Diffusion analysis and modeling of kinetic behavior for treatment of brine water using electrodialysis process

Fi Alkhrs ,Emn Slmn Bl Hj Hmi ,Ionnis Anstopoulos ,Zin Trlsi ,Wli Mrouk ,Nourin Ourlli Jn Frn?ois Fuvrqu

a Department of Chemistry,College of Science,Imam Abdulrahman Bin Faisal University,Dammam 31441,Saudi Arabia

b Laboratoire de Chimie Analytique et Electrochimie,D?epartement de Chimie,Universit?e de Tunis El Manar,Tunis 2092,Tunisia

c Department of Electronic Engineering,School of Engineering,Hellenic Mediterranean University,Chania 73100,Greece

d Laboratoire de Biophysique et Technologies M?edicales,Universit?e de Tunis El Manar,Tunis 1006,Tunisia

e Laboratory of Water,Membranes and Environmental Biotechnology,Soliman 8020,Tunisia

f Laboratoire d’Electrochimie Industrielle,Conservatoire National des Arts et M?etiers(CNAM)de Paris,Paris 75003,France

Received 17 December 2019;accepted 18 May 2020 Available online 17 March 2021

Abstract In this study,the removal of monovalent and divalent cations,Na+,K+,Mg2+,and Ca2+,in a diluted solution from Chott-El Jerid Lake,Tunisia,was investigated with the electrodialysis technique.The process was tested using two cation-exchange membranes:sulfonated polyether sulfone cross-linked with 10% hexamethylenediamine(HEXCl)and sulfonated polyether sulfone grafted with octylamine(S-PESOS).The commercially available membrane Nafion? was used for comparison.The results showed that Nafion? and S-PESOS membranes had similar removal behaviors,and the investigated cations were ranked in the following descending order in terms of their demineralization rates:Na+>Ca2+>Mg2+>K+.Divalent cations were more effectively removed by HEXCl than by monovalent cations.The plots based on the Weber－Morris model showed a strong linearity.This reveals that intra-particle diffusion was not the removal rate-determining step,and the removal process was controlled by two or more concurrent mechanisms.The Boyd plots did not pass through their origin,and the sole controlling step was determined by film-diffusion resistance,especially after a long period of electrodialysis.Additionally,a semi-empirical model was established to simulate the temporal variation of the treatment process,and the physical significance and values of model parameters were compared for the three membranes.The findings of this study indicate that HEXCl and S-PESOS membranes can be efficiently utilized for water softening,especially when effluents are highly loaded with calcium and magnesium ions.? 2021 Hohai University.Production and hosting by Elsevier B.V.This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

Keywords:Ionic exchange membrane;Electrodialysis;Brine water;Boyd diffusion model;Intraparticle diffusion

1.Introduction

Membranes are an essential component of electrochemical devices.Ion exchange membranes are the key components for electrodialysis;they are specifically used to remove undesirable ions from wastewater(Bel Hadj Hmida et al.,2010)and to extract toxic metal ions from effluents(Aji et al.,2017).Electrodialysis is an energy-efficient process for brackish water desalination(Patel et al.,2020)and is particularly promising for selective separation of ions from wastewater.

Several studies have been conducted concerning recovery,separation,neutralization,and concentration of either metals or acids through electro-membrane processes(Grzegorzek and Majewska-Nowak,2017).Membranes may be made from polymeric materials,either perfluorinated or not.Perfluorinated membranes,suchasNafion?,have superboxidativeandchemical resistance with a high proton electric conductivity of around 0.1 S/cm.Nevertheless,they have limited applications because of their high cost(Yee et al.,2012;Tzanetakis et al.,2003).

