# Selection of the Best Process Stream to Remove  Ca2+ Ion Using Electrodialysis from Sugar Solution

Authors: Jogi Ganesh Dattatreya Tadimeti; Shilpi Jain; Sujay Chattopadhyay; Prashant Kumar Bhattacharya
Journal: International Journal of Electrochemistry
 (2014)

---

## Abstract

Electrodialytic removal of calcium chloride (CaCl2, 25–50 mol·m−3) from 5% sugar solution was executed in batch recirculation mode. Calcium ion removal rate was monitored with (i) applied potential, (ii) feed flow rate, (iii) solution viscosity and conductivity, and (iv) catholyte streams (NaOH or sodium salt of ethylene diamine tetraacetic acid-acetic acid, Na2EDTA-AA). Unsteady state model for ion concentration change was written for the ED cell used. Linearized Nernst-Planck equation instead of Ohm’s law was applied to closely obtain the current density and concentration change theoretically. The model developed could closely predict the experimental observation. Mass transfer coefficients and specific energy densities were estimated for each combination of catholyte stream used. NaOH showed better performance for a short duration over Na2EDTA-acetic acid combination.


---

## Body

## 1. Introduction

In cane based sugar industry the sugar concentration in the extracted juice after lime (CaO + H2O) treatment and color removal (clarification step) usually reaches around 5% (mass basis). This stream subsequently enters into series of evaporators to get concentrated. Presence of excess calcium in the postfloculation and precipitation stage of clarified sugar juice creates series of nuisance [1] to the subsequent stages (evaporators, etc.) in sugar industries affecting product quality as follows.(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 metals ions.
(5)
Excess calcium is not hygienic as well.Therefore, removal of it at appropriate stage would drastically reduce operation and maintenance (evaporator scaling) cost and improve product quality. Electrodialysis (ED) was chosen to remove CaCl2 from its sugar solution. ED was applied earlier in sugar industry to recover tartrate and malate from grape sugar [2] and in demineralisation of beet sugar syrup, juice, and molasses [3, 4]. The technological difficulties arise due to fouling of ion exchange membranes mainly due to deposition of organic/inorganic molecules (sugars, proteins, Ca2+, Mg2+, etc.). With increase in solution viscosity fouling becomes even severe and affects the current efficiency and ion removal rate. The concentration polarization occurs around membrane surface leading to increase in ion resistance, and this is minimized with the help of suitable spacer design, temperature, pH, and flow rates applied [5–11].A batch recirculation ED process having a single diluate channel was performed to remove the CaCl2 from sugar solution. As reported elsewhere [5] during ED process concentration polarization arises around the membrane which limits the net salt transport. This issue was taken up and sorted out using different combination of anolyte and catholyte streams. Different electrolyte streams (NaOH, acetic acid-Na2EDTA mixture) were selected as catholyte keeping anolyte as HCl solution.In a batch mode electrodialysis with continuous recirculation of feed stream, properties like electrolyte concentration of diluate (feed tank), concentration profiles around that membrane, and all physical properties of the solution change with time. The effect of all these parameters is reflected in ion removal rate and current density of the ED cell. Therefore, an unsteady state model that can closely predict the ion removal rate and overall current density will be quite relevant in application point of view. Nernst-Planck equation (purely based on first principles) and irreversible thermodynamics were used to estimate current density and ion concentration [12].


## 2. Materials and Methods

### 2.1. Equipment

#### 2.1.1. Electrodialysis Setup

The experimental setup used for ED application is shown in the Figure1 [13]. The ED cell and setup were from Berghof, Germany. The electric field was applied across the cell stack by a built-in D.C. source. Voltage and current between the two electrodes were measured by a built-in digital voltmeter and ammeter, respectively. The ED cell consisted of three compartments as shown in the figure. Membranes used were obtained from Permionics, Gujarat, and cross-linked styrene and di-vinyl benzene gel was used as base material. Cation exchange membrane (CEM) separates the cathode compartment and anion exchange membrane (AEM) separates the anode compartment from the feed chamber. The effective membrane area for the cell, A
m, was 0.0037 m2 and the feed compartment thickness, h, was 0.002 m.Figure 1
Batch recirculation electrodialysis process showing the storage tanks, pumps, manual control valves, various chambers of the ED cell, electrodes, DC supply source, voltmeter, ammeter, and flow meters used in the experiment [13].


#### 2.1.2. Power Supply

The power supply was provided through a voltage stabilizer of 110/220 V A.C. with 50–80 Hz frequency. The same gave an output voltage 0–49.9 V DC and current 0–3.99 A. Four centrifugal pumps were inbuilt with the system for pumping the solution.


#### 2.1.3. Conductivity Meter

Solution conductivity was noted at regular interval through an offline conductivity meter (Systronics India) of 200 mMho with 5 ranges (accuracy ±1%).


#### 2.1.4. ED Cell Compartments and Solutions Used

1000 mL solutions of each stream (feed, catholyte, and anolyte) were taken in three chambers (Figure1), respectively. Each chamber was connected with the respective three compartments of the ED cell 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. Table 1 indicates membrane parameters obtained from Permionics India Ltd. The composition and flow rates of three streams used are reported in Table 2.Table 1
Membrane parameters as obtained from Permionics India Ltd.
Physical parameters
Cation exchange membrane
Anion exchange membrane
Transport number
0.91
0.9
Experimental resistance (ohm cm−2)
2.0–3.5
—
Max. pressure allowed (kgcm−2)
3.0
3.0
Thickness (mm)
0.11 to 0.15
0.09–0.11
Max. temperature (°C)
60
60Table 2
Different process variables chosen during ED experimentation [13].
Expt. number
Feed solution
Feed flow rate  (mL·min−1)
Anolyte solution
Anolyte flow rate  (mL·min−1)
Catholyte solution
Catholyte flow rate  (mL·min−1)
Voltage applied  (V)
Time (min)
1
25 mol·m−3 CaCl2 in 5% sugar solution
130
100 mol·m−3 HCl solution
830
100 mol·m−3 NaOH solution
830
4
685
2
25 mol·m−3 CaCl2 in 5% sugar solution
130
100 mol·m−3 HCl solution
830
25 mol·m−3 Na2EDTA + 25 mol·m−3 AA solution
830
4
240
3
50 mol·m−3 CaCl2 in 5% sugar solution
130
100 mol·m−3 HCl solution
830
50 mol·m−3 Na2EDTA + 50 mol·m−3 AA solution
830
4
240Synthetic solution of 5% sugar and calcium chloride (CaCl2) was prepared in distilled water. The concentration of sugar was kept unchanged but that of CaCl2 was varied. The synthetic solution having CaCl2 with initial concentrations of 25 mol·m−3 and 50 mol·m−3 were used in the diluate channel of ED cell. Dilute solution of HCl (100 mol·m−3) was used as anolyte in all experiments while NaOH (100 mol·m−3) was used as catholyte in experiment 1 and equimolar mixtures of acetic acid (AA) and Na2EDTA (25 mol·m−3 and 50 mol·m−3) were, respectively, used as catholyte in experiments 2 and 3 (Table 2).


#### 2.1.5. Viscosity Measurement

Viscosity measurement was carried out using Ubbelhood viscometer always fitted in a constant temperature bath to nullify any temperature effect on capillary flow.


### 2.2. Procedure

The chambers of the ED cell and membranes were washed thoroughly before each experiment was carried out. Initially, the feed solution containing 5% sugar and CaCl2 was used and was circulated at a constant rate (130 mL/min) through the feed compartment. The feed solution, anolyte, and catholyte were continuously recycled through the ED cell and that caused a continuous change in salt concentration of feed solution. The concentration was measured at regular intervals. For a fixed applied voltage (V), variation of current (“I” through the membrane stack) and concentration of salt (Ca2+ ions) was estimated from conductivity measurement and using standard calibration chart (mass concentration versus conductance) and was recorded with time (t).ED cell was dismantled; membranes were taken out, checked visually to find any deposition over the surfaces after each experiment. Membranes were then washed with distilled water and oven dried at 100°C for 24 hours and weighed to find any gain or loss in mass of membrane.


## 2.1. Equipment

### 2.1.1. Electrodialysis Setup

The experimental setup used for ED application is shown in the Figure1 [13]. The ED cell and setup were from Berghof, Germany. The electric field was applied across the cell stack by a built-in D.C. source. Voltage and current between the two electrodes were measured by a built-in digital voltmeter and ammeter, respectively. The ED cell consisted of three compartments as shown in the figure. Membranes used were obtained from Permionics, Gujarat, and cross-linked styrene and di-vinyl benzene gel was used as base material. Cation exchange membrane (CEM) separates the cathode compartment and anion exchange membrane (AEM) separates the anode compartment from the feed chamber. The effective membrane area for the cell, A
m, was 0.0037 m2 and the feed compartment thickness, h, was 0.002 m.Figure 1
Batch recirculation electrodialysis process showing the storage tanks, pumps, manual control valves, various chambers of the ED cell, electrodes, DC supply source, voltmeter, ammeter, and flow meters used in the experiment [13].


