Effects of process factors on performances of liquid membrane-based transfer of indole-3-acetic acid

The paper has aimed at studying the transfer of indole 3-acetic acid (IAA) from a feed aqueous solution to a stripping aqueous solution of NaOH using a chloroform bulk liquid membrane and trioctylamine (TOA) as a ligand (L). Initial molar concentrations of IAA in the feed phase, cIAA,F0 (10–4–10–3 kmol/m3), of TOA in the membrane phase, cL,M0 (10–2 and 10–1 kmol/m3), and of NaOH in the stripping phase, cNaOH,S0 (10–2 and 1 kmol/m3), were selected as process factors. Their effects on the final values of IAA concentration in the feed phase (cIAA,Ff) and stripping solution (cIAA,Sf), extraction efficiency (EF), distribution coefficient (KD), and recovery efficiency (ER) were quantified using multiple regression equations. Regression coefficients were determined from experimental data, i.e., cIAA,Ff,ex = 0.02–1 × 10–4 kmol/m3, cIAA,Sf,ex = 0.22–2.58 × 10–3 kmol/m3, EF,ex = 90.0–97.9%, KD,ex = 9.0–46.6, and ER,ex = 66.5–94.2%. It was found that cIAA,F0 had the most significant positive effect on cIAA,Ff and cIAA,Sf, whereas cNaOH,S0 had a major positive effect on EF, KD, and ER. A deterministic model based on mass transfer of IAA was developed and its parameters, i.e., mass transfer coefficient of IAA-L complex in the liquid membrane (0.82–11.5 × 10–7 m/s) and extraction constant (1033.9–1779.7 m3/kmol), were regressed from experimental data. The effect of cL,M0 on both parameters was significant.

Solute transfer through systems containing liquid membranes can be significantly enhanced by adding different carriers (ligands or extraction reagents) in the liquid membrane. Mass transfer assisted by a carrier takes place as follows: (1) the carrier reacts with the target compound (solute) at the interface between feed phase and membrane phase forming a chemical complex; (2) solute-carrier complex diffuses through liquid membrane and reaches the interface between membrane and stripping phase, where the decomplexation occurs; (3) the solute is released into the stripping phase, whereas the carrier diffuses back through membrane [10][11][12]23,25,26 . A suitable carrier facilitates the solute extraction (from feed phase) and transport (through membrane phase) as well as determines its purification 24 .
Mathematical modelling is an effective tool used to predict the performances of liquid membrane-based separation 11,[17][18][19][20]28,30,31 . Process performances depend on different factors, e.g., type and initial concentration of separating species in the feed phase, type of organic solvent in the membrane phase, type and concentration of carrier in the membrane phase, type and concentration of stripping agent in the stripping phase, type of separation equipment, stirring speed, temperature, pH of feed and stripping phases, volumes of feed, membrane, and stripping phases and their contact surface areas.
The transport of IAA through a chloroform BLM using TOA as a basic (cationic) carrier was studied in this paper. Statistical models based on a 2 3 factorial plan and a deterministic model based on mass transfer of IAA were used to predict the process performances under different operation conditions. Chloroform is widely used as BLM 21,23,24,32 . It has a lower viscosity (η = 0.58 cP) than other solvents, e.g., 1,2-dichloroethane (η = 0.73 cP), nitrobenzene (η = 1.62 cP), resulting in a faster mass transfer 21 . TOA carrier can heavily improve the separation efficiency. TBP, TOPO, and TOA carriers and chloroform BLM were used in a previous study to separate IAA from dilute aqueous solutions 32 . Separation efficiency was higher for TOA carrier, due to stronger donor-acceptor interactions between IAA and TOA, as opposed to weaker hydrogen bonds between IAA and the other two carriers.

