Journal of Membrane Science

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1 Journal of Membrane Science 326 (29) Contents lists available at ScienceDirect Journal of Membrane Science journal homepage: Modeling of clarified tropical fruit juice deacidification by electrodialysis Edwin Vera a, Jacqueline Sandeaux b, Françoise Persin c, Gérald Pourcelly b, Manuel Dornier d,, Jenny Ruales a a Escuela Politécnica Nacional, Department of Food Science and Biotechnology, P.O. Box , Quito, Ecuador b Institut Européen des Membranes, Université de Montpellier II, Place Eugène Bataillon, 3495 Montpellier Cedex 5, France c UMR 16, Université Montpellier II, Place Eugène Bataillon, 3495 Montpellier Cedex 5, France d CIRAD, Montpellier SupAgro, UMR 95 Qualisud, av. Agropolis, TA B-95/16, F Montpellier Cedex 5, France article info abstract Article history: Received 24 April 28 Received in revised form 13 October 28 Accepted 18 October 28 Available online 5 November 28 Keywords: Fruit juices Deacidification Conventional electrodialysis Bipolar electrodialysis Modeling Electrodialysis (ED) using two-stack configurations with homopolar or bipolar membranes was investigated for deacidification of tropical fruit juices (passion fruit, mulberry, naranjilla). The objective was to develop a mathematical treatment for ED to predict the behavior of a fruit juice at industrial scale from ED performances at laboratory scale. From parameters such as current efficiency, electric resistance of the anion exchange membrane, and coefficients of variation with temperature determined in a laboratoryscale stack, modeling was applied to a pilot-scale stack that has a total effective membrane area 7 times larger. If no fouling took place, and except for conductivity at ph higher than 3.8, the differences between the experimental and simulated values for ph, titrable acidity, voltage, and energy consumption were inferior to 7%, 16%, 2%, and 15%, respectively, for all the fruit juices and operating conditions. Moreover, the average electrical charge of citric acid species transferred was 2.16 for all fruit juices, indicating that the current transport was mainly due to the ionic species issued from the secondary dissociation of the citric acid. 28 Elsevier B.V. All rights reserved. 1. Introduction Electrodialysis (ED) is a better way to deacidify tropical fruit juices than by calcium salt precipitation, which involves chemical reagents and by ion-exchange resins, which strongly modify the aroma profile of the product and provide effluents during the regeneration step [1 3]. It would be useful to model ED to forecast the qualitative and quantitative results of the process and to help design installations. Modeling would also lower the number of feasibility studies, reducing costs [4]. Several modeling studies have been performed: transport of carbonate ions [5], production of lactic acid [6,7], production of acetic acid [8], ED of NaCl, HCl, and amino acids [9], concentration of citric acid [1], recovery of sodium lactate [11], recovery of sodium acetate [12] and others [13,14]. However, the models are very specific and adjustments are always needed for each case. The objective of the present study was to develop a mathematical treatment for fruit juice deacidification by ED to predict the behavior at industrial scale, using the ED performances at laboratory scale. This approach is of interest because it could Corresponding author. Tel.: ; fax: address: dornier@cirad.fr (M. Dornier). give guidelines about the operation of industrial installations. Two ED configurations involving homopolar or bipolar membranes were investigated (Fig. 1). The deacidification consisted of partial extraction of citrate and malate anions from the juice and partial neutralization of protons by hydroxyl ions provided either by a soda solution circulating in an adjacent compartment of juice (ED3C configuration) or by a bipolar membrane in contact with the juice (EDBM2C configuration). Previous works have shown that satisfactory ED performances in deacidification rate, current efficiency, and energy consumption were obtained for passion fruit, castilla mulberry, naranjilla, and araza treatment [15]. Moreover, changes in the sensorial characteristics of fruit juices were slight [16]. Membrane fouling was the main limitation of the process, but it was reduced by modifying current density and flow rate specifically for each juice. Citric and malic acids are generally responsible for the high acidity of fruit juices. Several mathematical models have been investigated to study the conductivity and behavior of citric acid during ED, but only for synthetic solutions [1,17,18]. In the present work, modeling was applied to ED deacidification of passion fruit, castilla mulberry, and naranjilla juices, in which mainly citric acid was present. Modeling of araza treatment was not investigated because malic acid is the most abundant acid in this juice. First, the equations employed to predict the behavior of ED treatment are presented in this document, and then the /$ see front matter 28 Elsevier B.V. All rights reserved. doi:1.116/j.memsci