### 2.1.2. Power Supply

The power supply was provided through a voltage stabilizer of 110/220 V A.C. with 50–80 Hz frequency. The same gave an output voltage 0–49.9 V DC and current 0–3.99 A. Four centrifugal pumps were inbuilt with the system for pumping the solution.


### 2.1.3. Conductivity Meter

Solution conductivity was noted at regular interval through an offline conductivity meter (Systronics India) of 200 mMho with 5 ranges (accuracy ±1%).


### 2.1.4. ED Cell Compartments and Solutions Used

1000 mL solutions of each stream (feed, catholyte, and anolyte) were taken in three chambers (Figure1), respectively. Each chamber was connected with the respective three compartments of the ED cell 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. Table 1 indicates membrane parameters obtained from Permionics India Ltd. The composition and flow rates of three streams used are reported in Table 2.Table 1
Membrane parameters as obtained from Permionics India Ltd.
Physical parameters
Cation exchange membrane
Anion exchange membrane
Transport number
0.91
0.9
Experimental resistance (ohm cm−2)
2.0–3.5
—
Max. pressure allowed (kgcm−2)
3.0
3.0
Thickness (mm)
0.11 to 0.15
0.09–0.11
Max. temperature (°C)
60
60Table 2
Different process variables chosen during ED experimentation [13].
Expt. number
Feed solution
Feed flow rate  (mL·min−1)
Anolyte solution
Anolyte flow rate  (mL·min−1)
Catholyte solution
Catholyte flow rate  (mL·min−1)
Voltage applied  (V)
Time (min)
1
25 mol·m−3 CaCl2 in 5% sugar solution
130
100 mol·m−3 HCl solution
830
100 mol·m−3 NaOH solution
830
4
685
2
25 mol·m−3 CaCl2 in 5% sugar solution
130
100 mol·m−3 HCl solution
830
25 mol·m−3 Na2EDTA + 25 mol·m−3 AA solution
830
4
240
3
50 mol·m−3 CaCl2 in 5% sugar solution
130
100 mol·m−3 HCl solution
830
50 mol·m−3 Na2EDTA + 50 mol·m−3 AA solution
830
4
240Synthetic solution of 5% sugar and calcium chloride (CaCl2) was prepared in distilled water. The concentration of sugar was kept unchanged but that of CaCl2 was varied. The synthetic solution having CaCl2 with initial concentrations of 25 mol·m−3 and 50 mol·m−3 were used in the diluate channel of ED cell. Dilute solution of HCl (100 mol·m−3) was used as anolyte in all experiments while NaOH (100 mol·m−3) was used as catholyte in experiment 1 and equimolar mixtures of acetic acid (AA) and Na2EDTA (25 mol·m−3 and 50 mol·m−3) were, respectively, used as catholyte in experiments 2 and 3 (Table 2).


### 2.1.5. Viscosity Measurement

Viscosity measurement was carried out using Ubbelhood viscometer always fitted in a constant temperature bath to nullify any temperature effect on capillary flow.


## 2.1.1. Electrodialysis Setup

The experimental setup used for ED application is shown in the Figure1 [13]. The ED cell and setup were from Berghof, Germany. The electric field was applied across the cell stack by a built-in D.C. source. Voltage and current between the two electrodes were measured by a built-in digital voltmeter and ammeter, respectively. The ED cell consisted of three compartments as shown in the figure. Membranes used were obtained from Permionics, Gujarat, and cross-linked styrene and di-vinyl benzene gel was used as base material. Cation exchange membrane (CEM) separates the cathode compartment and anion exchange membrane (AEM) separates the anode compartment from the feed chamber. The effective membrane area for the cell, A
m, was 0.0037 m2 and the feed compartment thickness, h, was 0.002 m.Figure 1
Batch recirculation electrodialysis process showing the storage tanks, pumps, manual control valves, various chambers of the ED cell, electrodes, DC supply source, voltmeter, ammeter, and flow meters used in the experiment [13].


## 2.1.2. Power Supply

The power supply was provided through a voltage stabilizer of 110/220 V A.C. with 50–80 Hz frequency. The same gave an output voltage 0–49.9 V DC and current 0–3.99 A. Four centrifugal pumps were inbuilt with the system for pumping the solution.


## 2.1.3. Conductivity Meter

Solution conductivity was noted at regular interval through an offline conductivity meter (Systronics India) of 200 mMho with 5 ranges (accuracy ±1%).


## 2.1.4. ED Cell Compartments and Solutions Used

1000 mL solutions of each stream (feed, catholyte, and anolyte) were taken in three chambers (Figure1), respectively. Each chamber was connected with the respective three compartments of the ED cell 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. Table 1 indicates membrane parameters obtained from Permionics India Ltd. The composition and flow rates of three streams used are reported in Table 2.Table 1
Membrane parameters as obtained from Permionics India Ltd.
Physical parameters
Cation exchange membrane
Anion exchange membrane
Transport number
0.91
0.9
Experimental resistance (ohm cm−2)
2.0–3.5
—
Max. pressure allowed (kgcm−2)
3.0
3.0
Thickness (mm)
0.11 to 0.15
0.09–0.11
Max. temperature (°C)
60
60Table 2
Different process variables chosen during ED experimentation [13].
Expt. number
Feed solution
Feed flow rate  (mL·min−1)
Anolyte solution
Anolyte flow rate  (mL·min−1)
Catholyte solution
Catholyte flow rate  (mL·min−1)
Voltage applied  (V)
Time (min)
1
25 mol·m−3 CaCl2 in 5% sugar solution
130
100 mol·m−3 HCl solution
830
100 mol·m−3 NaOH solution
830
4
685
2
25 mol·m−3 CaCl2 in 5% sugar solution
130
100 mol·m−3 HCl solution
830
25 mol·m−3 Na2EDTA + 25 mol·m−3 AA solution
830
4
240
3
50 mol·m−3 CaCl2 in 5% sugar solution
130
100 mol·m−3 HCl solution
830
50 mol·m−3 Na2EDTA + 50 mol·m−3 AA solution
830
4
240Synthetic solution of 5% sugar and calcium chloride (CaCl2) was prepared in distilled water. The concentration of sugar was kept unchanged but that of CaCl2 was varied. The synthetic solution having CaCl2 with initial concentrations of 25 mol·m−3 and 50 mol·m−3 were used in the diluate channel of ED cell. Dilute solution of HCl (100 mol·m−3) was used as anolyte in all experiments while NaOH (100 mol·m−3) was used as catholyte in experiment 1 and equimolar mixtures of acetic acid (AA) and Na2EDTA (25 mol·m−3 and 50 mol·m−3) were, respectively, used as catholyte in experiments 2 and 3 (Table 2).


## 2.1.5. Viscosity Measurement

Viscosity measurement was carried out using Ubbelhood viscometer always fitted in a constant temperature bath to nullify any temperature effect on capillary flow.


## 2.2. Procedure

The chambers of the ED cell and membranes were washed thoroughly before each experiment was carried out. Initially, the feed solution containing 5% sugar and CaCl2 was used and was circulated at a constant rate (130 mL/min) through the feed compartment. The feed solution, anolyte, and catholyte were continuously recycled through the ED cell and that caused a continuous change in salt concentration of feed solution. The concentration was measured at regular intervals. For a fixed applied voltage (V), variation of current (“I” through the membrane stack) and concentration of salt (Ca2+ ions) was estimated from conductivity measurement and using standard calibration chart (mass concentration versus conductance) and was recorded with time (t).ED cell was dismantled; membranes were taken out, checked visually to find any deposition over the surfaces after each experiment. Membranes were then washed with distilled water and oven dried at 100°C for 24 hours and weighed to find any gain or loss in mass of membrane.


## 3. Modeling of Ion Transport

Current density and limiting current density (LCD) of an ED cell is a function of a series of parameters, for example, physical (cell geometry, flow dynamics, spacer spacing, solution density, and viscosity) and chemical (ion concentration, transport number, and diffusivity) for a given set of membrane pairs. Precise estimate of these parameters and application of Nernst-Planck equation (assuming zero ion concentration on the membrane surface) would give a theoretical estimate of LCD which can also be determined experimentally from plot ofI versus V characteristics of the electrolyte in the ED cell [7, 9].