Different kinds of non-fluorinated membranes have been developed for uses in reverse osmosis,nano-filtration,microfiltration,ultra-filtration,electrodialysis,and fuel cell applications.These membranes compare with Nafion?ones.Examples include sulfonated-fluorinated poly(arylene ether)s(Ghassami et al.,2006)with superior membrane ion exchange capability and proton conductivity,sulfonated-polysulfoneblock-polyvinylidene fluoride(PVDF)copolymers with excellent thermal stability(Yang et al.,2004),and poly(ether ether ketone)-block-sulfonated polybutadiene(Zhao and Yin,2010).This reveals significant thermal constancy and enhanced mechanical features.In general,sulfonated polyaromatic membranes are cheap,thermally stable,and sufficiently resistant to chemical aggression.

Styrene-acrylonitrile copolymer blends have been also utilized to remove Cu(II)ions from waste effluents with the electrodialysis method(Caprarescu et al.,2015),achieving a removal rate of 70% under potentiostatic conditions.Modified montmorillonite-based polyethersulfone membranes have been used to investigate the removal of zinc ions from wastewater via a small-scale electrodialysis technique(Caprarescu et al.,2017).The tailored montmorillonite enhanced the separation effectiveness of final membranes.Caprarescu et al.(2018)tested membranes injected with natural fruit extracts for the removal of crystal violet from solution.The treatment process was conducted in electrodialysis cells at fixed voltage of 15 V.Approximately 96%of dye removal was obtained at 90 min,and the used membranes were stable up to 330°C.

The separation of monovalent and divalent ions from aqueous effluent is a persistent issue in industrial uses,particularly in regions where water salinity is significant.A distinct context is the production of drinking water.Calcium and magnesium cations should be partially removed to obtain suitable soft water.Alternatively,500 mg/L of total dissolved salts in drinking water is the lowest amount for human health.Therefore,the production of drinking water involves the removal of cations that cause water hardness(such as calcium and magnesium)and monovalent ions,and the latter are required to preserve the least amount of salinity.

Chott El-Jerid Lake,with a total surface of 5000 km2,is a dry salt lake in the southwest of Tunisia,close to the Algerian border.It should be noted that Chott El-Jerid Lake was a part of the Mediterranean Sea several thousand years ago.At present,Chott El-Jerid Lake collects water from the Northwest Mountains,which percolates through dry soils.The ionic composition of water in Chott El-Jerid Lake is representative of the brine collected from the wells in Southeast Tunisia,which has been diluted more than 100 times.

This study investigated the treatment of actual water containing monovalent and divalent cations,including Na+,K+,Mg2+,and Ca2+,with the electrodialysis method.Pristine water was obtained in winter from Chott El-Jerid Lake.The process was performed using a Hittorf cell along with two electrodes in platinized titanium with a galvanostatic mode,and the efficiency was tested using the two recently developed cation-exchange membranes.Diffusion analysis of the removal process was conducted,and the kinetic characteristics are discussed below.The removal process was also simulated with a semi-empirical model.

2.Materials and methods

2.1.Solid polymer electrolytes

Three types of cation-exchange membrane(CEM)were selected for this study.The sulfonated polyether sulfone crosslinked with 10% hexamethylenediamine(HEXCl)and sulfonated polyether sulfone grafted with octylamine(S-PESOS)(Mabrouk et al.,2011)were obtained from the French chemical group ERAS-Labo,situated in Saint-Nazaire-L‵es-Eymes.Nafion?membrane is commercially available.S-PESOS and HEXCl membranes have high perm-selectivity,low electrical resistance,and high mechanical and chemical stability.The polymeric anion-exchange membrane(PAEM)was used as an anionic exchange membrane as well(Bel Hadj Hmida et al.,2010).