2 E. Vera et al. / Journal of Membrane Science 326 (29) Fig. 1. Configurations of the ED cell. C1, C2, and CP are separate compartments; the two electrode compartments (EC) are connected. X + =K +,Na +,Ca 2+,Mg 2+.A =Cl,SO 4 2, PO 4 3. results of modeling equations are compared with experimental tests. 2. Materials and methods 2.1. Fruit juices The juices were obtained from fresh fruits gathered in Ecuador and treated as described previously by Vera et al. [2]. After enzymatic treatment, they were clarified by using crossflow microfiltration with a ceramic membrane of.2 m average pore diameter. Table 1 shows the main characteristics of the clarified juices. The initial ph was close to 3, and the acidity was mainly due to citric acid. Citrate was the major anion in passion fruit (94%), mulberry (78%), and naranjilla (91%) juices. Note that the titrable acidity measures the H + ions in the solution, and considering that these ions came from the dissociation of citric acid only, an equivalent concentration of citric acid can be calculated. Since the fruit juices contain several ionic species, the titrable acidity is not directly correlated to the total concentration of citric ions measured by HPLC. For instance, for one solution containing.2 N H 3 R and another with.2 N H 3 R +.1 N KOH, the titrable acidity is.2 N and.1 N, respectively, but the citric ion concentration measured by HPLC will be.2 N for both. The total amount of inorganic anions was 2%. Potassium was the most abundant cation (65 82%), but its amount was low (6 2%) compared to that of the protons in the organic acids. Viscosity and density were close to those of water Synthetic solutions To establish the mathematical model, the fruit juices were considered as simple citric acid solutions with identical values of ph and titrable acidities (Table 1). This assumption was based on the real composition of fruit juices, considering only the main charged compounds, since, theoretically, only ions are involved in ED. Consequently, only citric ions (>8% of anions) and potassium ions (>65% of cations) were considered. Then, citric acid and potassium hydroxide were mixed to obtain the acidity and ph required. The synthetic mixtures chosen were (H 3 R.283 mol dm 3 +KOH Table 1 Main characteristics of the clarified fruit juices. Passion fruit Castilla mulberry Naranjilla ph 2.95 ± ± ±.5 Conductivity (25 C, ms cm 1 ) 8.5 ± ± ±.3 Total soluble solids (g kg 1 ) 135 ± 3 8 ± 2 7 ± 2 Titrable acidity (meq dm 3 ) 7 ± ± ± 11 (g kg 1 ) 44.8 ± ±.5 ±.7 Citric ion (g kg 1 ) 4.9 ± ± ± 2.1 Malic ion (g kg 1 ) 1.6 ± ± ±.5 Total minerals (g kg 1 ) 6.7 ± ±.7 9. ±.4.15 mol dm 3 ), (H 3 R.136 mol dm 3 + KOH.75 mol dm 3 ), and (H 3 R.137moldm 3 + KOH.9 mol dm 3 ). These solutions were assumed to be similar to passion fruit, mulberry, and naranjilla juices, respectively. To verify this assumption, some ED tests were performed with synthetic solutions and the results were compared with the real fruit juice Equipment and operating conditions ED experiments were performed using two-stack designs as in Fig. 1: ED3C: the stack was equipped with two anion (AEM) and two cation (CEM) exchange membranes constituting three compartments besides the electrode compartments. EDBM2C: the stack was equipped with one AEM and two bipolar membranes (BM) constituting two compartments besides the electrode compartments. The ion-exchange membranes were Selemion CMV (Asahi glass), Neosepta AXE1 (or ASM) (Tokuyama), and Neosepta BP-1E (Tokuyama) as CEM, AEM, and BM, respectively (see Table 2). The results obtained in Vera et al. [1] were used to choose the anionic membrane. Moreover the AXE1 membrane is approved for food applications. Since no particular properties were required for the CEM and BM, standard membranes were chosen. The permselectivity of the membranes was similar to that of Neosepta CMX and AMX for example. The constants used to solve the equations of the model were obtained from the literature or from experiments performed with a PL-2 laboratory-scale stack under constant current density (more information can be found in Vera et al. [15]). In the present work, experiments were performed with a pilot-scale stack P-2 and compared with simulated results. Experiments in the P-2 stack were performed by arranging the stack in the same two basic configurations (i.e., ED3C and EDBM2C) used in the PL-2 cell. Table 2 shows the characteristics of the two ED pilots and their operating conditions. The main differences between the pilots were that, with the pilot-scale stack, the unit membrane area was 1 times larger, the number of unitary cells was 7 times greater, and the compartment spacing was 13 times smaller. Consequently, the total membrane area was 7 times larger with the pilot-scale stack. ED operations were carried out in batch mode, at constant electrical current. Several experiments were performed at current densities of 5, 75, 1, 15, 2, and 3 A m 2 and temperatures of 15, 25, and 35 C. Voltage, conductivity, and ph were monitored during all the experiments, which were performed until ph 4.5 was reached in the juice. These parameters were plotted against the electrical charge instead of time, since similar curves were obtained when plotting the results of the tests performed at the different current densities above mentioned. Considering that the current

3 474 E. Vera et al. / Journal of Membrane Science 326 (29) Table 2 Characteristics of the electrodialysis cells and operating conditions. PL-2 P-2 Active membrane area (cm 2 ) 2 2 Selemion CMV properties a meq/g, 3.5 b cm 2, t Na + =.92 Neosepta AXE1 properties a meq/g, 1.5 b cm 2, t Cl =.95 Neosepta BP-1 properties a V and yield >.98 for water dissociation Number of unitary cells 1 7 Width of compartments (cm) Height of compartments (cm) Thickness of compartments (cm) CP, C1, C EC Spacers (grid) No Yes Flow rate (dm 3 h 1 ) Linear speed (cm s 1 ) Volume of solutions (dm 3 ) CP C1 1 4 C2 (for ED3C) 1 1 EC 1 3 a According to the manufacturers. b Measured with NaCl.5 N at 25 C. density is constant during the deacidification process, the electrical charge was evaluated by the following equation: i t. For calculations related to the P-2 cell, the exposed electrode surface area was used, considering the shadow effect of the spacers. To determine the shadow effect, the geometry of the cell was considered (Fig. 2): Surface of