proposed. With this model, the calculation results are in good agreement with theexperimental data. 2001 Elsevier Science B.V. All rights reserved.
Keywords: Liquid surfactant membrane; Lactic acid; Permeation swelling; Complex; Extraction 1. Introduction
the mechanism of entrainment swelling in a LSMsprocess for the separation of lactic acid and gave a Recently, liquid surfactant membranes (LSMs) corresponding mathematical model [6]. The second have been widely applied in the field of biotechnol- one is called permeation swelling, which occurs when ogy [1–4]. Most of these products are obtained from there exists a difference of osmotic gradient between dilute aqueous solutions. However, during the extrac- the internal and the external aqueous phase. After all, tion process there exist phenomena that the external it is very important to solve the swelling problems for phase water permeates through the membrane phase the industrial process design as well as the perfection into the internal water phase to cause swelling of the emulsion [5]. Emulsion swelling is harmful to the Ohtake et al. [7] and Kinugasa et al. [8] proposed separation efficiency of LSMs because it not only that the permeation swelling was caused by the trans- dilutes the extractant concentration in the inner aque- membrane osmosis gradient between the internal and ous phase, but also has negative effect on the stability external aqueous phases. Colinart et al. [9] and Bart of the emulsion system. Swelling can be classified et al. [10] further pointed out that the characteristic into two completely different types. The first one is hydrophilic groups of surfactants make this process called entrainment swelling, which takes place only inevitably occur. Wang and Fu [11] proposed the in the initial dispersion process. We have proposed solubilization–diffusion mechanism for the perme-ation swelling and gave the corresponding mathemati- cal model for estimating the permeation swelling rate.
0376-7388/01/$ – see front matter 2001 Elsevier Science B.V. All rights reserved.
PII: S 0 3 7 6 - 7 3 8 8 ( 0 1 ) 0 0 4 7 0 - 7 J. Yuanli et al. / Journal of Membrane Science 191 (2001) 215–223 Nomenclature
the first “path” for water transporting the second “path” for water transporting mass molarity of electrolyte atinterface (kmol/kg) However, for carrier (extractant) facilitated transport, all above works do not take into account the carrier in the membrane phase, which belong to surface active radius coordinate of water diffusion inthe emulsion globules (m) agents and have special role in the separation process.
Thien et al. [12] and Bart et al. [5] experimentally studied the permeation swelling of LSMs where mem- brane phases contain some carriers. But the different effects on the permeation swelling by surfactants and carriers, respectively, during water transport process the mass of La− in the membranephase (kmol), which is neglected due were not explained. Only some empirical relations In this paper, based on the above works, the per- meation swelling mechanism of LSMs during the ex- traction process has been investigated. We take into account the effects on permeation swelling not only by surfactants but also by carriers. Moreover, a mathe- matical model for estimating the permeation swelling average volume multiple of waterabsorption amount per unit internal 2. The permeation swelling mechanism of LSMs
during extraction
Since carriers in the membrane phase are sur- face active agents, these molecules may also be adsorbed at the interface between the emulsion and defined as ϕiνimi − ϕeνeme the external aqueous phase. The adsorption of car- defined as ci,t − ce riers is competed with that of surfactant molecules, which form a layer at the interface to build up the configuration of LSMs. The composition of carri-ers at the interface will increase with the increased J. Yuanli et al. / Journal of Membrane Science 191 (2001) 215–223 Above description illustrates, that the diffusion of water caused by carrier–solute complex contradictsthe transport of solutes. The higher concentrationof carrier at the interface between emulsion andouter water phase may promote the transport of so-lute. On the other hand, the increasing concentrationof carriers also promotes the permeation swelling,which dilutes the concentration in the inner aqueousphase so that the efficiency of separation is directlydecreased.
Just like the water molecules in the membrane phase carried by the surfactant molecules, the wa-ter molecules in the membrane phase carried by thecarrier–solute complex are also separated from thecomplex and transport alone into the inner aqueous Fig. 1. Diffusion of water in an emulsion drop.
phase because the effect of chemical potential gra-dient is much stronger than the effect of hydration.
Therefore, the permeation swelling phenomena during concentration of carriers in the membrane phase. Then the extraction should be explained by the surfactant solute molecules in the external phase will react with solubilization–diffusion mechanism combined with the carriers. The carrier–solute complex is gradually the carrier–solute complex reaction–solubilization– transported into the membrane phase while interface adsorption reaches a dynamic equilibrium [13]. Withthe combination of carriers and solutes at the inter-face between the emulsion and the external aqueous 3. The mathematic model of permeation swelling
phase, hydrophilicity of the complex is much strongerthan that of pure carrier molecules. Therefore, the Based on the mechanisms described above, the fol- first “path” for water transport into the emulsion glob- ules is offered by the combination of surfactants and 1. The solute and the water molecules co-transport water molecules while the second “path” is caused by the combination of complexes (carrier and solute) 2. The emulsion globule size can be expressed as with water molecules. The diffusion of water in an emulsion globule is shown in Fig. 1.
droplets are evenly dispersed in the emulsion glob- The diffusion of water firstly makes the inner water droplets swell, which are located in the outer layer 3. The surfactants cause no internal circulation and of the emulsion globules (called water absorption coalescence within the emulsion globule.
zone). In the meantime, the inner water droplets in 4. Under the normal operational conditions, the vol- the internal layer still do not absorb the diffusion wa- ume of external aqueous phase is much larger than ter (no absorption zone). Then a sharp boundary — that of the internal aqueous phase and the inner “advancing front” appears between these two zones.
water droplets have relatively large surface area.