2.1.1.S-PESOS

Sulfonated poly arylene ether sulfone(SPES)has received extensive attention in membrane synthesis due to the proton exchange membrane fuel cell technique.However,there are some difficulties involved in handling these materials,and weakness and solubility have been observed during the heating process(Iojoiu et al.,2006).New materials using SPES embedded with different octylamine ratios were investigated(Mabrouk et al.,2012).Octylamine grafting depressed their water solubility and increased their softness and manageability.Ionic conductivity is dependent on the grafting rate.A membrane made from a polymer containing one sulfonated group per monomeric unit and 0.3 octyl sulfonamide group grafted per monomeric unit was chosen.The proton conductivity of this membrane was close to that of 1.0-mol/L H2SO4.Proton transport numbers were found to be near unity.This membrane is not cross-linked but is insoluble in water.However,it is soluble in polar aprotic solvents such as dimethylacetamide.

2.1.2.HEXCl

The sulfonated polyether sulfone,cross-linked with 10%HEXCl,is a new membrane prepared from polyether sulfone sulfochloride and from hexamethylenediamine.It has been cross-linked with an original method at low temperature using 1,6-hexamethylenediamine(Mabrouk et al.,2011).The water content when equilibrated in pure water was determined to be 54%.The sulfonation rate was close to be 1.10 mmol/g.The ionic protonic transport number determined by the Hittorf method was equal to 1.0.The polymeric material contains one free sulfonated group per monomeric unit,which is as same as S-PESOS.Being cross-linked,the membrane is insoluble in water and polar solvents.Its ionic conductivity is similar to that of S-PESOS.A higher rate of cross-linking tends to depress ionic conductivity and increase brittleness.

2.1.3.Nafion?

At the end of the 1960s,DuPont(Koryta et al.,1993)improved films based on Nafion?,which consists of perfluoro-sulfonic acid along with hydrophobic fluorocarbon spine and hydrophilic sulfonic acid pendant side chains.This Nafion-based film was mainly utilized as a perm-selective barrier in chlor-alkali electrolyses(Springer et al.,1991;Gottesfeld and Zawodzinski,1997).Nafion?membranes were commonly applied in polymer electrolyte fuel cells because of their superior proton conductivity and mild distention in water(Sahu et al.,2016;Mauritz and Moore,2004).This membrane was used with an equivalent weight of 1100 g/mol and a thickness of 178μm.Nafion?membranes have a high degree of sulfonation,leading to better removal of monovalent ions such as Na+and K+.The arrangement of hydrophilic/hydrophobic phase-separated structures in Nafion?can produce effective proton conduction(Mauritz and Moore,2004).

2.1.4.PAEM

PAEM,which was lately developed by Mabrouk et al.(2011),is easily prepared with excellent features that can be exploited in huge electrodialysis plants.Accordingly,PAEM has been recently utilized to separate nitrate anions from aquatic media(Bel Hadj Hmida et al.,2010).The anion-exchange film showed strong selectivity as compared with acetate anions removal.Anion-exchange films with a thickness of approximately 80μm were synthesized with a quaternization of poly(epichlorohydrin)(H55,Z?eon Chemicals)with 1,4-diazabicyclo[2.2.2]octane(Dabco,Aldrich),which was mentioned in Vassal et al.(1999).The electrochemical impedance and potentiometric methods were used to analyze the ionic conductivity of PAEM,and the transport numbers were determined with the Hittorf and Henderson methods.The water content and ion-exchange capacity(IEC)were measured as well.IEC was computed to be 0.56 mmol/g(Agel et al.,2001)whereas ionic conductivity was found to reach 10 mS/cm in potassium hydroxide aqueous solutions with a molar concentration range of 0.5－6.0 M at 273.15 K.The values of the Henderson transport number were higher than 0.95.By contrast,the Hittorf method provided superior values,in the range of 0.99－1.00.The water content was measured to be 13.0%－18.0%.Table 1 demonstrates the properties of the four membranes in this study.

2.2.Electrodialysis system of aqueous solution from Chott El-Jerid Lake

As shown in Fig.1,the electrodialysis cell was filled with the solutions from Chott El-Jerid Lake(55,30,and 40 mL in the central,cathodic,and anodic compartments,respectively),which were diluted 100 times.For actual solutions from Chott El-Jerid Lake,the initial pH value was 7.16 at 25°C.Table 2 shows the average composition of ions in the solutions.