membrane : S = b h (1) To estimate the surface shadowed by the spacer, the rods of the grid were assumed to partially hide the surface, because of the contact between the spacer and the membrane, consequently: Surface shadowed by the spacer : S s = b/a h d (/2) (2) Shadow effect : S s S = e (3) 4 a For the pilot-scale stack P-2, e =.8 mm, a = 1.7 mm, and = /4 rad; consequently the shadow effect was 9%, and the exposed surface area employed was 182 cm 2 instead of 2 cm Mathematical modeling of ED batch tests The principle of modeling was to consider the fruit juices as citric acid solutions with identical ph and titrable acidity. The following steps were performed: Calculate the concentration of the ionic species involved in the ED process, by solving the equations of the chemical equilibrium of citric acid. These equations will also give the ph in the juice compartment. The initial concentration depends on the fruit juice treated, and the variation of this concentration during the ED process was calculated by the general equation of electro-migration. Calculate the conductivity of the solutions with the concentration of the ionic species obtained previously, and with equations in the literature about the conductivity of ions or salts. Calculate the voltage applied to the ED cell with the conductivity of the solutions, the voltage for the electrochemical reactions at electrodes, and the electrical resistance of membranes obtained from manufacturers or experimental data. Calculate the energy consumption with the voltage. This computing was performed for each temperature (15, 25, or 35 C), taking into account the variation of equilibrium constants of citric acid, current efficiency, electric resistance, conductivity, and activity coefficients with temperature Calculation of the concentration of ionic species and ph in the juice compartment Citric acid is a weak acid showing three successive dissociations with the equilibrium constants k 1, k 2, k 3 and degrees of dissociation 1, 2, 3, respectively: H 3 R H 2 R + H + (4) H 2 R HR 2 + H + (5) HR 2 R 3 + H + (6) Fig. 2. Geometry of an ED compartment with spacer.

4 E. Vera et al. / Journal of Membrane Science 326 (29) The equilibrium constants are given by the following equations: k 1 = C H + C H 2 R f 1 (7) C H3 R k 2 = C H + C HR 2 C H2 R f 2 (8) k 3 = C H + C R 3 f 3 (9) C HR 2 where f i denotes the corresponding quotients of the activity coefficients according to: f 1 = H + H 2 R H3 R (1) f 2 = H + HR 2 H2 R (11) f 3 = H + R 3 (12) HR 2 The concentrations of the species present in solution can be expressed as a function of the dissociation degrees: C H3 R = ( )C a (13) C H2 R = 1C a (14) C HR 2 = 2C a (15) C R 3 = 3C a (16) where C a is the total concentration of citric acid under the different forms H 3 R, H 2 R,HR 2 and R 3 at time t. Use of Eqs. (7) (9) and (13) (16) yields: C a C H3 R = 1 + ((k 1 /f 1 C H +) + (k 1 k 2 /f 1 f 2 (C H + ) 2 ) + (k 1 k 2 k 3 /f 1 f 2 f 3 (C H +) 3 )) (17) C H2 R = k 1 C H3 R (18) f 1 C H + C HR 2 = k 1 k 2 f 1 f 2 (C H + ) 2 C H 3 R (19) C R 3 = k 1k 2 k 3 f 1 f 2 f 3 (C H + ) 3 C H 3 R (2) The analysis of fruit juices has shown that they could be assimilated to a mixture of citric acid and potassium hydroxide [16]. Thus, the electro-neutrality condition in the juice compartment (CP) was written as follows: C H + + C K + = C H2 R + 2C HR 2 + 3C R 3 + C OH (21) or considering the degrees of dissociation: C H + + C K + = ( )C a + C OH (22) The K + concentration is identical to the KOH concentration: C K + = C KOH (23) By accounting for water dissociation, H + + OH H 2 O (24) the OH concentration can be related to the H + one as C OH = k w C H + f w (25) with f w = H + OH (26) where k w is the equilibrium constant of water dissociation. Thus, Eq. (22) becomes: C H + = ( )C a + k w C KOH (27) f w C H + At low concentrations, the activity coefficients f i of the different ions can be calculated by the modified Debye Hückel expression [19]: ( ) I log i = Az 2 i 1 + I.3I (28) where A is a constant and I the ionic strength given by the following relation: I =.5 z 2 i C i (29) The different ions are H +,OH,K +,H 2 R,HR 2, and R 3. Therefore, by using Eqs. (14) (16), Eq. (29) becomes: I =.5{( )C a + C OH + C H + + C K +} (3) Combining Eqs. (22) and (3), the ionic strength can be calculated by the following expressions: I = ( )C a + C OH (31) in which C OH can be neglected at acidic ph. The change in concentration of citric acid C a during the ED treatment can be determined by the flux of citrate ions from the juice compartment to the C1 compartment: dc a dt = njs V juice F (32) where is the current efficiency experimentally measured in the PL-2 laboratory-scale stack, n the number of unit cells, j the current density, S the membrane area, V juice the volume of juice, and F Faraday s constant. From previous results [15], it was possible to assume that in case of negligible fouling, current efficiency was practically independent of the current density in the ranges of 1 2, 5 1, and 1 15 A m 2 for passion, mulberry, and naranjilla fruit juices, respectively, and that it was independent of feed flow rate in the range of dm 3 h 1. Thus a constant value can be introduced in Eq. (32). At a given time t, the total concentration of citric acid C a, can be calculated from Eq. (32). Then, the concentrations of the different ionic species involved can be calculated using Eqs. (17) (2), (28), and (31) via a trial and error procedure. Firstly, arbitrary initial values for C H + and i were assumed to estimate C i and f i via Eqs. (1) (12) and (14) (2) before obtaining a new estimate of C H + via Eq. (27). If the latter differed from that initially assumed by more than.1%, the iterative procedure was continued until convergence on C H Calculation of conductivity in the juice compartment Once the concentrations of all the ionic species had been calculated, it was possible to predict the electric conductivity of the solution undergoing ED de-acidification by accounting for all ionic contributions: = z i C i i (33) i Taking into account the different ions present in the synthetic mixture of citric acid and potassium hydroxide, and substituting