### 3.1. Determination of Bulk Concentration of Diluate Compartment

Concentration of ions was obtained through unsteady mass balance over diluate, catholyte, and anolyte compartments. The following assumptions were made [18].(i)
The ED cell and the feed tank are approximated to be a perfectly mixed flow reactor.
(ii)
Back diffusion of ions was ignored.
(iii)
Electroneutrality condition is always maintained.The mass balance equation of diluate compartment in the ED cell can be expressed as(1)
V
dilC
d
C
dil
d
t
=
Q
dil
C
T
dil
-
C
dil
-
η
i
A
m
z
F
,
where V
dilC is the volume of the diluate compartment (m
3) and t is time (s), C
T
dil and C
dil represent diluate concentrations leaving feed tank and leaving cell compartment (mol·m−3), Q
dil is the diluate volumetric flow rate (m3/s), η is the current efficiency, i is the current density (A·m−2), and A
m is the effective membrane area (m2).η can be obtained from the following equation [18, 19]:
(2)
η
=
t
+
,
CEM
+
t
-
,
AEM
-
1
,
where t
+
,
CEM is the transport number of cation in cation exchange membranes and t
-
,
AEM is the transport number of anion in anion exchange membrane.Similarly, unsteady state mass balance around feed tank can be written as(3)
d
V
T
C
T
dil
d
t
=
Q
dil
C
dil
-
C
T
dil
,
where V
T is the volume of feed tank (m3). During electrodialysis water transport occurs across the membranes due to electroosmosis and osmosis [19]. Volume change (due to water transport) was ignored as there was no net volume change noted experimentally.


### 3.2. Determination of the Current Density

#### 3.2.1. Overall Flux Equation

A pictorial representation of different concentration profiles possibly developed around the membrane is described in Figure2. The flux of ions passing through the membrane can be expressed by generalized Nernst Planck equation as [7]
(4)
N
j
=
-
D
j
∂
C
j
∂
x
-
z
j
C
j
F
D
j
R
T
∂
ψ
∂
x
,
where x is the distance measured from boundary layer in contact with the bulk solution in diluate channel towards the membrane, D
j is the diffusivity of ion (m2·s−1), C
j 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 ∂
ψ
/
∂
x is the potential gradient (V·m−1) and F is the Faraday constant (C·geqv−1).Figure 2
Depiction of ion transport and hypothetical linear concentration boundary layer formed across either side of the membrane in ED cell.The total molar flux of ion “j” through the ion exchange membrane, N
j
,
m, can be related to the current density, i, as [7]
(5)
N
j
,
m
=
t
j
,
m
i
z
j
F
,
where t
j
,
m is the transport number of ion j in the membrane, i is current per unit area of membrane or current density (A·m−2), and z
j is the charge of the ion.At steady stateN
j and N
j
,
m are equal; that is,
(6)
t
j
,
m
i
z
j
F
=
-
D
j
∂
C
j
∂
x
-
z
j
C
j
F
D
j
R
T
∂
ψ
∂
x
.
Assuming that a linear profile of the concentration distribution exists along the boundary layer, the linearized Nernst-Planck equation could be used instead of (6). Expression for the linearized Nernst-Planck equation when applied in the diluate chamber is [7]
(7)
t
j
,
m
i
z
j
F
=
D
j
C
j
,
b
dil
-
C
j
,
m
dil
δ
-
z
j
D
j
F
ξ
C
j
,
m
dil
R
T
,
where δ is the boundary layer thickness (m), C
j
,
b
dil and C
j
,
m
dil are concentrations of ions in bulk and at the membrane surface, respectively, of the diluate compartment, and ξ is the potential gradient (V·m−1) and is expressed as
(8)
ξ
=
ψ
δ
.
In (7) the first part, that is, D
j
C
j
,
b
dil
-
C
j
,
m
dil
/
δ, denotes flux due to molecular diffusion flux of ion arising out of concentration variation between solution bulk and boundary layer over membrane surface. The second part, that is, z
j
D
j
F
ξ
C
j
,
m
dil
/
R
T, shows flux due to externally applied potential over the membrane.


#### 3.2.2. Boundary Layer Thickness,δ Estimation

δ is estimated using film theory (equation (9)) and salt mass-transfer coefficient [7, 20]. Salt mass-transfer coefficient is usually determined based on salt diffusivity and suitable mass-transfer correlation, which in-turn is dependent on flow profile and physical properties of the fluids, cell geometry, and surface morphology of membranes used in ED cell [7, 9, 21, 22]:
(9)
δ
=
D
j
k
,
where, D
j and k are diffusivity and mass transfer coefficient of diffusing species in solution. Each of these parameters was separately estimated using standard correlations. The mass transfer coefficient was obtained from Sherwood number [7, 20, 21] as:
(10)
Sh
=
k
·
l
D
j
,
where l is the characteristic length (m). Sherwood number, Sh, is expressed as a function of Reynolds number, Re, and Schmidt number, Sc [7, 20]. The empirical expression of Sherwood number is based on cell geometry and spacer configuration chosen for the present cell as indicated in the following [17, 20, 23]:
(11)
Sh
=
a
·
Re
b
·
Sc
c
,
where Sc (Schmidt number, μ
/
ρ
D
j) is estimated from physical properties (viscosity and density) of the medium while Reynolds number (ρ
v
l
/
μ) indicates flow characteristics of the medium and channel spacing as “l” and a, b, c are the empirical constants, which are determined by fitting the data (Sh/Scc versus Re) for experiments where flow rate is varied. In this work, the values of a, b, and c are taken from literature [17] and are given in Table 3.Table 3
Values of different physical parameters used in the model.
Parameter
Value
Reference
Temperature,T
298 K
This work
Transport number of the cation in CEM,t
+
,
CEM
0.91
Table1
Transport number of the anion in AEM,t
-
,
AEM
0.9
Table1
Transport number of cation in the solution,t
Ca
2
+
,
s
0.4387
This work [7]
Transport number of anion in the solution,t
Cl
-
,
s
0.5613
This work [7]
Diffusivity of CaCl2 in 5% sugar solution at 25°C, D
CaCl
2
1.198 × 10−9 m2·s−1
This work [14, 15]
Diffusivity of Ca2+ ions at infinite dilution and  at 25°C, D
Ca
2
+
°
7.92 × 10−10 m2·s−1
This work [14]
Diffusivity of Ca2+ ions  in 5% sugar solutions at 25°C, D
Ca
2
+
7.11 × 10−10 m2·s−1
This work [14, 15]
Diffusivity of Cl− ions  in 5% sugar solutions at 25°C, D
Cl
-
18.2 × 10−10 m2·s−1
This work [14, 15]
Distance between adjacent membranes,l
2 × 10−3 m
This work
Area of the membrane,A
m
3.7 × 10−3 m2
This work
Charge on the calcium ion,z
Ca
2
+
+2
This work
Viscosity of 5% sugar solution,μ
9.92 × 10−4 Pa·s
[16]
Velocity of the feed stream,v
3.1 × 10−2 m·s−1
This work
Applied voltage,E
tot
4 V
This work
Current density initial value,i
(
0
)
122 A·m−2
This work
Current efficiency,η
0.81
This work
Sh number empirical equation constant,a
0.46 for catholyte NaOH
[17]
0.25 ± 0.03 for catholyte AA-Na2EDTA
This work
Sh number empirical equation constant,b
0.63 for any anolyte and catholyte
[17]
Sh number empirical equation constant,c
0.33 for any anolyte and catholyte
[17]Ionic diffusivity is entirely dependent on the size of hydrodynamic diameter of ions. Assuming infinite dilution this ionic diffusivity is estimated using the Nernst-Haskel equation (12) [14] as
(12)
D
°
=
R
T
1
/
z
+
+
1
/
z
-
F
2
1
/
λ
+
+
1
/
λ
-
,
where z
+ and z
- denote charges of cation and anion, respectively, while λ
+ and λ
- denote limiting ionic conductance in the solvent. Other parameters bearing meaning and units are as reported in the nomenclature.Diffusivity is a strong function of viscosity which was corrected using equation proposed by Yuan-Hui and Gregory [15]
(13)
D
D
°
=
μ
°
μ
.


#### 3.2.3. 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 becomes zero), the surface concentration on either side can be estimated from bulk concentration measurement (diluate/concentrate), current density, and limiting current density using (14) and (15) [19, 24]:
(14)
C
j
,
m
conc
=
C
j
,
b
conc
1
+
i
i
j
,
lim
⁡
,
(15)
C
j
,
m
dil
=
C
j
,
b
dil
1
-
i
i
j
,
lim
⁡
,
where C
j
,
m
conc and C
j
,
b
conc are the concentrations of ion j, on the membrane surface and in bulk of the concentrate compartment, respectively, in the ED cell. C
j
,
m
dil and C
j
,
b
dil are the concentrations of ion j, on the membrane surface and in the bulk of the diluate side, respectively, in the ED cell.