A current intensity(j)of 50 mA was applied in each experiment.As an electrical field was established on the electrodialysis cell,the ions of the cathode moved around the cathodic part,whereas the chloride ions were transported into the anodic section.The subsequent electrolytic reduction of water molecules in the cathodic section produced hydrogen as presented in Eq.(1):

By contrast,the formed hydroxide ions neutralized the oncoming sodium ions to create soda.In the anodic part,water molecules were oxidized to oxygen and hydrogen ions as shown in Eq.(2):

This process generated hydrochloric acid together with the chloride ions transferred from the central compartment across the anion-exchange film.The height of the solution in the middle compartment was found to partially fall,while it rose in the cathodic and anodic parts.The hydration of ions migrating throughout the anion-exchange films explains this occurrence(Banasiak and Sch¨afer,2009).

3.Results and discussion

To determine the capability of the studied membrane films to selectively transport monovalent and divalent ions from aqueous solution in Chott El-Jerid Lake,the concentrations of sodium,potassium,magnesium,and calcium in the middle compartment during the electrodialysis process were studied with the variation of time.

3.1.Treatment of sodium and potassium cations using three membranes

Throughout the process,the cation concentration efficiently decreased as time went by.The demineralization operation ofthe solution in the diluted(middle)section was investigated,with regard to the reduction in positive ion contents.In the solution,sodium ions were the major cation,and lithium was observed as traces.Fig.2 shows the concentrations of potassium and sodium against time during 125-min electrodialysis in the diluted central compartment using the three membranes.

Table 1Properties of four membranes in this study.

Fig.1.Photo of electrodialysis cell.

Sodium ions were the main cation for transfer through electrodialysis in the diluted solution from Chott El-Jerid Lake.The quantity of transferred sodium was about ten times higher than that of potassium for HEXCl and eight times higher for the S-PESOS and Nafion?membranes.In terms ofmigrated equivalence,this represented 15.2,21.0,and 23.7 mmol/L of sodium and 1.5,2.7,and 2.9 mmol/L of potassium for HEXCl,S-PESOS,and Nafion?,respectively.An inverse phenomenon was obtained by Bessi‵ere et al.(1999).They studied three cationic membranes and found that Nafion?demonstrated an ionic strength of 0.1 mol/L,and that the affinity for K+was higher than that for Na+,followed by Li+.Their findings may be attributed to the fact that the membrane prefers the ions with the weakest molar hydrated volume(Chaabouni et al.,2015;Maining and Melshelmer,1983).In this study,the water was natural and richer in Na+than in K+.This can explain the difference between the results from this study and those from Bessi‵ere et al.(1999).

Table 2Average characteristics of diluted solutions from Chott El-Jerid Lake.

The electrical mobility and conductivity of potassium in pure diluted water are higher than those of sodium.At 25°C,the molar conductivities of sodium and potassium were 50.1 and 74.5 S˙cm2/mol,respectively,and the electrical mobilities were 0.52 and 0.76 cm/s,respectively(Robinson et al.,1970).However,the higher initial mobility of sodium ions in the membranes from the solution can be attributed to the high concentration of sodium ions(1 087.5 mg/L)that partially prohibited potassium ions(335.5 mg/L)(Table 2).

Fig.2 demonstrates the estimated mass of cations in the diluted solution at the beginning and end of treatment.Clearly,Nafion?was the best membrane in terms of removing both sodium and potassium cations,of the three studied membranes.Nafion?is usually considered the reference membrane.Indeed,grafting of sulfonic acid groups to exact chain fragments in the polymer was shown to produce the configuration of clear hydrophilic/hydrophobic phase-separated structures(as with the Nafion?membrane),leading to effective proton conduction(Matsumoto et al.,2009;Jutemar and Jannasch,2010).Afterward,the high degree of sulfonation in the Nafion?membrane worked to improve water uptake and thus enhanced proton conduction.