5 476 E. Vera et al. / Journal of Membrane Science 326 (29) Eqs. (14) (16) in Eq. (33), the expression of the synthetic solution conductivity is synthetic = ( 1 H2 R HR R 3 )C a + C H + H + + C K + K + (34) Apelblat and Barthel [17] have established the equations for the molar conductivity of ionic species of citric acid and proton at 25 C. At each successive dissociation, the equations are the following: Primary dissociation: H + 1 = I I ln I I (35) H2 R = I I ln I I (36) Secondary dissociation: H + 2 = I I ln I I (37) HR 2 = I 55.46I ln I I (38) Tertiary dissociation: H + 3 = I I ln I I (39) R 3 = I I ln I I (4) The molar conductivity of proton, which appears in Eq. (34), is obtained considering Eqs. (35), (37), and (39) and the molar fraction of H + ions obtained from each dissociation of the citric acid (see Eq. (14) (16)): 1 H + = H H H (41) To determine K +, the conductivities of synthetic mixtures of citric acid (.2.7 mol dm 3 ) and KOH (.15 mol dm 3 ) were measured, and the constants of the equation were adjusted to fit the experimental data obtained. The expression found was K + = I I ln I 16.85I (42) From all Eqs. (34) (42), a theoretical value of synthetic solution conductivity can be evaluated. This value must be corrected by Eq. (43). Indeed, experiments performed with synthetic mixtures of citric acid and potassium hydroxide at identical ph and titrable acidity of the different juices at the initial condition (ph 3.) showed that a constant ratio was obtained between the juice and synthetic solution conductivities whatever the juice treated (Fig. 3): juice.89 synthetic (43) The decline in the juice conductivity can be explained by the presence of sugars, which increase the viscosity Calculation of energy consumption At constant current density, the energy consumption can be written as follows: W = js Udt (44) where U is the total voltage of the ED stack. It can be calculated by the relation [6,7,2]: U = U EC + nu C (45) κ juice ( m S cm -1 ) κ synthetic ( m S cm -1 ) y =.891 x R² =.963 Slope:.891±.55 Passion Mulberry Naranjilla Fig. 3. Relation of the conductivity of synthetic solutions and fruit juices at the initial conditions (ph 3.). with U EC and U C the voltage of the electrode compartment and unitary cell, respectively. Since rough platinum electrodes were used, the surface of the electrodes was much greater than the membrane area, and this facilitated the electrochemical reactions. Consequently, electrode overvoltage could be neglected because it is known that a rapid reaction occurs with a few millivolts overvoltage [21]. Then, the voltage of the electrode compartment would approximately be U EC = 2jSR sol + U el (46) with R sol the electric resistance of the solution and U el the theoretical voltage for electrochemical reactions at electrodes, which can be calculated by using the Nernst relation: R(T + 273) U el = U ± ln(qr) (47) n e F with U standard voltage (at 25 C, 1 kpa, 1 mol dm 3 ); R, gas constant; T, temperature; n e, number of transferred electrons; Qr, reaction quotient. The reactions that took place at electrodes are: for ED3C: 4OH O 2 + 2H 2 O + 4e U =.41 V (48) 4H 2 O + 4e 2H 2 + 4OH U =.828 V (49) for EDBM2C: 2H 2 O O 2 + 4H + + 4e U = V (5) 4H + + 4e 2H 2 U = V (51) Thus Eq. (46) becomes: U EC = 2jSR sol (52) In the simplest form, the unitary cell voltage can be assumed to be the sum of the following terms: U C = U sol + U m (53) U sol = jsr sol (54) 9 11

6 E. Vera et al. / Journal of Membrane Science 326 (29) with U sol, U m the potential drop across the solution and membranes, respectively: for ED3C: R sol = R juice + R C1 + R C2 (55) U m = j(2r AEM + r CEM ) (56) for EDBM2C: R sol = R juice + R C1 (57) Table 3 Parameters used in the modeling equations. Parameter (at 25 C) ED3C EDBM2C (%) 43.5 ± 1.8 a 34.3 ± 1.5 a r AEM ( cm 2 ) 63± 6 a 29 ± 2 a r CEM ( cm 2 ) 3 b U BM (V) 1.7 b a Experimental values obtained in the PL-2 cell in a previous work [15]. b Manufacturer values. U m = jr AEM + U BM (58) with r the electric resistance of membranes and U BM the potential drop at the bipolar membrane ED3C EDBM2C The electric resistances R juice, R C1, and R C2 are calculated from the conductivity of solutions [6,19,2,22]: R = e (59) S where e and S are the thickness and cross-section of each compartment, corresponding to the active membrane area. The conductivity of C1 and C2 compartments containing NaCl, NaOH, or H 3 R solutions was calculated from classical equations given by literature data [19,22]. Thus, the voltage can be evaluated from Eqs. (45), (52), and (54) Thermodynamic parameters of the modeling The parameters used for simulation were obtained either from literature data or from experiments performed with a laboratoryscale stack [15]. The dissociation constants of water and citric acid at 25 Care [23]: k w = pk 1 = 3.14, pk 2 = 4.77, pk 3 = 6.39 To evaluate the performances of ED at different temperatures, the same Eqs. (4) (59) were employed, and the variation with temperature was considered for the equilibrium constants of citric acid, current efficiency, electric resistance, conductivity, and activity coefficients. The variation of the citric acid dissociation constants vs. temperature are given as follows [19]: pk 1 = (T + 273) (6) T pk 2 = (T + 273) (61) T pk 3 = (T + 273) (62) T The values of the constant A in the