Jogi Ganesh Dattatreya Tadimeti, Anusha Chandra and Sujay Chattopadhyay^{*}  
Polymer and Process Engineering Department, I.I.T.Roorkee, SRE Campus, UP247 001, India  
Corresponding Author :  Sujay Chattopadhyay Polymer and Process Engineering Department I.I.T.Roorkee, SRE Campus UP247 001, India Tel: 919568189000 Email: [email protected]; [email protected] 

Received January 22, 2015; Accepted February 16, 2015; Published February 24, 2015  
Citation: Tadimeti JGD, Chandra A, Chattopadhyay S (2015) Optimum Concentrate Stream Concentration in CaCl2 Removal from Sugar Solution Using Electrodialysis. J Chem Eng Process Technol 6:216. doi:10.4172/21577048.1000216  
Copyright: © 2015 Tadimeti JGD et al. This is an openaccess article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.  
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Batch electrodialysis (ED) with continuous recirculation was carried out to remove CaCl2 from sugar solution at room temperature. Role of limiting process parameters e.g. (i) concentrate concentration, (ii) sugar mass% cum solution viscosity and (iii) ionic conductivity on electrolyte removal rate were investigated. Unsteady state mass balance defining ion transport through the ED cell with its initial and boundary conditions were solved with linearized Nernst Planck equation. A new Sherwood number expression appropriate to the cell geometry and process parameters (physical properties and conductivity ratios) is developed as . . . Ë Ë d b c Dil Conc Sh a Re Sc = to estimate mass transfer coefficients and ionic flux. Electrolyte removal percentage can’t be correctly estimated from ED cell current instead model based estimates of the flux components due to concentration gradient (chemical potential) and applied electric potential could closely predict the experimental data on electrolyte removal. The ratios of electrolytes removal rates (with and without sugar) can be expressed as power function of viscosity ratios as 0.28 c DSC DSC C percentremoval percentremoval μ μ = . This factor of 0.28~0.3 resembles close similarity with Sc number in the Sh number correlation, indicating that the removal rate is a strong function of flow and physical properties of the system. An optimum electrolyte concentration of concentrate, sugar mass% in diluate, and applied electric potential was estimated.
Keywords  
Electro dialysis; Solution conductivity; Mass transfer coefficient; Ionic flux; Specific energy consumption  
Introduction  
Presence of excess calcium in the post floculation and precipitation stage of clarified sugar juice creates series of nuisence [1] to sugar industries affecting product quality (listed below). Therefore, removal of it at appropriate stage would drastically reduce operation and maintainence cost and improve product quality. [1]  
1. Scale formation in the evaporators  
2. Improper crystallization  
3. Molasses percentage may increase due to inversion of sugar in alkaline medium  
4. Storage is hampered because of hygroscopic nature of these metal ions  
5. Excess calcium is not hygienic as well  
Application of electrodialysis (ED) is propsoed to remove the dissolved calcium ions (commonly as CaCl_{2}). Electrodialysis (ED) is a polar (cation and anion exchange) membrane based ion removal technique driven by externally applied electric potential as the main driving force. Briefly, the diluate (feed solution) containing electrolyte(s) is placed between two oppositely charged membranes through which the dissociated ions get selectively permeated. CaCl_{2} (strong electrolyte) removal via electrolydialysis could be quite interesting to explore from industry point of view. Earlier electrodialysis (ED) was applied in sugar industry to recover speciality chemicals e.g. tartrate and malate from grape sugar [2], and in demineralisation of beet sugar syrup, juice and molasses [3,4]. Major technical obstacles arose due to poor membrane stability at higher temperatures commonly maintained to reduce solution viscositypumping cost and fouling due to deposition of organic molecules (sugars, proteins etc.). Difference in ionic mobility in solution and membrane causes drop in counterion concentration at the membrane surface, which causes concentration polarization and adds up complexity to the existing difficulties [511]  