This advancing front is moving towards the center of Then water molecules, carried by surfactants and the emulsion globules with extraction. Moreover, the by carrier–solute complexes diffuse in the mem- diffusion of water in the emulsion globules is consis- brane phase as the main transport mode.
tent with that of solutes [14–16]. The different sizedistribution of inner water droplets in the emulsion globules is created by the emulsion preparation pro- Wang and Fu [11] obtained the water flux carried by cess, so a Sauter mean diameter dp32 is usually used the surfactants (the first “path”) due to the different as the mean diameter of inner water droplet.
J. Yuanli et al. / Journal of Membrane Science 191 (2001) 215–223 1 = ϕiνimi − ϕeνeme.
During lactic acid (HLa) extraction by LSMs, where only the external volume and concentration are 2CO3 is used as the internal phase reagent and it dissociates inside the water phase according to: measured at different time interval, respectively, ci,tcan be obtained immediately.
solubilization–diffusion mechanism for carrier–solute complex transporting water (the second “path”), thereis an equilibrium relationship between the reactant When tributyl phosphate (TBP) is used as a carrier, bulk concentration m2 in water phase and its inter- the solute from the feed phase diffuses onto the inter- facial concentration mm2 at water–membrane phase face of the emulsion globules, where it reacts with the (e) + (C4H9O)3PO(m) Similar to the water flux offered by the different = (C4H9O)3PO3H+La−(m) osmotic gradient due to the electrolytes, the water fluxproduced by the different osmotic gradient due to the The carrier–solute complex diffuses onto the interface of the internal phase, where it decomposes due to thehigh pH value in the internal phase and reacts with thestripping reagent Na carrier. Then the total concentration of internal phaseaffecting the osmotic gradient can be expressed by π2 = ci,t − ce where ci,t is determined by Eq. (12).
Under the pure electrolyte condition, Wang and Fu [11] gave the penetration distance δ caused by waterpermeation: δ = 9kw1 π1Mwt Ve0ce0 = Vece + Vmcm + Vi[La−]i where λ is the average volume multiplied by the wa- Because the membrane phase is non-hydrophilic, ter absorption amount per unit internal phase volume equivalent to the original internal water phase volume.
Based on the “co-transport” theory, the water perme- Ve0ce0 = Vece + Vi[La−]i ation produced by carrier–solute complex has the samepenetration distance δ. Therefore, for two cases, the Substituting Eqs. (6) and (8) into Eq. (5) gives water fluxes can be expressed, respectively, as J. Yuanli et al. / Journal of Membrane Science 191 (2001) 215–223 Then the total water flux into the emulsion globulesshould be given as = D(kw1ρw π1 + kw2 π2) dVe = d(Vi + Vm) = dVi Fig. 2. Water solubility coefficient, kw vs. wT (TBP) for dif- ferent lactic acid solution concentrations, lines are fitted by the experimental data (298 K, Span 80, ws = 5%, kerosene); [HLa] (mol l−1): (᭿) 0; 0.06 (᭹); 0.10 (᭡); 0.14 (᭢).
(TOA) were used as the carrier (extractant) and the The experimental apparatus and method were given Substituting Eqs. (21) and (23) into Eq. (20) yields The water solubility coefficients of membrane phases containing surfactant and carrier were mea- sured by gas chromatography using Porapak Q col- Combining Eq. (19) with Eq. (24) and then integrating umn, a thermal conductivity detector (TCD) and 32 = 1.2d32,0, we finally get the calcu- 2 as carrier gas. GDX-103 was selected as the lation model for the permeation swelling rate during stationary phase. In order to shorten the analysis π1 + kw2 π2) There is no adjustable parameters in Eq. (25). Dif- time, other components were backflushed as soon as fusivity D can be estimated by Wilke–Chang relation- the water wave appeared. The detailed method was ship [17]; the two different water solubility coefficients described in [19]. The corresponding experimental re- kw1 and kw2 are experimentally measured; the osmotic The density method was used to determine the 4. Experimental
The membrane phase consisted of kerosene with an 5. Results and discussion
average molecular weight of 190. Span 80 (sorbitanmonooleate) or L113B (polyamine) were used as the By gas chromatography [19] the solubility of wa- surfactant. Tributyl phosphate (TBP) or trioctyl amine ter in the membrane phases containing surfactants J. Yuanli et al. / Journal of Membrane Science 191 (2001) 215–223 Fig. 3. Water solubility coefficient, kw vs. wT (TOA) for dif-ferent lactic acid solution concentrations, lines are fitted by the Fig. 5. Water solubility coefficient, k experimental data (298 K, Span 80, w lactic acid solution concentrations, lines are fitted by the experi- (mol l−1): (᭿) 0; 0.06 (᭹); 0.10 (᭡); 0.14 (᭢).
mental data (298 K, L113B, ws = 5%, kerosene); [HLa] (mol l−1):(᭿) 0; 0.06 (᭹); 0.10 (᭡); 0.14 (᭢).