Fig.2.Changes in concentrations of remaining mono-ions(Na+and K+)and divalent ions(Ca2+and Mg2+)in diluted solution from Chott El-Jerid Lake as a function of time using three membranes(pH=7.16,T=25°C,and j=50 mA,where T is the temperature).

The average demineralization rates of sodium and potassium were 31.22%,45.76%,and 51.96% for HEXCl,SPESOS,and Nafion?membranes,respectively.This also confirms that Nafion?is the best membrane in terms of removing both sodium and potassium cations.Shee et al.(2008)and Shee and Bazinet(2009)found that the average demineralization rate was 53% for a demineralized chitooligomer solution with a current intensity of 10 mA and a 60-min electrodialysis time.

3.2.Treatment of calcium and magnesium ions using three membranes

Fig.2 also gives the results of calcium and magnesium ions in the treated water.The mobility,conductivity,and hydration play important roles in explaining the differences in the removal rates and fluxes of Ca2+and Mg2+through cationexchange membranes.Ca2+is less hydrated than Mg2+.Ca2+may be separated from its hydrated layer(Tansel et al.,2006)and transferred via the cation-exchange membrane more easily.Meanwhile,the ionic mobilities in pure water were 61.65×10－9and 55.0×10－9m2/(s˙V)for Ca2+and Mg2+,respectively(Strathmann,2004).This agrees with the difference in the removal rate of cations.

As with the cases of sodium and potassium ions,Nafion?is the best membrane in removing calcium cations(Fig.2).The same behavior was also found for magnesium ions(Fig.2).Table 3 demonstrates that the concentrations of sodium,potassium,calcium,and magnesium significantly declined after 125 min of electrodialysis.For S-PESOS and Nafion?,the investigated cations were ranked in the following descending order in terms of their demineralization rates:Na+>Ca2+>Mg2+>K+.The main driving force impacting the monovalent ions was the large difference in ion concentration(Na+>K+),whereas low molar hydrated volume was dominant for divalent ions(Ca2+>Mg2+).For the K+,Ca2+,and Mg2+system,the membranes were more selective for divalent ions than for potassium ions.As the ion charge increased,the affinity of the membrane rose,and the electrostatic attraction increased as well,owing to the high ionvalence(Chaabouni et al.,2015).Additionally,the divalent cations were more effectively removed by the HEXCl membrane than the monovalent ones(Na+and K+).This difference can be attributed to the lower chain mobility in the membrane.Notably,the three membranes do not have the same structure and properties(Table 1).HEXCl is the only one that is crosslinked,and its water content is much higher(52.80%)than those of S-PESOS(21.96%)and Nafion?(35.00%).High water content may destruct the mechanical property of the membrane and cannot provide sufficient ionic conductivity.The Nafion?membrane displays both the highest IEC and conductivity,thereby leading to the highest demineralization rate.

Table 3Average demineralization rates of Na+,K+,Ca2+,and Mg2+using three membranes after 125-min electrodialysis.

3.3.Diffusion analysis of electrodialysis process

The analysis of removal rate for a certain system is an important phase in the design of removal processes.Metal ion removal using different materials(membranes)involves several successive steps:(1)solute mass transfer in bulk solution,which is considered a fast process;(2)solute diffusion through solution film across the material particles,namely,external film diffusion;(3)solute mass transfer within material particles,namely,intraparticle diffusion;and(4)solute interface or attachment either physically or chemically onto a matrix(Lima et al.,2015).Typically,the last step is very fast in comparison with the previous steps,and the final removal rate is largely determined by the second or the third steps,depending on which step is slower,or an integration of both steps(Valderrama et al.,2008).Accordingly,the Boyd intraparticle diffusion model and Weber－Morris kinetic model were utilized to identify which step was the rate-determining step and whether intraparticle diffusion or external film diffusion controlled the removal rate.The Weber－Morris kinetic model is as follows:

whereqtis the removal capacity(mg/g)at timet,Kidis the intra-particle diffusion rate constant(mg/(g˙min0.5)),andCis a constant with its value proportional to the boundary layer(mg/g).