In a batch recirculation ED process diluate and concentrate streams get depleted and enriched respectively with time. With increase in electrolyte concentration in the concentrate channel, back diffusion (from concentrate to diluate stream) appears affecting overall ion removal percentage. With a given diluate stream concentration, initially the current density increases with applied electric potential. Finally, it reaches a limiting value at an electric potential where no excess ions are available to transport current in solution, thus, concentration drops to zero (theoretically) at membrane surface. This is called limiting current density. Applying an electric potential above this value would result in electrolysis of water and generating H+ and OH ions. In batch recirculation mode, the diluate stream is recycled back to the ED cell to remove left over ions, therefore, gradual lowering of concentration of diluate stream occurs. Unlike continuous electrodialysis the current density keeps changing with time as is with the electrolyte concentration. Energy wastage due to water spliting is avoided by restricting current density below limiting value. Modeling of batch ED with continuous recirculation becomes more challenging as streams’ electrolyte concentration changes with time. Commonly Ohm’s law is applied [1215] to evaluate current based on overall applied electric potential and resistances. But, it fails to predict several experimental current density majorly governed by ionic diffusion process, which limits the maximum magnitude of current for an applied voltage. Wen et al. [16] experimentally verified this fact and concluded that rise in ohmic resistance with lowering of diluate concentration is not significant and claimed that back emf (due to concentration polarization across the membrane) generation reduced the effective applied electric potential across the cell pair. Theoretical estimate of back emf becomes difficult due to nonavialability of correct procedure. This ensured that a model probably from first principles would give us appropriate estimation of ion flux. Linearized NernstPlank flux equation (formulated from first principles) provided closure prediction of current density and ion flux and can quantitatively estimate drop in ion concentration. The entire batch operation was subdivided into small multiple equilibrium steps involved in irreversible thermodynamics [17].  
Kabay et al. [18] carried out batch removal of bivalent Ca^{2+} and Mg^{2+} ions under constant applied DC potentials (3 V,5 V and 10 V) and flowrates (0.6, 1.2 and 1.8 L.min^{1}) and compared energy consumptions. Although time of operation is reduced with applied electric potential but energy consumption has increased. While, flow rate variation did not show much effect on ion removal rate. Several studies [2,18] are reported on Ca^{2+} ion removal using batch recirculation electrodialysis but, role of concentrate concentration on ion removal rate was not emphasized adequately. Herein, we tried to explore few querries: (i) Is there any optimum concentrate concentration for a given diluate composition? (ii) Is there any role of non electrolyte and its concentration (density and viscosity) on ion removal rate and energy consumption? (iii) Can we theoretically model the ion transport and estimate the transport properties? (iv) Is there a generalization possible? To the best of our knowledge, answers to these questions lacks clarity and quantitativeness. Answers to these issues might give a better insight to ion transport mechanism and optimize concentrate compartment.  
In cane based sugar industry concentration of sugar in the juice after clarification step (after lime treatment and color removal) commonly reaches ~5% (mass basis). CaCl_{2} concentration is chosen based on free lime concentration left in clarified juice and the stream entering into evaporator. Role of non electrolyte (sugar), concentrate concentration and CaCl_{2} viscosity on removal were investigated. A model accounting all experimental observations was used to estimate transport properties involved.  
Materials and Methods  
Equipment  
Electro dialysis setup: The experimental setup layout used for Electrodialysis (ED) application is shown in Figure 1. The ED cell assembly was tailor made in the laboratory and graphite sheets were used as electrodes (0.08×0.04 m^{2}). An electric DC potential was applied across the cell stack (consisted of two cell pairs containing a concentrate and a diluate channel each.) through a builtin DC source. Voltage and current between two electrodes were continually monitored through a builtin digital voltmeter and ammeter respectively. Cross linked Styrenedivinyl benzene copolymer membranes were obtained from Permionics Ltd. India and used as ion exchange membranes. The properties of the membranes were listed in Table 1. Experiments were performed at a constant applied electric potential of 4 V and a fixed flowrate for all streams.  
Power Supply: The power supply was provided through a voltage stabilizer of 110/220 V AC with 5080 Hz frequency. The same gave an output voltage 020 V DC and had an ammeter that can measure currents from 0200 mA. Three centrifugal pumps were inbuilt with the system for pumping the solution.  
Conductivity Measurement: Solution conductivity was noted at regular interval through an off line Conductivity and TDS meter CM183 from Elico India.  