#### 3.2.4. Estimation of Current Density and Limiting Current Density (i and i
j
,
lim
⁡)

LCD (of a single electrolyte) is estimated using the following equation [5, 9]:
(16)
i
j
,
lim
⁡
=
C
j
,
b
dil
D
j
z
j
F
δ
(
t
j
,
m
-
t
j
,
b
)
,
where t
j
,
m and t
j
,
b are transport numbers of ion j in membrane and electrolyte solution, respectively.Considering ion flux in the diluate side of the IEM, (15) is used to calculate concentration of ion j, at the membrane surface of diluate side C
j
,
m
dil.The current density can be expressed by (17) after substitution of (15) and (16) in (6):
(17)
i
=
C
j
,
b
dil
D
j
z
j
ξ
F
R
T
×
t
j
,
m
-
t
j
,
b
z
j
F
+
ξ
δ
t
j
,
m
-
t
j
,
b
R
T
-
t
j
,
m
z
j
F
-
1
,
where ξ the potential gradient can be estimated from Nernst equation given as follows [18, 19]:
(18)
ξ
=
-
2
t
j
,
m
-
1
R
T
δ
F
ln
⁡
⁡
γ
b
dil
C
j
,
b
dil
γ
m
dil
C
j
,
m
dil
,
where γ
m
dil and γ
b
dil 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 can be estimated using Debye-Huckel limiting law [25].


## 3.1. Determination of Bulk Concentration of Diluate Compartment

Concentration of ions was obtained through unsteady mass balance over diluate, catholyte, and anolyte compartments. The following assumptions were made [18].(i)
The ED cell and the feed tank are approximated to be a perfectly mixed flow reactor.
(ii)
Back diffusion of ions was ignored.
(iii)
Electroneutrality condition is always maintained.The mass balance equation of diluate compartment in the ED cell can be expressed as(1)
V
dilC
d
C
dil
d
t
=
Q
dil
C
T
dil
-
C
dil
-
η
i
A
m
z
F
,
where V
dilC is the volume of the diluate compartment (m
3) and t is time (s), C
T
dil and C
dil represent diluate concentrations leaving feed tank and leaving cell compartment (mol·m−3), Q
dil is the diluate volumetric flow rate (m3/s), η is the current efficiency, i is the current density (A·m−2), and A
m is the effective membrane area (m2).η can be obtained from the following equation [18, 19]:
(2)
η
=
t
+
,
CEM
+
t
-
,
AEM
-
1
,
where t
+
,
CEM is the transport number of cation in cation exchange membranes and t
-
,
AEM is the transport number of anion in anion exchange membrane.Similarly, unsteady state mass balance around feed tank can be written as(3)
d
V
T
C
T
dil
d
t
=
Q
dil
C
dil
-
C
T
dil
,
where V
T is the volume of feed tank (m3). During electrodialysis water transport occurs across the membranes due to electroosmosis and osmosis [19]. Volume change (due to water transport) was ignored as there was no net volume change noted experimentally.


## 3.2. Determination of the Current Density

### 3.2.1. Overall Flux Equation

A pictorial representation of different concentration profiles possibly developed around the membrane is described in Figure2. The flux of ions passing through the membrane can be expressed by generalized Nernst Planck equation as [7]
(4)
N
j
=
-
D
j
∂
C
j
∂
x
-
z
j
C
j
F
D
j
R
T
∂
ψ
∂
x
,
where x is the distance measured from boundary layer in contact with the bulk solution in diluate channel towards the membrane, D
j is the diffusivity of ion (m2·s−1), C
j 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 ∂
ψ
/
∂
x is the potential gradient (V·m−1) and F is the Faraday constant (C·geqv−1).Figure 2
Depiction of ion transport and hypothetical linear concentration boundary layer formed across either side of the membrane in ED cell.The total molar flux of ion “j” through the ion exchange membrane, N
j
,
m, can be related to the current density, i, as [7]
(5)
N
j
,
m
=
t
j
,
m
i
z
j
F
,
where t
j
,
m is the transport number of ion j in the membrane, i is current per unit area of membrane or current density (A·m−2), and z
j is the charge of the ion.At steady stateN
j and N
j
,
m are equal; that is,
(6)
t
j
,
m
i
z
j
F
=
-
D
j
∂
C
j
∂
x
-
z
j
C
j
F
D
j
R
T
∂
ψ
∂
x
.
Assuming that a linear profile of the concentration distribution exists along the boundary layer, the linearized Nernst-Planck equation could be used instead of (6). Expression for the linearized Nernst-Planck equation when applied in the diluate chamber is [7]
(7)
t
j
,
m
i
z
j
F
=
D
j
C
j
,
b
dil
-
C
j
,
m
dil
δ
-
z
j
D
j
F
ξ
C
j
,
m
dil
R
T
,
where δ is the boundary layer thickness (m), C
j
,
b
dil and C
j
,
m
dil are concentrations of ions in bulk and at the membrane surface, respectively, of the diluate compartment, and ξ is the potential gradient (V·m−1) and is expressed as
(8)
ξ
=
ψ
δ
.
In (7) the first part, that is, D
j
C
j
,
b
dil
-
C
j
,
m
dil
/
δ, denotes flux due to molecular diffusion flux of ion arising out of concentration variation between solution bulk and boundary layer over membrane surface. The second part, that is, z
j
D
j
F
ξ
C
j
,
m
dil
/
R
T, shows flux due to externally applied potential over the membrane.


### 3.2.2. Boundary Layer Thickness,δ Estimation

δ is estimated using film theory (equation (9)) and salt mass-transfer coefficient [7, 20]. Salt mass-transfer coefficient is usually determined based on salt diffusivity and suitable mass-transfer correlation, which in-turn is dependent on flow profile and physical properties of the fluids, cell geometry, and surface morphology of membranes used in ED cell [7, 9, 21, 22]:
(9)
δ
=
D
j
k
,
where, D
j and k are diffusivity and mass transfer coefficient of diffusing species in solution. Each of these parameters was separately estimated using standard correlations. The mass transfer coefficient was obtained from Sherwood number [7, 20, 21] as:
(10)
Sh
=
k
·
l
D
j
,
where l is the characteristic length (m). Sherwood number, Sh, is expressed as a function of Reynolds number, Re, and Schmidt number, Sc [7, 20]. The empirical expression of Sherwood number is based on cell geometry and spacer configuration chosen for the present cell as indicated in the following [17, 20, 23]:
(11)
Sh
=
a
·
Re
b
·
Sc
c
,
where Sc (Schmidt number, μ
/
ρ
D
j) is estimated from physical properties (viscosity and density) of the medium while Reynolds number (ρ
v
l
/
μ) indicates flow characteristics of the medium and channel spacing as “l” and a, b, c are the empirical constants, which are determined by fitting the data (Sh/Scc versus Re) for experiments where flow rate is varied. In this work, the values of a, b, and c are taken from literature [17] and are given in Table 3.Table 3
Values of different physical parameters used in the model.
Parameter
Value
Reference
Temperature,T
298 K
This work
Transport number of the cation in CEM,t
+
,
CEM
0.91
Table1
Transport number of the anion in AEM,t
-
,
AEM
0.9
Table1
Transport number of cation in the solution,t
Ca
2
+
,
s
0.4387
This work [7]
Transport number of anion in the solution,t
Cl
-
,
s
0.5613
This work [7]
Diffusivity of CaCl2 in 5% sugar solution at 25°C, D
CaCl
2
1.198 × 10−9 m2·s−1
This work [14, 15]
Diffusivity of Ca2+ ions at infinite dilution and  at 25°C, D
Ca
2
+
°
7.92 × 10−10 m2·s−1
This work [14]
Diffusivity of Ca2+ ions  in 5% sugar solutions at 25°C, D
Ca
2
+
7.11 × 10−10 m2·s−1
This work [14, 15]
Diffusivity of Cl− ions  in 5% sugar solutions at 25°C, D
Cl
-
18.2 × 10−10 m2·s−1
This work [14, 15]
Distance between adjacent membranes,l
2 × 10−3 m
This work
Area of the membrane,A
m
3.7 × 10−3 m2
This work
Charge on the calcium ion,z
Ca
2
+
+2
This work
Viscosity of 5% sugar solution,μ
9.92 × 10−4 Pa·s
[16]
Velocity of the feed stream,v
3.1 × 10−2 m·s−1
This work
Applied voltage,E
tot
4 V
This work
Current density initial value,i
(
0
)
122 A·m−2
This work
Current efficiency,η
0.81
This work
Sh number empirical equation constant,a
0.46 for catholyte NaOH
[17]
0.25 ± 0.03 for catholyte AA-Na2EDTA
This work
Sh number empirical equation constant,b
0.63 for any anolyte and catholyte
[17]
Sh number empirical equation constant,c
0.33 for any anolyte and catholyte
[17]Ionic diffusivity is entirely dependent on the size of hydrodynamic diameter of ions. Assuming infinite dilution this ionic diffusivity is estimated using the Nernst-Haskel equation (12) [14] as
(12)
D
°
=
R
T
1
/
z
+
+
1
/
z
-
F
2
1
/
λ
+
+
1
/
λ
-
,
where z
+ and z
- denote charges of cation and anion, respectively, while λ
+ and λ
- denote limiting ionic conductance in the solvent. Other parameters bearing meaning and units are as reported in the nomenclature.Diffusivity is a strong function of viscosity which was corrected using equation proposed by Yuan-Hui and Gregory [15]
(13)
D
D
°
=
μ
°
μ
.