(Span 80 or L113B) and carriers (TBP or TOA), wasmeasured, respectively, after the membrane phases in the membrane phase increases with the increase were mixed with dilute lactic acid solution (mem- in mass concentration of carriers (TBP or TOA) for brane phase volume: water phase volume = 1:1). In different lactic acid solution concentrations. While the meantime, the water solubility values of the same in Figs. 4 and 5, the same relationships at surfac- membrane phases were measured after the membrane tant (L113B) mass concentration of 5% are obtained.
phases were mixed with a solution without solutes.
Therefore, Figs. 2–5 illustrate that the water solubility The results are consistent with Wang’s experimental in the membrane phases containing TOA are much smaller than those of membrane phases containing It is shown in Figs. 2 and 3 that at surfactant (Span TBP at same surfactant concentration; the water solu- 80) mass concentration of 5%, the solubility of water bility in the membrane phases containing L113B aremuch smaller than those of membrane phases contain-ing Span 80 at the same carrier concentration. After20 min mixing, high lactic acid solution concentra-tions cause high solubility of water in the membranephases. That is, the solubility of lactic acid–carriercomplexes in the membrane phases increases with in-creasing solute concentrations in the external phases.
Compared with Wang’s experimental data [11], it isobvious that the solubility of water in the membranephases containing carriers is higher than those of themembrane phases without carriers.
As can be seen from Fig. 6, the permeation swelling rate changes with time for different surfactant (Span80) concentrations at carrier (TBP) mass concentra-tion of 5%, the line is calculated by Eq. (25). The per-meation swelling rate increases with higher surfactant Fig. 4. Water solubility coefficient, kw vs. wT (TBP) for different concentration. It illustrates that at a constant carrier lactic acid solution concentrations, lines are fitted by the experi-mental data (298 K, L113B, w concentration the more surfactant molecules, the more (᭿) 0; 0.06 (᭹); 0.10 (᭡); 0.14 (᭢).
water molecules into the membrane phase. Moreover, J. Yuanli et al. / Journal of Membrane Science 191 (2001) 215–223 Fig. 6. Permeation swelling rate changes with time for differentsurfactant (Span 80) concentrations, lines are calculated by Eq. (25) Fig. 8. Permeation swelling rate changes with time for different feed concentrations, lines are calculated by Eq. (25) (Span 80, T = 5%, [Na2CO3] = 0.6 mol l−1, [HLa] = 0.1 mol l−1); s × 100: (᭡) 2; (᭹) 5; (᭿) 8.
s = 5%, [Na2CO3] = 0.6 mol l−1, TBP, wT = 5%); cf (mol l−1): it also shows the synergistic effects in water solubi- concentrations at surfactant (Span 80) mass concen- lization by different surfactants and carriers [5]. Under tration of 5%, the line is calculated by Eq. (25). The normal LSMs experimental condition, the surfactant permeation swelling rate also increases with higher concentration in LSMs is much larger than its critical carrier concentration. Furthermore, the permeation micelle concentration so that too much surfactants re- swelling rate increases with increasing external solute sult in higher swelling. This result is consistent with concentration. The results verify that a second “path” Wang and Fu [11]. Therefore, it is necessary to ad- causing permeation swelling exists. Therefore, we not just surfactant concentration to produce a stable liquid only should take into account the carrier molecular membrane for the separation purpose.
structure for solute extraction, but also the hydrophilic From Fig. 7, it is shown that the permeation swelling property of the carrier–solute complex formed in the rate changes with time for different carrier (TBP) Fig. 8 shows that the permeation swelling rate changes with time for different feed concentrations,the line is calculated by Eq. (25). As can be seenfrom Fig. 8, higher feed concentration causes higherpermeation swelling rate just because higher feedconcentration might increase the osmotic gradient inthe second “path” for permeation swelling.
It is shown in Fig. 9 that the permeation swelling rate changes with time for different internal reagentconcentrations. It is clear that higher internal reagentconcentration leads to higher permeation swelling andreason is just like that in Fig. 8. This result is consistentwith that of Chaudury and Pyle [20], who proposethat higher internal reagent concentration do harmfulto the stability of LSMs.
Fig. 7. Permeation swelling rate changes with time for different By means of the model developed in this paper, we carrier (TBP) concentrations, lines are calculated by Eq. (25) (Span80, w can have a more clear understanding and a quantitative s = 5%, [Na2CO3] = 0.6 mol l−1, [HLa] = 0.1 mol l−1); wT × 100: (᭡) 2; (᭹) 5; (᭿) 8.
concept to the permeation swelling. It is also possible J. Yuanli et al. / Journal of Membrane Science 191 (2001) 215–223 Data for solubility of water in the membrane phases with addition of surfactant Span 80, L113B, and carrierTBP and TOA are measured by gas chromatography.
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