ED Cell Compartments and Solutions Used: 1000 ml solutions of each stream (concentrate, diluate and Electrode rinsing solution (ERS)) were taken in three tanks (Figure 1) respectively. Each solution tank was connected with its respective flow points of the ED unit through flexi tubing. Solutions were circulated at a constant rate by three centrifugal pumps and the solution flow rates were measured using rotameters connected to each stream. The detailed concentrations of different electrolyte streams were reported in Table 2. Concentrate and diluate solutions were always prepared using deionized water (conductivity <10.0 μS). Electrodialysis experiments were carried out in three sets. (i) DSC1DSC6 (diluate stream having 25 mol.m^{3} CaCl_{2} and 5 mass% sugar and six different concentrate streams having CaCl_{2} concentrations varying as 5, 10, 20, 25, 30, and 40 mol.m^{3}), (ii) C1C6 (diluate stream having 25 mol.m^{3} CaCl_{2} and six different concentrate streams with CaCl_{2} concentrations as 5, 10, 20, 25, 30, and 40 mol.m^{3}) and (iii) S1S4 (4 different diluate streams with 25 mol.m^{3} CaCl_{2} with amount of sugar varying from 520 mass% and concentrate stream having concentration of 25 mol.m^{3} CaCl_{2}). For convenience DSC4 is renamed as S1 (5 mass% sugar) as both the experiments are identical and other values of sugar concentration are defined as S2 (10 mass% sugar), S3 (15 mass% sugar) and S4 (20 mass% sugar). Detailed information was reported in Table 2. Aqueous solution of NaCl (50 mol.m^{3}) was used as ERS in all experiments (Table 2). The detailed specifications of ED unit are indicated in Table 3.  
Limiting current density (LCD): LCD of the ED cell was estimated using the method reported in the literature [5,15] by plotting cell resistance (V/I) vs. inverse of current (1/I).  
Viscosity measurement: Ubbelhood viscometer was fitted in a constant temperature bath to measure solution viscosity at a desired temperature (±1°C). Sugar concentration was varied between 020 mass%, while CaCl_{2} concentration was varied between 050 mol.m^{3} to estimate the solution viscosity.  
Modelling of ion transport: Current density and LCD (limiting current density) of an ED cell is a function of series of parameters e.g. flow (cell geometry, flow dynamics, spacer orientation, solution density and viscosity) and physical (ion concentration, transport number and diffusivity) parameters for a given set of membrane pairs. Precise estimation of these parameters and application of NernstPlank equation (assuming zero ion concentration on the membrane surface) would give a theoretical estimate of LCD which can be determined experimentally from plot of V/I vs. 1/I [5,6].  
Determination of bulk concentration of diluate compartment  
The ED process was carried out well below LCD all through.  
The concentration of ion can be obtained from unsteady mass balance across diluate, concentrate, and electrode compartments. The unsteady state mass balance equation was formulated based on the assumptions already mentioned in the literature [12].  
The mass balance equations for diluate and concentrate compartments in the ED cell are written as [12,13]  
(1)  
(2)  
Where, , are the volumes of diluate and concentrate compartments (m^{3}) respectively, N is number of cell pairs, t is time (s), and represents diluate concentrations, leaving diluate feed tank and leaving diluate cell compartment (mol.m^{3}) respectively, and represents diluate concentrations, leaving concentrate feed tank and leaving concentrate cell compartment (mol.m^{3}) respectively, and , are the diluate and concentrate streams volumetric flow rate (m3.s^{1}), the current efficiency, t is the current density (A.m^{2}), is the effective membrane area (m^{2}).  
can be estimated from the following equation [12,13]:  
(3)  
Where, s the transportnumber of cations in cation exchange membranes and is the transportnumber of anions in anion exchange membrane.  
Similarly, unsteady state mass balance around feed tank can be written as  
(4)  
(5)  
Where and are volumes of concentrate and diluate feed tanks (m3) respectively. During electrodialysis water transport occurs across the membranes due to electroosmosis and osmosis [13]. In the present work volume change (due to water transport) is ignored as there was no major net volume change observed (concentrate and diluate compartments) experimentally.  