### 3.2.3. 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 becomes zero), the surface concentration on either side can be estimated from bulk concentration measurement (diluate/concentrate), current density, and limiting current density using (14) and (15) [19, 24]:
(14)
C
j
,
m
conc
=
C
j
,
b
conc
1
+
i
i
j
,
lim
⁡
,
(15)
C
j
,
m
dil
=
C
j
,
b
dil
1
-
i
i
j
,
lim
⁡
,
where C
j
,
m
conc and C
j
,
b
conc are the concentrations of ion j, on the membrane surface and in bulk of the concentrate compartment, respectively, in the ED cell. C
j
,
m
dil and C
j
,
b
dil are the concentrations of ion j, on the membrane surface and in the bulk of the diluate side, respectively, in the ED cell.


### 3.2.4. Estimation of Current Density and Limiting Current Density (i and i
j
,
lim
⁡)

LCD (of a single electrolyte) is estimated using the following equation [5, 9]:
(16)
i
j
,
lim
⁡
=
C
j
,
b
dil
D
j
z
j
F
δ
(
t
j
,
m
-
t
j
,
b
)
,
where t
j
,
m and t
j
,
b are transport numbers of ion j in membrane and electrolyte solution, respectively.Considering ion flux in the diluate side of the IEM, (15) is used to calculate concentration of ion j, at the membrane surface of diluate side C
j
,
m
dil.The current density can be expressed by (17) after substitution of (15) and (16) in (6):
(17)
i
=
C
j
,
b
dil
D
j
z
j
ξ
F
R
T
×
t
j
,
m
-
t
j
,
b
z
j
F
+
ξ
δ
t
j
,
m
-
t
j
,
b
R
T
-
t
j
,
m
z
j
F
-
1
,
where ξ the potential gradient can be estimated from Nernst equation given as follows [18, 19]:
(18)
ξ
=
-
2
t
j
,
m
-
1
R
T
δ
F
ln
⁡
⁡
γ
b
dil
C
j
,
b
dil
γ
m
dil
C
j
,
m
dil
,
where γ
m
dil and γ
b
dil 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 can be estimated using Debye-Huckel limiting law [25].


## 3.2.1. Overall Flux Equation

A pictorial representation of different concentration profiles possibly developed around the membrane is described in Figure2. The flux of ions passing through the membrane can be expressed by generalized Nernst Planck equation as [7]
(4)
N
j
=
-
D
j
∂
C
j
∂
x
-
z
j
C
j
F
D
j
R
T
∂
ψ
∂
x
,
where x is the distance measured from boundary layer in contact with the bulk solution in diluate channel towards the membrane, D
j is the diffusivity of ion (m2·s−1), C
j 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 ∂
ψ
/
∂
x is the potential gradient (V·m−1) and F is the Faraday constant (C·geqv−1).Figure 2
Depiction of ion transport and hypothetical linear concentration boundary layer formed across either side of the membrane in ED cell.The total molar flux of ion “j” through the ion exchange membrane, N
j
,
m, can be related to the current density, i, as [7]
(5)
N
j
,
m
=
t
j
,
m
i
z
j
F
,
where t
j
,
m is the transport number of ion j in the membrane, i is current per unit area of membrane or current density (A·m−2), and z
j is the charge of the ion.At steady stateN
j and N
j
,
m are equal; that is,
(6)
t
j
,
m
i
z
j
F
=
-
D
j
∂
C
j
∂
x
-
z
j
C
j
F
D
j
R
T
∂
ψ
∂
x
.
Assuming that a linear profile of the concentration distribution exists along the boundary layer, the linearized Nernst-Planck equation could be used instead of (6). Expression for the linearized Nernst-Planck equation when applied in the diluate chamber is [7]
(7)
t
j
,
m
i
z
j
F
=
D
j
C
j
,
b
dil
-
C
j
,
m
dil
δ
-
z
j
D
j
F
ξ
C
j
,
m
dil
R
T
,
where δ is the boundary layer thickness (m), C
j
,
b
dil and C
j
,
m
dil are concentrations of ions in bulk and at the membrane surface, respectively, of the diluate compartment, and ξ is the potential gradient (V·m−1) and is expressed as
(8)
ξ
=
ψ
δ
.
In (7) the first part, that is, D
j
C
j
,
b
dil
-
C
j
,
m
dil
/
δ, denotes flux due to molecular diffusion flux of ion arising out of concentration variation between solution bulk and boundary layer over membrane surface. The second part, that is, z
j
D
j
F
ξ
C
j
,
m
dil
/
R
T, shows flux due to externally applied potential over the membrane.


## 3.2.2. Boundary Layer Thickness,δ Estimation

δ is estimated using film theory (equation (9)) and salt mass-transfer coefficient [7, 20]. Salt mass-transfer coefficient is usually determined based on salt diffusivity and suitable mass-transfer correlation, which in-turn is dependent on flow profile and physical properties of the fluids, cell geometry, and surface morphology of membranes used in ED cell [7, 9, 21, 22]:
(9)
δ
=
D
j
k
,
where, D
j and k are diffusivity and mass transfer coefficient of diffusing species in solution. Each of these parameters was separately estimated using standard correlations. The mass transfer coefficient was obtained from Sherwood number [7, 20, 21] as:
(10)
Sh
=
k
·
l
D
j
,
where l is the characteristic length (m). Sherwood number, Sh, is expressed as a function of Reynolds number, Re, and Schmidt number, Sc [7, 20]. The empirical expression of Sherwood number is based on cell geometry and spacer configuration chosen for the present cell as indicated in the following [17, 20, 23]:
(11)
Sh
=
a
·
Re
b
·
Sc
c
,
where Sc (Schmidt number, μ
/
ρ
D
j) is estimated from physical properties (viscosity and density) of the medium while Reynolds number (ρ
v
l
/
μ) indicates flow characteristics of the medium and channel spacing as “l” and a, b, c are the empirical constants, which are determined by fitting the data (Sh/Scc versus Re) for experiments where flow rate is varied. In this work, the values of a, b, and c are taken from literature [17] and are given in Table 3.Table 3
Values of different physical parameters used in the model.
Parameter
Value
Reference
Temperature,T
298 K
This work
Transport number of the cation in CEM,t
+
,
CEM
0.91
Table1
Transport number of the anion in AEM,t
-
,
AEM
0.9
Table1
Transport number of cation in the solution,t
Ca
2
+
,
s
0.4387
This work [7]
Transport number of anion in the solution,t
Cl
-
,
s
0.5613
This work [7]
Diffusivity of CaCl2 in 5% sugar solution at 25°C, D
CaCl
2
1.198 × 10−9 m2·s−1
This work [14, 15]
Diffusivity of Ca2+ ions at infinite dilution and  at 25°C, D
Ca
2
+
°
7.92 × 10−10 m2·s−1
This work [14]
Diffusivity of Ca2+ ions  in 5% sugar solutions at 25°C, D
Ca
2
+
7.11 × 10−10 m2·s−1
This work [14, 15]
Diffusivity of Cl− ions  in 5% sugar solutions at 25°C, D
Cl
-
18.2 × 10−10 m2·s−1
This work [14, 15]
Distance between adjacent membranes,l
2 × 10−3 m
This work
Area of the membrane,A
m
3.7 × 10−3 m2
This work
Charge on the calcium ion,z
Ca
2
+
+2
This work
Viscosity of 5% sugar solution,μ
9.92 × 10−4 Pa·s
[16]
Velocity of the feed stream,v
3.1 × 10−2 m·s−1
This work
Applied voltage,E
tot
4 V
This work
Current density initial value,i
(
0
)
122 A·m−2
This work
Current efficiency,η
0.81
This work
Sh number empirical equation constant,a
0.46 for catholyte NaOH
[17]
0.25 ± 0.03 for catholyte AA-Na2EDTA
This work
Sh number empirical equation constant,b
0.63 for any anolyte and catholyte
[17]
Sh number empirical equation constant,c
0.33 for any anolyte and catholyte
[17]Ionic diffusivity is entirely dependent on the size of hydrodynamic diameter of ions. Assuming infinite dilution this ionic diffusivity is estimated using the Nernst-Haskel equation (12) [14] as
(12)
D
°
=
R
T
1
/
z
+
+
1
/
z
-
F
2
1
/
λ
+
+
1
/
λ
-
,
where z
+ and z
- denote charges of cation and anion, respectively, while λ
+ and λ
- denote limiting ionic conductance in the solvent. Other parameters bearing meaning and units are as reported in the nomenclature.Diffusivity is a strong function of viscosity which was corrected using equation proposed by Yuan-Hui and Gregory [15]
(13)
D
D
°
=
μ
°
μ
.