expression of the activity coefficients, Eq. (28), are[19]:.528 at 15 C..5115at25 C at 35 C. The variation of current efficiency, electric resistance of membranes, and conductivity vs. temperature can be expressed by using the following general equation: X(T) = X(T ref ) {1 + T (T T ref )} (63) with X(T) the current efficiency, electric resistance, or conductivity at temperature T, T the coefficient of variation with temperature, Ω T ( C) Fig. 4. Variation of the electric resistance of the AEM with the temperature (measured in the PL-2 cell). T ref the reference temperature (25 C), T ref and T are expressed by the same unit. The current efficiency used for modeling was the average of the values presented in Vera et al. [15] at 25 C, at current densities between 5 and 2 A m 2, without fouling for the clarified juices of passion fruit, naranjilla, and mulberry. The average value at 25 C is presented in Table 3. The membrane electric properties at 25 C of cation exchange membrane and bipolar membrane were taken from manufacturers specifications (Table 3). For the anion exchange membrane, the values reported in Vera et al. [15] at 25 C were taken (Table 3). Experiments of deacidification at 15, 25, and 35 C were performed to calculate the coefficients of variation with temperature of current efficiency and electric membrane resistance according to Eq. (63). The conductivities of citric acid solutions and fruit juices, from 1 to 4 C, were measured to obtain the coefficient of variation with temperature of conductivity, also using Eq. (63). The data used to calculate the coefficient of variation with temperature of current efficiency are in Vera et al. [15]. The data for the evaluation of the coefficients of variation with temperature of electrical resistance and conductivity are shown in Figs. 4 and 5. The calculated values are given in Table 4. Table 4 Coefficients of variation with temperature experimentally determined. Parameter T (% K 1 ) 1.5 a r membrane 4.15 a citric acid 2.1 passion fruit 2.23 mulberry 2.4 naranjilla 2.1 a Values obtained in the PL-2 cell. 3 4

7 478 E. Vera et al. / Journal of Membrane Science 326 (29) Conductivity (ms.cm - ¹) Temperature ( C) Mulberry ph 3 Mulberry ph 4 Naranjilla ph 3 Naranjilla ph 4 Passion fruit ph 3 Passion fruit ph 4 H3R.136M + KOH.75M H3R.137M + KOH.9M H3R.283M + KOH.15M Fig. 5. Variation of the conductivity of the solutions with the temperature. 4. Results and discussion Figs. 5 9 show the comparison between the results of experiments performed with synthetic solutions or fruit juices with the two ED configurations (Fig. 1) of the pilot-scale stack P-2 (symbols) with modeling values (continuous lines) Titrable acidity For modeling, the titrable acidity expressed in mol dm 3 was evaluated by the following equation, in which citric acid was considered as three functional acids: TA = 3C a C KOH (64) 3 The evolution of ph and titrable acidity was measured from experiments performed with the passion fruit, mulberry, and naranjilla juices and the synthetic solutions prepared as described in Section 2.2. Similar ph variations vs. titrable acidity were obtained whatever the ED configuration used for deacidification. A very low difference (<16%) was observed between the simulation results obtained for the three temperatures investigated (15, 25, and 35 C). As shown in Fig. 6, simulated values fitted experimental results well for the three fruit juices tested. One can conclude: the fruit juices can be considered as simple citric acid and KOH solutions, the calculation of C a from Eq. (32) and those of ionic distribution are correct, the estimation of TA from Eq. (64) is correct Evolution of ph, TA, conductivity, and voltage ph and TA evolution during deacidification with the two ED configurations is shown in Fig. 7. The ph of the juices increased 4 regularly. On the other hand, the TA decreased linearly with the electrical charge transferred, which is a consequence of Eq. (32) and the assumption that the current efficiency is constant. The high acidity of passion fruit juice involved the highest amount of electrical charge. In all cases, the simulated values were in good agreement with the experimental data over the entire range studied. Fig. 8 exhibits the evolution of conductivity. At the beginning of ED, experimental and calculated values were similar, but a gap appeared for ph higher than 3.8. This gap might be due to the molar conductivity of ionic species ( H2 R, HR 2, R 3, H +, K + Eqs. (34) (4)), which increased exponentially with the ionic strength, which in turn increased during ED because the citric acid dissociation became greater at higher ph. Even if the equations for calculation of the molar conductivity of ionic species of citric acid were established by Apelblat and Barthel [17] for diluted solutions (<.1 M), acceptable results were obtained for the first part of the deacidification process (Fig. 8). The modeling of conductivity was not improved since the overall voltage was not affected by the gaps between the experimental and calculated values, probably due to the low resistances of solutions compared with the membrane resistances, which were 6 9 times higher in the P-2 module. Fig. 9 allows comparison between measurements and modeling of the overall voltage of the cell. This parameter is directly related to the current density. As expected, similar values (about V) were obtained for the three fruit juices when an identical current density (1 A m 2 ) was applied (ED3C configuration), and increasing values (from 2 to 5 V) were obtained for increasing current densities (from 1 to 2 A m 2, EDBM2C configuration). Nevertheless, for an identical current density, higher voltage values were always obtained with the EDBM2C configuration. A