Determination of the current density  
Overall flux equation :The current density was estimated using following assumptions (usually valid for all practical situations) [13]. The solution between the two membranes was assumed, thoroughly mixed to ensure uniform concentration throughout. Stationary membrane surfaces leads to the formation of static boundary layer whose thickness is mainly governed by solution viscosity and existing turbulence. Fluid flow alone can determine the boundary layer thickness [5]. Ion transport due to convection was ignored [19] because the direction of ion transport was perpendicular to the direction of the flow. Transmembrane pressure was assumed to be zero. Stable boundary layers are formed along the concentrate and diluate compartments of the membrane due to difference in viscosity of feed and concentrate solution. The current density can be estimated from mass balance equation either for cations through CEM or anions through AEM, assuming overall (sum) transport numbers to be unity. The flux of ions passing through the membrane can be expressed by generalized Nernst Plank equation as [5]  
(6)  
Where, x is the distance measured from boundary layer in contact with the diluate channel towards the membrane, is the diffusivity of ion j (either cation or anion) (m^{2}.s^{1}), ‘ is the concentration of ion j (mol.m^{3}), ‘R’ is the universal gas constant (8.314 J.mol^{1}.K^{1}), ‘T’ is the temperature (K), ‘z_{j}’ is the charge of diffusing species j, and N_{j} is the electric potential gradient (V.m^{1}) and F is the faradays constant (Columb.geqv^{1}).  
The total molar flux of ion ‘j’ through the ion exchange membrane, can be related to the current density, i as  
(7)  
The subscript m denotes either AEM or CEM, is the transport number of ion ‘j’ in the membrane, i is current per unit area of membrane or current density (A.m2) and is the charge of the ion.  
At steady state and are equal, i.e.:  
(8)  
Assuming that a linear profile of the concentration distribution exists along the boundary layer, the linearized NernstPlanck equation could be used instead of Eq. (8). Expression for the linearized Nernst Planck equation when applied in the diluate chamber is [5]:  
(9)  
Where, δ is the boundary layer thickness (m), and are concentrations of ions in bulk and at the membrane surface respectively of the diluate compartment, while is the electric potential gradient (V.m^{1}) and is expressed as  
(10)  
where, δ is the boundary layer thickness.  
In Eq. (9) the first part, i.e., denotes contribution due to molecular diffusion while the second part i.e., reflects the effect of voltage on iontransfer through the membrane  
Boundary layer thickness, δ estimation: δ is estimated using film theory (Eq. (11)) [5,20] and salt masstransfer coefficient. Salt masstransfer coefficient is usually determined based on salt diffusivity and suitable masstransfer correlation, which inturn is dependent on flow profile and physical properties of the fluids, cell geometry, surface morphology of membranes used in ED cell [5,6,19,21,22].  
(11)  
Where, k and k are diffusivity and mass transfer coefficient of diffusing species in solution. Each of these parameters were separately estimated using standard correlations. The mass transfer coefficient was obtained from Sherwood number. [5,19,20] as:  
(12)  
Where, l is the characteristic length (m). Sherwood number Sh, is expressed as a function of Reynolds number, Re and Schmidt number, Sc [5,20]. The empirical expression of Sherwood number is based on cell geometry and spacer configuration chosen for the present cell is indicated below [2024]  
(13)  
Where, Sc (Schmidt’s number, is estimated from physical properties (viscosity and density) of the medium while Reynolds number, indicates flow characteristics of the medium [20] and represent the conductivity ratios of diluate and concentrate, while ‘a’ ‘b’ ‘c’ ‘d ’ are the empirical constants.  
Ionic diffusivity is a strong function of hydrodynamic diameter of ions. Assuming infinite dilution ionic diffusivity is estimated using the NernstHaskel equation (Eq. 14) [25] as:  
(14)  
Where z_{+} and z_{} denote charges of cation and anion respectively while λ_{+} and λ_{} denotes limiting ionic conductance in the solvent. Other parameters bearing meaning and units are as reported in the nomenclature.  