## 3.2.3. 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 becomes zero), the surface concentration on either side can be estimated from bulk concentration measurement (diluate/concentrate), current density, and limiting current density using (14) and (15) [19, 24]:
(14)
C
j
,
m
conc
=
C
j
,
b
conc
1
+
i
i
j
,
lim
⁡
,
(15)
C
j
,
m
dil
=
C
j
,
b
dil
1
-
i
i
j
,
lim
⁡
,
where C
j
,
m
conc and C
j
,
b
conc are the concentrations of ion j, on the membrane surface and in bulk of the concentrate compartment, respectively, in the ED cell. C
j
,
m
dil and C
j
,
b
dil are the concentrations of ion j, on the membrane surface and in the bulk of the diluate side, respectively, in the ED cell.


## 3.2.4. Estimation of Current Density and Limiting Current Density (i and i
j
,
lim
⁡)

LCD (of a single electrolyte) is estimated using the following equation [5, 9]:
(16)
i
j
,
lim
⁡
=
C
j
,
b
dil
D
j
z
j
F
δ
(
t
j
,
m
-
t
j
,
b
)
,
where t
j
,
m and t
j
,
b are transport numbers of ion j in membrane and electrolyte solution, respectively.Considering ion flux in the diluate side of the IEM, (15) is used to calculate concentration of ion j, at the membrane surface of diluate side C
j
,
m
dil.The current density can be expressed by (17) after substitution of (15) and (16) in (6):
(17)
i
=
C
j
,
b
dil
D
j
z
j
ξ
F
R
T
×
t
j
,
m
-
t
j
,
b
z
j
F
+
ξ
δ
t
j
,
m
-
t
j
,
b
R
T
-
t
j
,
m
z
j
F
-
1
,
where ξ the potential gradient can be estimated from Nernst equation given as follows [18, 19]:
(18)
ξ
=
-
2
t
j
,
m
-
1
R
T
δ
F
ln
⁡
⁡
γ
b
dil
C
j
,
b
dil
γ
m
dil
C
j
,
m
dil
,
where γ
m
dil and γ
b
dil 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 can be estimated using Debye-Huckel limiting law [25].


## 4. Numerical Estimation of Parameters

The sequence of steps followed to obtain theoretical estimate of concentration variation is described using flow chart (Figure3). The differential equations (1) and (3) were integrated using Euler method with 1 s time step. Few crucial parameters and their evaluation method are presented below.Figure 3
MATLAB program algorithm showing calculation steps followed to estimate process parameters.


### 4.1. Determination of Transport Number of Ion in Solution

Bulk transport numbert
j
,
b is the fraction of total current carried by the ion type which is a function of diffusion coefficient and ionic mobility of hydrated species. Ions in solution get hydrated with solvent molecules and difference in hydration ability causes variation in size, diffusivity, and mobility of such species. Thus, ions do not transport current equally in solution. The transport number was estimated using following equation [7]:
(19)
t
j
,
b
=
z
j
D
j
∑
j
=
1
n
z
j
D
j
.
For a binary-ion salt solution, n
=
2, j
=
1 for cation and j
=
2 for anion, respectively.


### 4.2. Determination of Current from Resistance Measurement

Initial current density estimation is essential to obtain salt concentration at membrane surface and start numerical integration which may be evaluated either experimentally or from applied potential and solution resistance using Ohm’s law. The potential applied may be expressed as(20)
E
tot
-
E
el
=
R
tot
·
J
,
where E
el is the potential drop near the electrodes, R
tot is the overall resistance (ohm) of the ED cell, and J is the current (A). The overall resistance is the sum of resistances of individual chambers:
(21)
R
tot
=
R
anolyte
+
R
diluate
+
R
catholyte
,
where resistance of anolyte, catholyte, and diluate channel are determined either directly from conductivity measurement or from extended Kohlrausch-equation [19, 25]. The conductivity and the resistance are related as
(22)
Resistance
=
1
Λ
L
A
m
,
where Λ is the conductivity of solution (mho·m−1), L is the gap between membranes or the compartment thickness (m), and A
m is the effective membrane area (m2).


### 4.3. Determination of Specific Energy Consumption

The specific energy consumption,E
sp (kWh·kg−1), was obtained using the following equation:
(23)
E
sp
=
∫
t
1
t
2
ε
A
m
i
(
t
)
d
t
M
Ca
Cl
2
Δ
n
Ca
Cl
2
(
t
)
,
where ε is the applied potential in V, A
m is the area of the membrane in m2, i
(
t
) is the current density as a function of time in A·m−2, M
Ca
Cl
2 is the molecular mass of CaCl2 (=111.02 g/mol), and Δ
n
Ca
Cl
2
(
t
) is the number of moles of CaCl2 removed from the feed solution at various time intervals.


## 4.1. Determination of Transport Number of Ion in Solution

Bulk transport numbert
j
,
b is the fraction of total current carried by the ion type which is a function of diffusion coefficient and ionic mobility of hydrated species. Ions in solution get hydrated with solvent molecules and difference in hydration ability causes variation in size, diffusivity, and mobility of such species. Thus, ions do not transport current equally in solution. The transport number was estimated using following equation [7]:
(19)
t
j
,
b
=
z
j
D
j
∑
j
=
1
n
z
j
D
j
.
For a binary-ion salt solution, n
=
2, j
=
1 for cation and j
=
2 for anion, respectively.


## 4.2. Determination of Current from Resistance Measurement

Initial current density estimation is essential to obtain salt concentration at membrane surface and start numerical integration which may be evaluated either experimentally or from applied potential and solution resistance using Ohm’s law. The potential applied may be expressed as(20)
E
tot
-
E
el
=
R
tot
·
J
,
where E
el is the potential drop near the electrodes, R
tot is the overall resistance (ohm) of the ED cell, and J is the current (A). The overall resistance is the sum of resistances of individual chambers:
(21)
R
tot
=
R
anolyte
+
R
diluate
+
R
catholyte
,
where resistance of anolyte, catholyte, and diluate channel are determined either directly from conductivity measurement or from extended Kohlrausch-equation [19, 25]. The conductivity and the resistance are related as
(22)
Resistance
=
1
Λ
L
A
m
,
where Λ is the conductivity of solution (mho·m−1), L is the gap between membranes or the compartment thickness (m), and A
m is the effective membrane area (m2).


## 4.3. Determination of Specific Energy Consumption

The specific energy consumption,E
sp (kWh·kg−1), was obtained using the following equation:
(23)
E
sp
=
∫
t
1
t
2
ε
A
m
i
(
t
)
d
t
M
Ca
Cl
2
Δ
n
Ca
Cl
2
(
t
)
,
where ε is the applied potential in V, A
m is the area of the membrane in m2, i
(
t
) is the current density as a function of time in A·m−2, M
Ca
Cl
2 is the molecular mass of CaCl2 (=111.02 g/mol), and Δ
n
Ca
Cl
2
(
t
) is the number of moles of CaCl2 removed from the feed solution at various time intervals.


## 5.  Results and Discussions

### 5.1. Role of Sugar and CaCl2 Concentration on Solution Viscosity and Influence of Temperature

Sugar solution viscosity increases nonlinearly (Figure4) with increase in sugar concentration (5 to 20 wt%). Viscosity values range between 0.72 and 1.5 mPa·s with increase in sugar concentration. These values were very much comparable with the literature reported data [16]. Solution viscosity does not show any appreciable change with CaCl2 concentration (0–50 mol/m3) (Figure 5). Influence of temperature on CaCl2 solution viscosity was recorded at 20, 25, 32, 37, and 42°C and viscosity decreases between 1.22 and 0.7 mPa·s. Nearly ~43% lowering in solution viscosity with temperature rise between 20 and 42°C is noted in Figure 5.Figure 4
Effect of wt% of sugar on solution viscosity at 20°C.Figure 5
Effect of concentration of CaCl2 in 5 wt% sugar solution on solution viscosity at different temperatures.