The experimental data were fitted by the Weber－Morris kinetic model.Figs.3 and 4 show that none of the plots ofqtversust0.5passedthroughtheir origin withoutthey-interceptbeing equal(or close)to zero.The negativey-intercept indicates the effect of high resistance of external film diffusion(McKay,1983).However,the Weber－Morris plots for all cations demonstrated linearity in thet0.5range of 3－8 min0.5.This indicates that intraparticle diffusion was not the rate-determining step,and the removalprocessmightbecontrolledbytwoormoresimultaneous mechanisms.More importantly,for all the studied ions,theKidvalue obtained with Nafion?was higher than that with S-PESOS,followed by that of HEXCl.This can be attributed to the more rapid mass transfer of monovalent and divalent ions through the membrane structure.

Fig.3.Plots of Weber－Morris model for removal of Na+and K+using three membranes(pH=7.16,T=25°C,and j=50 mA).

Fig.4.Plots of Weber－Morris model for removal of Ca2+and Mg2+using three membranes(pH=7.16,T=25°C,and j=50 mA).

The experimental data were fitted by the Boyd diffusion model(Viegas et al.,2014),which is expressed by

whereFtrefers to fractional attainment of equilibrium at timet,qerepresents solid-phase concentration in equilibrium,andBtdenotes the Boyd parameter.According to this model,intraparticle diffusion is the removal rate-determining step when the plot ofBtversus timetdisplays a straight line and crosses its origin.If the Boyd plot does not cross the origin or is far away from linearity,the controlling step is determined by film diffusion resistance.Figs.5 and 6 show thatBthad a linear relationship withtfor the studied ions using the three membranes.They-intercept values from zero clearly show that film diffusion was the determining step in the removal process through the membrane matrix.Additionally,the Boyd plots had two linear segments with a significant difference in intercept values.In the first segment with zeroy-intercept values,the removal process was controlled by a combination of intraparticle diffusion with film diffusion resistance,and intraparticle diffusion was dominant.After 60 min of electrodialysis,the process was completely driven by film diffusion.

The rate-determining step verifies the practical conditions needed to develop the removal process.When film diffusion controls the removal process,the mixing and turbulence of the solution should be improved.When intraparticle diffusion is dominant,fine membrane structures should be exploited.

3.4.Simulation of electrodialysis via semi-empirical model

For the 125-min electrodialysis,empirical models were used to investigate the kinetic behavior of the electrodialysis process for the four cations using the three membranes.The removal rateRtat timetcan be calculated as follows:

whereC0andCtare the initial concentration and the concentration at timet,respectively.At final timetf,the final concentrationCfcan be experimentally determined to be slightly lower than the concentration at equilibrium(Ce),where the removal rate reaches its maximal value(Rmax),andRmaxis expressed as

Fig.5.Plots of Boyd model for removal of Na+and K+using three membranes(pH=7.16,T=25°C,and j=50 mA).

According to the temporal variation of electrodialysisbased removals of Na+,K+,Ca2+,and Mg2+(see the supplementary data),a slight change of curvature(inflection point)was found at approximately(10±1.5)min.Therefore,a cubic polynomial should at least be used to establish the relationship between removal rate and time,which is given as follows:

whereα,β,γ,andδare the coefficients for the cubic polynomial.Nevertheless,with regard to the boundary conditions such asRt,starting from zero and reaching a maximum value(Rmax)aftertf,a semi-empirical model was used to investigate the dimension equation and estimate the significance of eventual parameters:

wheret0,t1,andтare the time parameters(min).Table 4 presents the estimated parameter values of the semiempirical model for simulation of the removal of Na+,K+,Ca2+,and Mg2+using the three membranes.