Materials and methods
Materials. IAA, chloroform, TOA, and NaOH, which were provided by Merck (Germany), were analytical grade reagents used without further purification. Three-phase system involved in the mass transfer process consists of: (1) a feed (F) aqueous solution of IAA; (2) a membrane (M) phase consisting of a chloroform BLM and TOA as a ligand (L); (3) a stripping (S) aqueous solution of NaOH.
Experimental setup and process parameters. A scheme of experimental setup used to study the transfer of IAA from the feed phase to stripping phase is shown in Fig. 1. The tube in tube setup consists of an outer glass tube, containing the feed solution (at the upper part) and membrane phase (at the bottom part), and an inner glass tube, containing the stripping solution [32][33][34] . The internal diameter of outer tube was D in = 0.042 m, whereas the external and internal diameters of inner tube were d = 0.021 m and d in = 0.019 m, respectively. The values of phase volumes were V F = 20 × 10 -6 m 3 , V M = 50 × 10 -6 m 3 , and V S = 7 × 10 -6 m 3 .
According to the schematic representation in Fig. 1, the mass transfer process in the experimental setup occurs as follows: (1) IAA diffuses through F phase towards interface between F and M phases; Mathematical modelling. Statistical models. The effects of process factors (c IAA,F0 , c NaOH,S0 , and c L,M0 ) on dependent variables (responses), i.e., c IAA,Ff , c IAA,Sf , E F , K D , and E R , were quantified using statistical models based on a 2 3 factorial plan 35,36 . According to a 2 3 factorial plan, 8 experimental runs (1-8 in Table 1) were conducted at 2 levels (inferior and superior) of process factors. Dimensionless values of process factors are given by Eqs. (1)  Table 1) were performed. Statistical models described by Eq. (7) link the process dimensionless factors, x j (j = 1..3), and their interactions (x 1 x 2 , x 1 x 3 , x 2 x 3 , and x 1 x 2 x 3 ) to the process responses, y i (i = 1..5), i.e., y 1 = c IAA,Ff × 10 4 , y 2 = c IAA,Sf × 10 3 , y 3 = E F , y 4 = K D , and y 5 = E R . Regression coefficients, β ki (k = 1..8, i = 1..5), were determined based on experimental data summarized in Table 1.
Mass transfer-based model. Some characteristic parameters of mass transfer process in the three-phase system, i.e., association constants in membrane phase (K as,M ) and feed solution (K as,F ), repartition constants of species The partial mass balance of L species in the three-phase system, considering perfectly mixed phases, is given by Eq. (12)     An increase in extraction and recovery efficiencies and distribution coefficient with an increase in c L,M0 and c NaOH,S0 was reported in the related literature 10,11,13,18,25,27,30 . A higher level of c L,M0 leads to an increase in the concentration of IAA-L complex in the membrane phase, resulting in enhanced mass transfer of this complex. On the other hand, a higher value of c NaOH,S0 determines enhanced mass transfer of IAA-L complex by increasing the concentration of L released in the membrane phase after decomplexation 10,11,13 . Moreover, a decrease in extraction and recovery efficiencies with an increase in c IAA,F0 was found by other researchers 18 .   (25) express the process responses depending on dimensionless factors and their interactions. Regression coefficients, β ki (k = 1..8, i = 1..5), which were determined by processing the experimental data presented in Table 1, are summarized in Supplementary Tables S1-S5 along with their corresponding values of standard errors (SE ki ), t statistics (t ki ), and p-values (p ki ). The coefficients that are statistically significant (p ki ≤ α = 0.05, where α is the significance level) are written in bold. Supplementary Tables S1-S5 contain also the values of multiple determination coefficient (R 2 ), adjusted R 2 (R 2 adj ), regression standard error (RSE), F statistic (F), and significance F (p-value for F).
Tabulated results indicate that Eqs.  Table 2. The mean logarithmic concentration of IAA in the feed phase, c IAA,F,m , and mean total flux of IAA, J IAA,tot,m , were calculated using Eqs. (31) and (32). Moreover, c IAA,Ff and c IAA,Sf predicted by Eqs. (21) and (22) can be used in Eqs.  Table 2, i.e., 0.382-4.418 × 10 -9 kmol/(m 2 ·s), are consistent with those estimated in other related studies 17,37 .   (Fig. 2). The levels of k IAA-L,M and K ext , which are summarized in Table 3, indicate the following issues: (1) k IAA-L,M increases with an increase in c NaOH,S0 (up to 5%) and decreases with an increase in c L,M0 (about 14 times); (2) K ext increases with an increase in c NaOH,S0 (up to 1.4 times) and c L,M0 (up to 1.7 times). The effect of x 2 and x 3 (dimensionless c NaOH,S0 and c L,M0 ) on mass transfer coefficient and extraction constant can be predicted using Eqs. (33) and (34) (R 2 = 1, RSE = 0), obtained based on data given in Table 3. Multiple regression Eq. (34) indicates an increase in extraction constant with an increase in x 2 , x 3 , and x 2 x 3 , the effect of x 3 being higher. Multiple regression Eq. (33) highlights that the effect of x 3 on y = k IAA-L,M,calc is over 30 times higher than the effects of x 2 and x 2 x 3 . Equation (35) was obtained by neglecting the contributions of x 2 and x 2 x 3 in Eq. (33). Results specified in Supplementary Table S12 indicate that Eq. (35) fits very well the data presented in Table 3 (R 2 = 0.998, R 2 adj = 0.998, RSE = 0.300, F = 1198.4, p = 8.3E−04). According to Eq. (35), the mass transfer coefficient is higher at lower levels of initial molar concentration of TOA in the membrane phase.     www.nature.com/scientificreports/ The effects of dimensionless factors on process responses, i.e., final values of molar concentration of IAA in the feed phase (c IAA,Ff ) and stripping solution (c IAA,Sf ), extraction efficiency (E F ), distribution coefficient (K D ), and recovery efficiency (E R ), were quantified using statistical models based on a 2 3 factorial plan. Experimental values of process responses were as follows: c IAA,Ff,ex = 0.02-1 × 10 -4 kmol/m 3 , c IAA,Sf,ex = 0.22-2.58 × 10 -3 kmol/m 3 , E F,ex = 90.0-97.9%, K D,ex = 9.0-46.6, and E R,ex = 66.5-94.2%. Taking into account the statistically significant factors and their interactions, the results of regression analysis indicated the following aspects: (1) all factors and their binary and ternary interactions influenced c IAA,Ff ; (2) c IAA,Sf increased with an increase in c IAA,F0 , c NaOH,S0 , and their binary interaction; (3) higher levels of E F and K D were obtained at low values of c IAA,F0 and high values of c L,M0 and c NaOH,S0 ; (4) higher levels of E R were obtained at low values of c IAA,F0 and high values of c NaOH,S0 ; (5) c IAA,F0 had the most significant (positive) effect on c IAA,Ff and c IAA,Sf , whereas c NaOH,S0 had a major (positive) effect on E F , K D , and E R . A very strong positive correlation (r = 0.95) was found between E F and K D . A deterministic model based on mass transfer of IAA in the system containing the BLM was developed and its parameters, i.e., mass transfer coefficient of IAA-L complex in the liquid membrane (k IAA-L,M = 0.82-11.5 × 10 -7 m/s) and extraction constant (K ext = 1033.91-1779.66 m 3 /kmol), were regressed from experimental data. The process factors in terms of c NaOH,S0 and c L,M0 had positive effects on K ext , whereas c L,M0 had a major negative effect on k IAA-L,M .

Conclusions
The results obtained in this study indicate that IAA was successfully transported through a chloroform BLM using TOA as a carrier. Mathematical models developed in the paper could be used to control and optimize the separation of IAA in systems containing liquid membranes.