### 5.2. Role of Sugar and CaCl2 Concentration on Electrical Conductivity of Electrolyte

Figure6 shows plot of CaCl2 concentration on the electrical conductivity, which was estimated in presence and absence of sugar. Electrical conductivity increases almost linearly with rise in CaCl2 concentration (5 to 50 mol·m−3). The CaCl2, being a strong electrolyte, dissociates completely in solution, thus increasing number of ions per unit volume available for ionic conductance. On the contrary, sugar addition dampens the conductivity value. This is possibly because sugar is a water soluble nonelectrolyte which does not change the number of ionic species responsible for current carriage; thus, presence of inert sugar molecules basically increases crowding in solution.Figure 6
Effect of molar concentration of CaCl2 in water with and without sugar on electrical conductivity of solution.


### 5.3. Effect of Applied Potential on Ion-Removal Rate

The applied potential is a crucial parameter to define removal rate and efficiency. With increased potential, ion removal rate increases causing rapid lowering of batch time [26]. In a batch operation, with gradual lowering of ion concentration the current density keeps dropping. Once, the concentration reaches below limiting value the solution resistance becomes very high and heating starts. At this increased temperature electrolysis of water starts and a major portion of applied potential gets consumed without much gain in ion removal. Thus, overall energy consumption increases affecting process efficiency [5, 22].Three different voltages (4 V, 8 V, and 12 V) were applied keeping other process parameters unchanged. Figure7 shows effect of applied potential on Ca2+ ion removal rate. With higher potential, the ion removal rate increases. This is quite obvious because with increased electrical driving force (potential), more current passes through the solution as long as resistance remains unchanged. It is interesting to note that at lower potential, the ion removal rate remains linear for a long duration (>240 min) indicating Ohm’s law might be applicable. This is not observed with higher potentials. With −8 V, the nonlinearity appears at time ~180 min while the same happens at time ~120 min for −12 V. Possibly unwanted electrode reactions (water splitting) initiate at early stages with increased potential. This certainly influences the ion removal rate showing variation in slope of the concentration drop curve. This indicates that at higher voltage rapid depletion of ions and a nonlinear rise in resistance occurs. Rapid nonlinear rise in solution resistance was also observed earlier by different scientists [8, 9].Figure 7
Effect of applied potential on the feed concentration. Process conditions are feed: 130 mL/min with CaCl2 (50 mol·m−3) in 5 wt% sugar solution; anolyte: 830 mL/min with HCl (100 mol·m−3); catholyte: 830 mL/min with Na2EDTA (50 mol·m−3) + AA (50 mol·m−3); applied voltage: 4 V, 8 V and 12 V.


### 5.4. Effect of Flow Rate on Ion Removal Rate

Change in ion removal rate with variation in feed flow rate, without disturbing catholyte and anolyte streams conditions (flow rate, components, concentration, etc.), was analyzed and reported in Figure8. Feed flow rates were varied as 80, 130, and 180 mL/min and change in ion removal rate was noted after nearly 60 min of ED operation. A slow rise in removal rate with increased flow rate was observed. Increased flow rate possibly increased turbulence which reduced thickness of stationary boundary film over membrane surface. This lowered the overall ion transfer resistance and increased ion removal rate.Figure 8
Effect of feed flow rate on CaCl2 removal from sugar solution. Process conditions of feed: 80 mL/min, 130 mL/min and 180 mL/min with CaCl2 (50 mol·m−3) in 5% sugar solution; anolyte: 830 mL/min with HCl (100 mol·m−3); catholyte: 830 mL/min with Na2EDTA (50 mol·m−3) + AA (50 mol·m−3); applied voltage: 8 V.


### 5.5. Model Prediction of Experimental “i” and Ca2+ Ion Concentration

The batch mode of electrodialysis with continuous recirculation under an applied potential becomes an unsteady state process. The electrolyte concentrations of diluate (feed tank) and concentrate streams, solution resistance (conductivity), concentration profile around membrane, and bulk physical properties of the solution become time dependent. The cumulative effects of all these parameters are reflected in diluate (feed tank) concentration and overall current density of the ED cell. Therefore, the mathematical model emphasizes two crucial parameters: (i) electrolyte (CaCl2) concentration of the diluate stream (feed tank) and (ii) overall current density of the cell. Unsteady state mass balance around the diluate channel/tank is written in terms of important process variables, for example, vessel volume, flow rate, concentration, current density, current efficiency, and membrane area. Nernst Planck equation and irreversible thermodynamics are used to estimate the ionic flux through the boundary layer over the membrane. The model proposed closely predicts experimental data between the chosen range of process condition of Ca2+ ion (Figures 9 and 10) and current density with time (Figure 9) in the ED cell.Figure 9
Plot of limiting current density,i
lim
⁡
⁡ (A·m−2), experimental current density, i (A·m−2), and molar concentration of diluate tank, C
expt
dil
T (mol·m−3) (shown as discrete data points), versus time for a given set of operating condition: experiment 1 (feed flow rate = 130 mL·min−1; anolyte = 100 mol·m−3 HCl; catholyte = 100 mol·m−3 NaOH; applied voltage = 4 V) [13]. Theoretically predicted values of current and concentration variation with time are shown by continuous line.Figure 10
Close resemblance of theory (continuous line) with experimental molar concentration of CaCl2 of the diluate tank (mol·m−3) (discrete data points) versus time (min) for specified ED operating conditions: (i) experiment 2 (feed flow rate = 130 mL·min−1; anolyte = 100 mol·m−3 HCl; catholyte = 25 mol·m−3 Na2EDTA + 25 mol·m−3 AA; applied voltage = 4 V). (ii) Experiment 3 (feed flow rate = 130 mL·min−1; anolyte = 100 mol·m−3 HCl; catholyte = 50 mol·m−3 Na2EDTA + 50 mol·m−3 AA; applied voltage = 4 V) [13].Molar concentration of the recirculating feed solution was obtained by solving coupled differential equations. Equations (1) and (3) and physical process parameters values are listed in Table 3. Solution steps (using MATLAB code) are discussed in Figure 3. The concentration estimates so obtained were used to estimate current density, i(17). The theoretical model could closely predict the experimental data (Experiments 1, 2, and 3) of concentration variation (Figures 9 and 10). Experiments 2 and 3, performed with two different concentrations of CaCl2 (25 and 50 mol·m−3) in feed solution, behaved in the same manner (Figure 10). This supports the fact that the method adopted in concentration estimation was correct and reproducible.Initially solute concentration (25 mol·m−3) of the feed solution drops steadily in experiment 1, the rate of which slows down after nearly 200 min (Figure 9). The experimental current density also follows same trend (Figure 9). A steady drop in current density from 120 A·m−2 to 40 A·m−2 during first 200 min was recorded possibly due to rapid lowering in ionic concentration in the diluate under applied potential of 4 V.