In general diffusivity of ions from electrolytes e.g. NaCl, CaCl_{2}, LiCl in water are closely related to changes in solution viscosity at constant temperature. Therefore, necessary correction of diffusivity on viscosity is essential. Li et al. [26] experimentally verified that diffusivity of ions in an electrolyte solution is inversely proportional to the solution viscosity.  
(15)  
Therefore, the estimated diffusivities were corrected due to solution viscosity.  
Estimation of Membrane Surface Concentration:The membrane surface concentration of ions is dependent on current density under an applied voltage. As long as the ED operation is executed below limiting current (surface concentration would become zero at limiting current), the surface concentration on either side can be estimated from bulk concentration measurement (diluate/concentrate), current density and limiting current density using Eqs. (16) and (17) [13,27].  
(16)  
(17)  
Where, and are the concentrations of ion j, at the membrane surface and in bulk of the concentrate compartment respectively in the ED cell. and are the concentrations of ion j, at the membrane surface and in the bulk of the diluate side respectively in the ED cell.  
Estimation of current density and limiting current density ( i and i _{j,lim}): LCD (of a single electrolyte) is estimated from linearized Nernst Planck equation [6,8]:  
(18)  
Where, t_{j,m} and t_{j} are transport numbers of ion j in membrane and electrolyte solution respectively.  
Considering ion flux in the diluate side of the IEM, Eq. (17) is used to calculate concentration of ion j, at the membrane surface of diluate side  
The current density can be expressed by Eq. (17) after substitution of Eqs. (17) and (18) in Eq. (8).  
(19)  
Where ξ, the electric potential gradient can be estimated from Nernst equation given below [12,13]  
(20)  
Where and are the mean ionic activity coefficients corresponding to the ions at the wall of IEM and in the bulk of solution respectively within the diluate channel and they are estimated using Debye–Huckel limiting law.  
Numerical Estimation of Parameters  
The sequence of steps followed in the model to estimate current density and concentration change is described in the flow chart (Figure 2). The differential equations (Eqs. (1), (2), (4) and (5)) were integrated using Euler method using 1 second step size interval. Initial process conditions were obtained from literature. Few crucial parameters and their estimation techniques which were not taken up earlier are presented below.  
Experimental current density and concentration of Ca_{2+} ions  
The current flowing through the electrolyte solution of the ED cell under an applied voltage was recorded in ammeter. Ca^{2+} ions concentration was estimated from conductivity measurement and using standard calibration chart (mass concentration vs. conductance).  
Estimation of mass transfer coefficients  
Mass transfer correlations for the electro dialysis process based on the cell geometry were reported earlier by several authors [15,24]. They expressed Sherwood number (Sh) as a power function of Reynolds (Re) and Schmidt number (Sc) determined from their experimentation. In this report we have developed a suitable mass transfer correlation using the LCD and current density expressions that suits all of our experimental results.  
LCD was estimated experimentally for the case where both concentrate and diluate concentrations were 25 mol.m^{3} of CaCl_{2} in water (Figure 3). Using this LCD value and Eqs. (11), (12) and (18) along with physical properties of the electrolytes reported in Table 3, the mass transfer coefficient was estimated. Which was subsequently used to evaluate Sherwood number as a function of system flow parameters e.g. Reynolds number, Schmidt number and dimensionless ratio of conductivities Eq. (13). It was found that Sh.Sc 0.33 was a linear function of Re0.63, where Sh.Sc‑0.33 = 0.0583 . Re0.63.  
The constant 0.0583 is a product of parameters a and For the set with same CaCl_{2} concentration in concentrate and diluate streams, the ratio of conductivity values is close to unity ~1.0. This makes the factor a =0.0583. The factor was optimized to fit each experimental data point (concentration and current density with time). From each of this optimum value, d was obtained knowing for any set and is found out to be 0.131. The Sherwood number correlation suitable for the ED cell flow channel geometry was obtained as  
(21)  
The proposed equation (Eq. 21) has been validated and reported in Appendix.  
Determination of transport number of ion in solution  
Transport number t_{j} of ion j is the fraction of total current carried by the ion type which is a function of diffusion coefficient and ionic mobility of hydrated species. Difference in hydration ability influences size, diffusivity and mobility of the ion. Thus, ions do not transport current equally in solution. The transport number was estimated from the following equation [5]:  
(22)  
For a binaryion salt solution, n = 2, j= 1 for cation and j = 2 for anion and transport number is measured.  