previous study has shown that the lower performances of EDBM2C were related to both the lower conductivity of solutions in the compartments adjacent to the juice and proton leakage through the AEM from the C1 compartment containing citric acid, inducing ph changes inside the membrane and consequently modifications of citric acid dissociation towards a non-conductive molecular form [15]. The difference between the simulated values vs. the experimental values of voltage was always inferior to 2% for both configurations and all the juices, except for mulberry juice, and particularly in the EDBM2C configuration, where the difference reached 5%. There is no clear explanation of this result, but there are two possible causes: (a) the high fouling observed for mulberry juice, due to the precipitation of proteins/polyphenol complexes at basic ph [15], and/or (b) the model solution characteristics used are not representative of real mulberry juice. When both ED configurations were compared, the modeling for ED3C was less accurate for passion fruit, but more accurate for mulberry and naranjilla. No explanation was found for this behavior. Note also that the electric resistance of the boundary layers, the junction voltages, and the Donnan potentials had not been considered in the modeling, but acceptable results were obtained. From Eq. (54) the contribution of the potential drop at membranes (U m ) to the unitary cell voltage (U C ) can be evaluated. A value of about 9% was found for the two ED configurations. This means that the electric resistance of membranes is the main parameter in energy consumption. This behavior is different from those obtained in ED demineralization, where the solutions have too much influence on energy consumption Evolution of energy consumption In Fig. 1 the energy consumption per mol of H 3 R transferred is plotted as a function of current density and temperature. Straight lines were obtained from both experimental and calculated values

8 E. Vera et al. / Journal of Membrane Science 326 (29) ph ph TA (mol.dm -3 ) Passion Synth. solution Model..1.2 TA (mol.dm -3 ) Mulberry Synth. solution Model ph TA (mol.dm -3 ) Naranjilla Synth. solution Model Fig. 6. ph variation as a function of the titrable acidity for the three fruit juices, synthetic solutions and modeling. Pilot P-2, ED3C configuration (similar curves were found for the EDBM2C configuration). whatever the fruit juices treated (r 2 >.998). The gap between the experimental and calculated values was lower than 15%. Experimental tests at different temperatures were performed only in the PL-2 cell. The straight lines do not go through the origin because some terms in the equations such as the potential for the electrochemical reactions at electrodes and the potential drop at the bipolar membrane do not depend on current density. As expected, the increase in temperature decreased the energy consumption because it increased the solution conductivity and consequently it decreased the overall voltage of the cell. Note that the influence of temperature was more significant at higher current densities. The use of temperatures higher than the ambient one would not be more expensive since the Joule effect heats the solutions (between 5 and 1 C for our operating conditions). On the contrary, additional energy would be necessary to work at low temperatures. Nevertheless, high temperatures are not recommended because product quality (sensorial, nutritional) could be deteriorated and microorganisms might grow Evaluation of electrical charge of citric acid species transferred an electric charge equal to 1 [15]. But as citric acid bears three acid functions, the electrical charge must be given by the following equation: z a = z i x i (65) with x i the molar fraction of each ionic species bearing the charge z i. Thus, Eq. (65) can be written as z a = x H2 R + 2x HR 2 + 3x R 3 (66) At ph 3, the molecular (H 3 R) and monoionized species (H 2 R ) are the main species, 56.9% and 42.3%, respectively. These proportions change with ph and can be different in the bulk and inside the membrane. Consequently, the value of z a would be 1 z a 3. The transport number of citric acid (t a ) through the AEM separating the juice and C1 compartments is given by t a = Fz aj a j (67) In the model presented here, the current efficiency,, experimentally determined with a laboratory-scale stack, was used to evaluate the citric acid concentration as a function of time (Eq. (32)). In a previous study, the value of was calculated by considering that the ionic species of citric acid crossing the AEM bore where J a is the overall citric acid flux. Use of Eqs. (32) and (67) yields: z a = t a (68)

9 48 E. Vera et al. / Journal of Membrane Science 326 (29) ED3C 5. EDBM2C ph ph ,3,3 TA ( mol dm -3 ),2,1 TA ( mol dm -3 ),2,1, , Passion Mulberry Naranjilla Modeling Fig. 7. Evolution of ph and TA with the electrical charge transferred during ED. The symbols represent the experimental data and the continuous line the calculated values using the mathematical model. Pilot P-2 ED3C: 1 A m 2,25 C, 15 dm 3 h 1 for the three juices. EDBM2C: 2 A m 2,25 C, 15 dm 3 h 1 for passion fruit, 1 A m 2, 25 C, 15 dm 3 h 1 for mulberry, 15 A m 2,25 C, 15 dm 3 h 1 for naranjilla. ED3C EDBM2C 9 9 Conductivity (ms.cm-¹) Conductivity (ms.cm-¹) Passion Mulberry Naranjilla Modeling Fig. 8. Evolution of conductivity with the electrical charge transferred during ED. The symbols represent the experimental data and the continuous line the calculated values using the mathematical model. Pilot P-2 ED3C: 1 A m 2,25 C, 15 dm 3 h 1 for the three juices. EDBM2C: 2 A m 2,25 C, 15 dm 3 h 1 for passion fruit, 1 A m 2, 25 C, 15 dm 3 h 1 for mulberry, 15 A m 2,25 C, 15 dm 3 h 1 for naranjilla.