The proposed semi-empirical model(Eq.(9))shows that at timet′,when the inflection point appeared(see the supplementary data),the removal rate reached its maximum value(Fig.7),andt′is expressed as follows:

It should be noted that the semi-empirical model has a limited validity domain(t?[0,tL]),where at the upper limiting time(tL)the removal rate reaches its maximum value(RL),andRLandtLare expressed as follows:

Therefore,RLshould be identical to the equilibrium value.However,in the case oft>tL,theRtvalue estimated from Eq.(9)tends to decrease,and the semi-empirical model no longer describes the phenomenon that should indicate the equilibrium state.Moreover,whent=tL,Rtwill be equal toRL.Therefore,the semi-empirical model was revised to be a piecewise continuous function:

Fig.6.Plots of Boyd model for removal of Ca2+and Mg2+using three membranes(pH=7.16,T=25°C,and j=50 mA).

Table 4Estimated parameter values of semi-empirical model for simulating removal of Na+,K+,Ca2+,and Mg2+using three membranes.

Additionally,allтvalues in Table 2 were found to be slightly close to the final experimental time(tf=125 min).Therefore,the final experimental time is equivalent to the time constant in kinetic process and is in causal correlation with the experimental equilibrium duration when the removal rate practically reaches its maximum value.Moreover,theтandRmaxdata pair in Table 4 showed an interesting duality.This should be an important criterion for optimal and economic choice of ions for removal by electrodialysis and of membranes for use.

Moreover,all electrodialysis processes exhibited similar kinetic behavior for all ions and membranes.As indicated in Fig.7,the chemical process started with a non-null rate,and it was slowly accelerated since the initial time,and then decreased to reach a very low removal rate value near equilibrium.In fact,as clearly observed in Fig.7,the rate of the electrodialysis process is decreased by time toward a null value.It is expected that the variation amount of ion concentration approaches very small values at infinite time.

Fig.7.Chemical removal rate of Mg2+versus time using Nafion?membrane(pH=7.16,T=25°C,and j=50 mA).

Nevertheless,the slight increase in the removal rate in a short time period from the beginning of the electrodialysis process(t′≤10 min)indicated that the removal was very slightly accelerated before the intra-diffusion phenomenon occurred.This effect can be confirmed by the Boyd kinetics during the first time range(Figs.5 and 6).

4.Conclusions

This study focused on the cationic treatment of the diluted solution from Chott El-Jerid Lake in Tunisia via electrodialysis using two recently developed cation-exchange membranes:HEXCl and S-PESOS.Their removal capacities were compared with that of the commercial membrane Nafion?.The treatment process was carried out under the conditions of pH=7.16,T=25°C,and a 50-mA current intensity for a dialysis duration of 125 min.With the S-PESOS membrane,the investigated cations were ranked in the following descending order in terms of their demineralization rates:Na+>Ca2+>Mg2+>K+.By contrast,the divalent cations were better treated using the HEXCl membrane.The Weber－Morris model revealed that intra-particle diffusion was not the only removal rate-determining step,and the treatment process was controlled by two or more concurrent mechanisms.Meanwhile,the Boyd diffusion model plots did not cross the origin,demonstrating that the sole controlling step was determined by film-diffusion resistance,particularly at an extended dialysis time.A semi-empirical model was developed to analyze the degree of modeling the temporal variation of the ion removal rate,and an ion-membrane characteristic time parameter was adopted to evaluate the experimental equilibrium duration for each ion and membrane.The kinetic modeling found that the removal rate slightly increased over a short time period from the beginning of electrodialysis.This finding indicated that the removal process was mildly accelerated before intra-diffusion occurred.

Acknowledgements

The authors are grateful to Imam Abdulrahman Bin Faisal University and Tunis El Manar University for providing facilities and encouragement.

Appendix A.Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.wse.2020.05.002.

Declaration of competing interest

The authors declare no conflicts of interest.