Determination of current  
Initial current density estimation is essential to obtain salt concentration at membrane surface, and to start numerical integration, which may be evaluated either experimentally or from the applied electric potential and solution resistances using Ohms law. The applied electric potential may be expressed as  
(23)  
Where, Where, E_{el} is the electric potential drop near the electrodes, R_{tot} is the overall resistance (ohm) of the ED cell and I is the current (A). The overall resistance is the sum of individual values:  
(24)  
Where, resistance of ERS, concentrate, and diluate channels were estimated either directly from conductivity measurement from extended Kohlrauschequation [13,28]. The conductivity and the resistance are related as  
(25)  
Where, Δ is the conductivity of solution (S.m^{1}), L is the gap between membranes or the compartment thickness (m), Am is the effective membrane area (m^{2}).  
Determination of the and  
and are the mean ionic activity coefficients of salt at membrane and in bulk respectively in the diluate. These were estimated using DebyeHuckel limiting law [28].  
(26)  
Where γ ± is the mean ionic activity of a salt in an electrolyte solution and I_{s} is the ionic strength defined as,  
(27)  
Where m_{j} is molality (mol/kg solution) of the ion ‘j’ having charge .  
CaCl_{2} solution (with 5% sugar) densities were estimated experimentally and these data were linearly regressed (R2=0.984) and used whenever required (Figure 4).  
Determination of specific energy consumption  
The specific energy consumption, (kWh.kg^{1}) was estimated from the following equation  
(28)  
Where, ε is the applied electric potential in volt, is the area of the membrane in m^{2}, i (t ) is the current density (A.m^{2}) as a function of time, is the molecular mass of CaCl_{2}(=111.02 g.mol^{1}), and is the number of moles of CaCl_{2} removed from the feed solution at various time interval.  
Results  
Role of Sugar (mass%) and CaCl_{2} concentration on solution viscosity and influence of temperature  
Sugar solution viscosity measurement at constant temperature shows nonlinear (Figure 5) rise with sugar (5 to 20 mass%). Viscosity values were found to be between 0.72  1.5 mPa.s with increase in sugar mass%. These values were very much comparable with the literature reported data [29]. Solution viscosity does not show appreciable change with CaCl_{2} concentration (050 mol.m^{3}) (Figure 6). Viscosity measurement of CaCl_{2} solution at 20, 25, 32, 37, 42°C show lowering between 1.18 to 0.6 mPa.s. Almost ~37% lowering in viscosity was recorded (Figure 6).  
Effect of Sugar and CaCl_{2} concentration on electrical conductivity  
Figure 7 shows plot of electrical conductivity with CaCl_{2} concentration, estimated in presence and absence of sugar. Solution conductivity increases almost linearly with rise in CaCl_{2} concentration (5 to 50 mol.m^{3}). CaCl_{2}, a strong electrolyte, dissociates completely in solution and increase number of ions per unit volume available for ionic conductance. Addition of sugar dampens the ion conductivity values. This may be due to sugar, a water soluble nonelectrolyte, doesn’t dissociate and change the number of ions responsible for current carriage, therefore, presence of inert sugar molecules causes increase in crowding in solution.  
Experimental results and model prediction  
The LCD measurement by plotting V/I vs. 1/I (Figure 3) (diluate and concentrate concentrations are 25 mol.m^{3} CaCl_{2}) shows a minima at 0.013 mA^{1} which corresponds to the applied electric potential ~6 V. All experiments were categorically performed at 4 V, hoping current density to remain always below limiting value because, initial concentration of CaCl_{2} in the diluate stream was kept unchanged for all experiments.  