10 E. Vera et al. / Journal of Membrane Science 326 (29) ED3C 55 EDBM2C Voltage (V) 11 9 Voltage (V) Passion Mulberry Naranjilla Modeling Fig. 9. Evolution of voltage with the electrical charge transferred during ED. The symbols represent the experimental data and the continuous line the calculated values using the mathematical model. Pilot P-2 ED3C: 1 A m 2,25 C, 15 dm 3 h 1 for the three juices. EDBM2C: 2 A m 2,25 C, 15 dm 3 h 1 for passion fruit, 1 A m 2,25 C, 15 dm 3 h 1 for mulberry, 15 A m 2,25 C, 15 dm 3 h 1 for naranjilla. 3. ED3C - PL2 15 C 3. EDBM2C PL2 25 C W (kwh/mol H 3R) C W (kwh/mol H3R) C 25 C 35 C j ( A m -2 ) j ( A m -2 ) 1.6 ED3C - P2 1.6 EDBM2C P2 15 C W (kwh/mol H3Cit) C 25 C 35 C W (kwh/mol H3Cit) C 35 C. 1 2 j (A.m-²) j (A.m-²) 3 4 Passion Mulberry Naranjilla Modeling Fig. 1. Evolution of energy consumption with the electrical charge transferred during ED. The symbols represent the experimental data and the continuous line the calculated values using the mathematical model. (Experimental points at 15 C: full symbols, 25 C: empty symbols, 35 C: grey symbols. Flow rate 114 dm 3 h 1 for PL-2, 15 dm 3 h 1 for P-2).

11 482 E. Vera et al. / Journal of Membrane Science 326 (29) za 3 2 Except for conductivity at ph higher than 3.8, the simulated values of titrable acidity, ph, voltage, and energy consumption agreed with the experimental results obtained with both synthetic solutions and fruit juices. Therefore, one can assume that in case of negligible fouling, a fruit juice behaves as a simple citric acid solution with similar ph and titrable acidity. For modeling, most of the parameters were obtained from the literature, and some of them were determined from experiments performed in a laboratory-scale stack, that is, the current efficiency, electric resistance of the anion exchange membrane, and coefficients of variation with temperature. Note that the modeling applied to a pilot developing a total effective membrane area 7 times greater than the laboratory-scale stack gave results in good agreement with those experimentally obtained, particularly for energy consumption. This is important, since it means that the cost of deacidification in an industrial pilot could be evaluated from experiments performed at laboratory scale. Finally, for citric acid under the conditions evaluated, the prevailing ionic species crossing through the AEM membrane was found to be the one bearing two electrical charges. Acknowledgments ph This research was supported by the IFS, Stockholm, and the OPCW, The Hague, through the grant E3328 to E. Vera. Fig. 11. Evolution of the electrical charge of citric acid as a function of ph. If the water dissociation is neglected at the AEM, the transport number can be written as t a = 1 t inorg.anions t Na + (69) with t inorg anions, part of current transported by the inorganic anions; t Na +, part of current transported by the Na + co-ions in the ED3C configuration. Indeed, HPLC and emission spectrophotometry with ICP analyses performed in a previous study [16] showed that the inorganic anions were extracted with organic ones and that the sodium concentration increased in the juices treated with ED3C. This increase was probably due to the NaOH (.2 mol dm 3 in the C2 compartment) and NaCl (.1 mol dm 3 in the C1 compartment) dialysis arising from compartments adjacent to the juice because of the concentration gradient. Nevertheless, loss of permselectivity of the anion exchange membrane was low, and the concentration of the other cations remained constant. Results of this previous study [16] gave for the transport numbers, t inorg anions.4 and t Na +.2, showing a very low contribution of the inorganic anions and sodium ion to the current efficiency. Consequently Eq. (69) gives t a.94 and Eq. (68) gives z a An identical value of z a was obtained for the three fruit juices. Consequently, the HR 2 was the prevailing ionic form of citric acid crossing through the AEM. Previous work dealing with the transport number of sulfuric acid (HSO 4 or SO 4 2 ) also found that there was a prevailing ionic form and showed that only the sulfate ion bearing two electrical charges crossed the membrane [24]. The variation of z a vs. ph can be calculated from the distribution of citric acid species. From Fig. 11,az a of 2.16 gives a ph of 5.9. This ph value allows the determination of distribution of ionic species in the membrane as follows: 5.2% H 2 R, 71.8% HR 2, 23% R 3.Nevertheless, this result must be analyzed carefully taking into account the complexity of the membrane material. 5. Conclusions Nomenclature a distance between the grid rods (m) A constant AEM anion exchange membrane b wide of the membrane (m) BM bipolar membrane C concentration (mol dm 3 ) CEM cation exchange membrane C1, C2 electrodialysis compartments CP juice compartment d diameter of the grid rods (m) e compartment thickness (m) EC electrode compartment ED electrodialysis ED3C conventional electrodialysis with 3 compartments EDBM2C bipolar electrodialysis with 2 compartments f quotient of the activity coefficients (dimensionless) F Faraday s constant (96 5 C mol 1 ) h length of the membrane (m) H 3 R citric acid HPLC High pressure liquid chromatography i current intensity (A) I ionic strength (mol dm 3 ) j current density (A m 2 ) J a overall citric acid flux (mol h 1 m 2 ) k equilibrium constant n number of unitary cells (dimensionless) n e number of transferred electrons P-2 electrodialysis pilot-scale stack PL-2 electrodialysis laboratory-scale stack Qr reaction quotient r membrane electric resistance ( m 2 ) R gas constant (8.31 J mol 1 K 1 ) R electric resistance () S membrane area (m 2 ) S s surface of the membrane shadowed by the spacer t time (s) t i transport number of i T temperature ( C) TA titrable acidity (mol dm 3 ) U voltage (V) V volume (dm 3 ) W energy consumption (kwh mol 1 ) x molar fraction (dimensionless)

12 E. Vera et al. / Journal of Membrane Science 326 (29) X(T) z current efficiency, electric resistance or conductivity at temperature T electrochemical valence (dimensionless) Greek letters dissociation coefficient (dimensionless) T coefficient of variation with temperature activity coefficient (dimensionless) angle corresponding to the section of contact between the grid rods and the membrane (rad) conductivity (ms cm 1 ) molar conductivity (S cm 2 mol 1 ) constant (3.1416) current efficiency (dimensionless) References [1] E. Vera, J. Ruales, M. Dornier, J. Sandeaux, R. Sandeaux, G. Pourcelly, Deacidification of the clarified passion fruit juice using different configurations of electrodialysis, J. Chem. Technol. Biotechnol. 78 (23) [2] E. Vera, J. Ruales, M. Dornier, J. Sandeaux, F. Persin, G. Pourcelly, F. Vaillant, M. Reynes, Comparison of different methods for deacidification of clarified passion fruit juice, J. Food Eng. 59 (23) [3] M. Fidaleo, M. Moresi, Electrodialysis applications in the food industry, Adv. Food Nutr. Res. 51 (26) [4] E. Fontes, P. Bosander, Modelling and simulation of separation processes, Filtr. Sep. (November 2) [5] V. Nikonenko, K. Lebedev, J.A. Manzanares, G. Pourcelly, Modelling the transport of carbonic acid anions through anion-exchange membranes, Electrochim. Acta 48 (23) [6] N. Boniardi, R. Rota, G. Nano, B. Mazza, Lactic acid production by electrodialysis. Part II. Modelling, J. Appl. Electrochem. 27 (1997) [7] E.G. Lee, S.H. Moon, Y.K. Chang, I.K. Yoo, H.N. Chang, Lactic acid recovery using two-stage electrodialysis and its modelling, J. Membr. Sci. 145 (1998) [8] E. Eysmondt, V. Racki, C. Wandrey, The continuous production of acetic acid by electrodialysis integrated fermentation. Modelling and computer simulation, Chem. Biochem. Eng. 7 (3) (1993) [9] G. Kraaijeveld, V. Sumberova, S. Kuindersma, H. Wesselingh, Modelling electrodialysis using the Maxwell Stefan description, Chem. Eng. J. 57 (1995) [1] L.P. Ling, H.F. Leow, M.R. Sarmidi, Citric acid concentration by electrodialysis: ion and water transport modelling, J. Membr. Sci. 199 (22) [11] M. Fidaleo, M. Moresi, Modelling the electrodialytic recovery of sodium lactate, Biotechnol. Appl. Biochem. 4 (24) [12] M. Fidaleo, M. Moresi, Modelling of sodium acetate recovery from aqueous solutions by electrodialysis, Biotechnol. Bioeng. 91 (25) [13] M. Fidaleo, M. Moresi, Optimal strategy to model the electrodialytic recovery of a strong electrolyte, J. Membr. Sci. 26 (25) [14] M. Fidaleo, M. Moresi, Assessment of the main engineering parameters controlling the electrodialytic recovery of sodium propionate from aqueous solutions, J. Food Eng. 76 (26) [15] E. Vera, J. Sandeaux, F. Persin, G. Pourcelly, M. Dornier, J. Ruales, Deacidification of clarified tropical fruit juices by electrodialysis. Part I. Influence of operating conditions on the process performances, J. Food Eng. 78 (27) [16] E. Vera, J. Sandeaux, F. Persin, G. Pourcelly, M. Dornier, G. Piombo, J. Ruales, Deacidification of clarified tropical fruit juices by electrodialysis. Part II. Characteristics of the deacidified juices, J. Food Eng. 78 (27) [17] A. Apelblat, J. Barthel, Conductance studies on aqueous citric acid, Z. Naturforsch. 46a (1991) [18] S. Novalic, F. Jagschits, J. Okwor, K. Kulbe, Behaviour of citric acid during electrodialysis, J. Membr. Sci. 18 (1995) [19] R.A. Robinson, R.H. Stokes, Electrolyte Solutions, 2nd edition, Butterworths Publications, London, 1959, pp , , [2] T. Wen, S.S. Solt, Y.F. Sun, Modelling the cross flow spirally wound electrodialysis (SpED) process, Desalination 13 (1995) [21] S. Parker, Encyclopedia of Science and Technology, 5th edition, McGraw-Hill Companies Inc. Publications, Mexico, 25. [22] V.M.M. Lobo, Handbook of Electrolyte Solutions, Elsevier, New York, [23] D. Lide, Handbook of Chemistry and Physics, 84th edition, National Institute of Standards & Technology, Editorial CRC, U.S.A., 23. [24] Y. Lorrain, G. Pourcelly, C. Gavach, Transport mechanism of sulfuric acid through an anion exchange membrane, Desalination 19 (1997)