Current density and concentrate concentration variation were noted at regular interval for all the experiments and reported in Figures 8^{1}0. With progress of electrodialysis current density gets lowered (Figure 8) while, concentrate CaCl_{2} concentration increased (Figure 9). Lowering of the initial CaCl_{2} concentration in concentrate stream (C6 to C1, Figure 8) for the same diluate stream current density dropped. Similar trend was noted with increase in sugar mass% in the diluate channel (DSC6 to DSC1, Figure 8), but overall current density values were lower than the corresponding nonsugar cases (Figures 8 and 10) shows current density is a strong function of sugar concentration i.e. with increase in sugar mass% (S1, 5% to S4, 20%) the current density drops.  
The ion removal percentage estimated from the initial and final CaCl_{2} concentration of the diluate channel (Figure 11) doesn’t show any trend with concentrate concentration. Experiments C5 and DSC2 showed higher ion removal among their corresponding sets C1C6 and DSC1DSC6 respectively (Figure 11). This possibly hints at presence of a series of complex reaction taking place in ion transport.  
Presence of sugar in the diluate (DSC1DSC6) stream reduced ion removal rate compared to corresponding nonsugar cases (C1 C6). This may be attributed to tremendous defiance experienced by hydrated calcium ions in presence of inert sugar molecules.  
Eqs. (1), (4), (2) and (5) along with initial conditions (Table 3) were solved as per the reported sequence (Figure 2) using MATLAB. The solution gave us theoretical estimate of concentration. Predicted molar concentration of both concentrate and diluate stream shows nice agreement with all experimental data. This is represented by continuous line (Figures 8^{1}0) showing an excellent agreement with the experimental data.  
Effect of concentrate stream concentration  
Influence of concentrate stream concentration on (i) overall current density (Figure 8), and (ii) ion removal rate (percentage) from diluate solution (Figure 11) were experimentally estimated. Figure 8 shows increase in current density with rise in initial concentration of CaCl_{2}, which decreases slowly with time. This is true for both types of diluate with sugar and without sugar. Initially high current density value is probably due to availability of dissociated Ca^{2+} and 2Cl^{} ions of CaCl_{2} (a strong electrolyte). With increase in CaCl_{2} concentration, more such dissociated species appear per unit volume which reduces overall solution resistance and increases current density under a given electric potential. A slow drop in current value appeared due to gradual depletion of ions from diluate compartment. Figure 11 showing percentage removal from diluate stream didn’t follow any trend probably due to involvement of several competing factors in overall ion removal. The current density values (Figure 8) don’t predict the net ion removal percentage, instead overall ion removal depends on effective or net flux existing in the cell. Effective ion removal rate is due to cumulative addition of two competing processes namely: (i) An external applied electric potential and (ii) chemical potential (or diffusive transport) arising out of concentration gradient across the membrane. The applied electric potential always tries to push Ca^{2+} ions towards the appropriate electrode while, the direction of chemical potential or diffusive transport is decided by the concentration gradient across the membrane. Flux components arising out of an applied electric potential (hence forth defined as current flux), concentration gradient (diffusive flux) and overall (net) flux were estimated from model and presented in Figure 12.  
The current flux increased with CaCl_{2} concentration in the concentrate stream in the sequence C1C6 and DSC1DSC6. The trend is similar to the current density behavior indicated before. The diffusive component is favorable for C1 and DSC1 (values are positive), while for C2 and DSC2 it is favorable till initial 40 minutes but thereafter it becomes unfavorable. This leads to crossover of net flux and current flux lines (Figures 12a12c). Similar crossover doesn’t arise with any set, because, the diffusive component remained consistently either positive or negative for the rest of the experiment. Ion removal being a complex process gets influenced by e.g. concentrate concentration, the solution viscosity, conductivity, concentration of nonelectrolyte (taken up in the following section) even if the applied electric potential, flow rate and cell geometry were kept unchanged. Concentrate Ca^{2+} concentration being lower than diluate stream the diffusive part becomes favorable for initial 40 minutes and thereafter it gets reversed causing cross over.  
Investigation on role of sugar concentration in ion removal  
Effect of sugar concentration of diluate channel on (i) current density (Figure 10), (ii) concentrate concentration variation (Figure 10), (iii) Ion removal rate (Figure 11) and (iv) net flux Figures 12(d) were experimentally found out.  
With increase in sugar concentration the current density drops (Figure 10) thus, current density is maximum with 5% sugar and minimum with 20% sugar and slowly it decreases with time. Gradual lowering in current density between 5%  20% sugar (S1S4) may be due to increase in solution viscosity (Figure 5) and reduction in ion conductivity (Figure 7). Thus, hydrated ions experience more resistance under an applied electric potential. Slow drop in current density with time is due to depletion of ions from diluate channel. Gain in concentrate channel concentration supports ion transport from diluate to concentrate channel. The slope of the line indicating ion accumulation rate in concentrate is highest with 5% sugar (S1) while it is the minimum with 20% (S4) sugar concentration. This is due to increase in solution resistance with nonelectrolyte sugar molecules. The percent salt removal from diluate stream (Figure 11) supports above fact indicating drop in ion removal rate with increasing sugar concentration.  
Estimation of different flux components e.g. current flux, diffusive flux and net flux are presented in Figure 12d. The current flux decreased with increase in the mass% of sugar i.e. in the order of 5%  20% (SS4) and thus, effective flux decreases with sugar mass% (Figure 12d).  
It is also interesting to note (Figure 13) the ratio of removal rates with sugar and without sugar remains almost constant with concentrate concentration change. Similar constancy is also noted with viscosity ratios and average current density ratios as well. This is possibly due to impermeable (to sugar molecules) nature of ionic membrane used in electro dialysis. This has been confirmed from UV analysis of the concentrate stream before and after operation (Figure 14). No peak is noticed at 400nm (λmax for sugar). Sugar is not an electrolyte and its role is limited to the diluate channel only. The ratios of removal rates (with and without sugar) can be expressed by a simple power function of viscosity ratios as  
(29)  
This factor of 0.28~0.3 resembles close similarity with Sc number in the Sh number correlation, indicating that the removal rate is a strong function of flow and physical properties of the system.  
Mass transfer coefficient and specific energy  
Local mass transfer coefficients of ions (cation/anion) and specific energy consumption were estimated using Eqs. (12) and (28) respectively and reported in Figure 15. Mass transfer coefficient directly relates the speed of ion transport phenomena and is a strong function of local parameters of the system. Figure 15 shows local mass transfer coefficients ‘k’ are always higher with nonsugar cases than those with sugar ones. Presence of nonelectrolyte (sugar) reduces mass transfer coefficient and increases overall specific energy consumption to execute a desired separation. Experiments C1 and DSC1 are more energy efficient having lowermost specific energy consumption estimates. Favorable diffusional flux and low current values for these sets (C1, DSC1) probably encourage reduction in energy consumption.  
Conclusion  
Removal of CaCl_{2} from 5% sugar solution was carried out in batch recirculation electrodialysis mode. All experiments, were performed below LCD to avoid water electrolysis. Role of electrolyte concentration in concentrate channel, sugar mass% in diluate stream in ion removal were evaluated. Concentrate concentration variation doesn’t follow any trend to predict ion removal rate. Presence of sugar (in the diluate stream) increases the solution viscosity, reduces ion diffusivity and electrical conductivity thus, lowers ion removal rate compared to those without sugar cases. The linearized Nernst Plank equation efficiently predicted the experimental data and was extensively used to calculate various fluxes (current, diffusional and net), mass transfer coefficients for ions, specific energy consumption. Increase in concentrate concentration reduced overall cell resistance causing higher current density. Diffusional flux plays a major role in deciding overall or net flux. The experiments C1, C2, DSC1 and DSC2 showed favorable diffusional flux and higher ion removal rate with simultaneous reduction of energy consumption. Therefore, an optimum electrolyte concentration of concentrate, sugar mass% in diluate, and applied external electric potential can be obtained from this apparatus Figure 16.  
Acknowledgements  
Financial support to execute the experimental work is gratefully acknowledged to IIT Roorkee (No. IITR/SRIC/244/FIGSchA), India.  
References  

Table 1  Table 2  Table 3 
Figure 1  Figure 2  Figure 3  Figure 4  Figure 5  Figure 6 
Figure 7  Figure 8  Figure 9  Figure 10  Figure 11  Figure 12a 
Figure 12b  Figure 12c  Figure 12d  Figure 13 
Figure 14  Figure 15  Figure 16 