### 5.6. Role of Catholyte Composition and a Probable Mechanism for Smooth Operation of ED

CaCl2 is a strong electrolyte and preferentially exists in ionized (Ca2+ and 2Cl−1) state in the aqueous solution containing sugar (5%). Water molecules form a hydration sphere around each dissociated ion and stabilize it. On application of external potential these hydrated species start crossing polar membranes charged with counter ions and cause concentration polarization buildup across the polar membrane.The approach adopted here is to minimize the concentration polarization. Ca2+ ion crosses the cation exchange membrane. This was accomplished by either (i) precipitating out the ions or by (ii) complexing out before a back diffusion sets in. Two different catholyte streams were chosen with a definite purpose, for example, (i) 0.1 N NaOH (which forms an insoluble precipitate of Ca2+ ion (23)) and (ii) a mixture of acetic acid and di-sodium salt of EDTA (Na2EDTA, a well-known complexing agent for bivalent cation (Ca2+) after it crosses the CEM, (24)). Hydrated Ca2+ ions cross cation exchange membrane (CEM) and reaches catholyte compartment where it may precipitate or dissolve based on the electrolyte (s) and pH of the catholyte stream. Ca2+ ions react with the NaOH of catholyte stream and forms Ca(OH)2. As the solubility product of Ca(OH)2 in water is very low (~10−6), it experiences high probability of precipitation over membrane surface facing higher pH. Once this precipitate comes in contact with electrolyte containing Na2EDTA, it reacts and forms a stable complex, CaNa2EDTA, which washes out the precipitate formed and cleans the membrane surface. The scheme of overall reaction is presented as follows:
(24)
Ca
2
+
+
2
(
OH
-
)
⟶
Ca
OH
2
⟶
CO
2
CaC
O
3
+
H
2
O
(25)
Ca
2
+
+
Na
2
EDTA
⟶
Ca
Na
2
EDTA
+
2
H
+
Bivalent cation are well known for their low solubility at high pH and often precipitate out as metal hydroxides [27]. This precipitation problem was also observed with calcium ion reported here when NaOH was used in catholyte stream. Figure 11 shows NaOH (100 mol·m−3) as catholyte streams although increases ion removal rate initially, but vigorous fouling prevented the process from running for long duration. With NaOH as catholyte, Ca(OH)2 precipitation was extensive which turned the membrane color from brownish yellow to white and probably blocked the swollen membrane pores on the rare side. Although this approach completely arrested the reverse transport of Ca2+ ions but continuous operation was limited due to membrane fouling, increased resistance, and drop in current density. Frequent acid wash helped in improving the membrane performance but continuous operation was not feasible.Figure 11
Comparison of Ca2+ ions (feed solution, 25 mol·m−3) removal rate between two different techniques adopted. Case 1: anolyte = 100 mol·m−3 HCl; catholyte = 100 mol·m−3NaOH. Case 2: anolyte = 100 mol·m−3 HCl; catholyte = 25 mol·m−3 Na2EDTA + 25 mol·m−3 AA [13].Formation of white solid powder was noted over the membrane (CEM) surface facing catholyte stream (NaOH, higher pH) in experiment 1 and experiment 3. The white powder over membrane was investigated further to have better understanding of the problem which arose after ED operation for specified duration. Quantitative estimations of the fouled membrane were made by gravimetric method. The CEM membrane after ED experimentation was taken out, washed, and weighed, after drying and equilibration. The used membrane (equilibrated 24 hours at 100°C) was found to increase in mass over its initial mass (equilibrated) before ED. Gain of mass in used membrane is reported in Table4.Table 4
Specific energy consumption, mass transfer coefficient, average running cost estimated, and gravimetric analysis.
Expt.
Specific energy consumption for CaCl2 removal, E
sp (kWh·kg−1)
Average running cost (INR/g of CaCl2 removed)
Mass transfer coefficient,
k (m·s−1) × 105
% weight gained by CEM due to fouling
1
2.4023
4.7
1.928
22
2
2.4027
3.4
1.174
3
3
2.4027
1.9
1.173
17The white deposit on the membrane surface could be removed by immersing the membrane in a dilute HCl (10% in water) solution. Immediately after immersion bubbling from the fouled surface of the membrane was observed. For complete dissolution of the white deposit, the membrane was left immersed in the solution for ~30 minutes until bubbling stopped. Subsequently the membrane was removed, washed repeatedly with deionized water, and dried in oven (100°C for 24 hours) and weighed. A blank test was simultaneously performed using a fresh membrane to record the difference between used and fresh membrane. For an applied potential the dry mass of the used membrane was found to be dependent on its duration of application, electrolyte concentration, and electrolyte stream pH.Multiple samples of the used membrane were tested and formation of bubbles was confirmed. Once the bubbling stopped after immersing the membrane in dilute HCl solution, the piece was taken out, washed, dried, and equilibrated before weighing. Mass of the membrane did not deviate much from its initial value. This indicated possibility of CO2 evolution from the reaction of HCl with CaCO3. The most probable sequence of the overall reaction occurring over the membrane surface and its subsequent cleaning with dilute HCl may be explained by the following scheme:
(26)
CO
2
(
air
)
+
2
O
H
-
⟶
CO
3
2
-
+
H
2
O
(27)
Ca
(
OH
)
2
+
CO
2
⟶
CaC
O
3
(
s
)
+
H
2
O
(28)
CaC
O
3
s
+
HCl
⟶
Ca
Cl
2
+
C
O
2
g
+
H
2
O
At higher pH, solubility of CO2 (air) increases in NaOH solution (catholyte stream) which results in formation of HCO
3
-
1/CO
3
2
-. These ions subsequently react with NaOH to form Na2CO3 providing the source for CaCO3 precipitation from Ca(OH)2. Conversion of Ca(OH)2 to CO
3
-
2 is (27) is thermodynamically favorable and moves forward. Nearly 1000 times higher value of solubility product of Ca(OH)2 [5.5
×
10
-
6] over CaCO3 [3.39
×
10
-
9] [28] drives the process faster.Formation of CaCO3 not only increased membrane resistance to ion transport but also made the ED operation discontinuous. The process was made uninterrupted by changing the electrolyte composition of the catholyte stream. Here we report application of Na2EDTA-acetic acid solution as catholyte stream; the chelating agent continuously complexes with the precipitated CaCO3 and formed corresponding salt CaNa2EDTA. The pH of catholyte stream was adjusted between 3.5–5.0 (Table 2) and the anolyte was maintained as HCl (100 mol·m−3). This combination showed negligible fouling even after long (240 min) operation time (Table 4).The mass transfer coefficients estimated from Sherwood number correlation (11) showed higher values while NaOH (100 mol·m−3) was used as catholyte stream compared to Na2EDTA-acetic acid (AA) combination (Table 4). Reduced mass transfer coefficient with Na2EDTA-acetic acid stream may be attributed to higher solution resistance arising possibly due to weak dissociation of acetic acid of Na2EDTA + AA combination than that of NaOH. The dissociation constant can get further affected due to Na2EDTA (a bulky diffusing species). Thus, reduction in mass transfer coefficient lowered Ca2+ ion removal rate.As of now, we have understood that chemical composition and concentration of anolyte/catholyte streams play crucial role in controlling overall resistance and ion removal rate. The specific energy consumption,E
sp, estimated from (23) (Table 4) shows lower value with NaOH compared to the streams containing Na2EDTA + AA.The average running cost to remove unit mass of CaCl2 is reported in Table 4. The cost is dependent on concentration of the electrolyte stream and time of ED operation. Cost is inversely proportional to initial concentration of the stream and directly proportional to operation time. Energy due to pumping is the major contribution to the overall costs estimate in a batch ED operation for a given time.


## 5.1. Role of Sugar and CaCl2 Concentration on Solution Viscosity and Influence of Temperature

Sugar solution viscosity increases nonlinearly (Figure4) with increase in sugar concentration (5 to 20 wt%). Viscosity values range between 0.72 and 1.5 mPa·s with increase in sugar concentration. These values were very much comparable with the literature reported data [16]. Solution viscosity does not show any appreciable change with CaCl2 concentration (0–50 mol/m3) (Figure 5). Influence of temperature on CaCl2 solution viscosity was recorded at 20, 25, 32, 37, and 42°C and viscosity decreases between 1.22 and 0.7 mPa·s. Nearly ~43% lowering in solution viscosity with temperature rise between 20 and 42°C is noted in Figure 5.Figure 4
Effect of wt% of sugar on solution viscosity at 20°C.Figure 5
Effect of concentration of CaCl2 in 5 wt% sugar solution on solution viscosity at different temperatures.


## 5.2. Role of Sugar and CaCl2 Concentration on Electrical Conductivity of Electrolyte

Figure6 shows plot of CaCl2 concentration on the electrical conductivity, which was estimated in presence and absence of sugar. Electrical conductivity increases almost linearly with rise in CaCl2 concentration (5 to 50 mol·m−3). The CaCl2, being a strong electrolyte, dissociates completely in solution, thus increasing number of ions per unit volume available for ionic conductance. On the contrary, sugar addition dampens the conductivity value. This is possibly because sugar is a water soluble nonelectrolyte which does not change the number of ionic species responsible for current carriage; thus, presence of inert sugar molecules basically increases crowding in solution.Figure 6
Effect of molar concentration of CaCl2 in water with and without sugar on electrical conductivity of solution.


## 5.3. Effect of Applied Potential on Ion-Removal Rate

The applied potential is a crucial parameter to define removal rate and efficiency. With increased potential, ion removal rate increases causing rapid lowering of batch time [26]. In a batch operation, with gradual lowering of ion concentration the current density keeps dropping. Once, the concentration reaches below limiting value the solution resistance becomes very high and heating starts. At this increased temperature electrolysis of water starts and a major portion of applied potential gets consumed without much gain in ion removal. Thus, overall energy consumption increases affecting process efficiency [5, 22].Three different voltages (4 V, 8 V, and 12 V) were applied keeping other process parameters unchanged. Figure7 shows effect of applied potential on Ca2+ ion removal rate. With higher potential, the ion removal rate increases. This is quite obvious because with increased electrical driving force (potential), more current passes through the solution as long as resistance remains unchanged. It is interesting to note that at lower potential, the ion removal rate remains linear for a long duration (>240 min) indicating Ohm’s law might be applicable. This is not observed with higher potentials. With −8 V, the nonlinearity appears at time ~180 min while the same happens at time ~120 min for −12 V. Possibly unwanted electrode reactions (water splitting) initiate at early stages with increased potential. This certainly influences the ion removal rate showing variation in slope of the concentration drop curve. This indicates that at higher voltage rapid depletion of ions and a nonlinear rise in resistance occurs. Rapid nonlinear rise in solution resistance was also observed earlier by different scientists [8, 9].Figure 7
Effect of applied potential on the feed concentration. Process conditions are feed: 130 mL/min with CaCl2 (50 mol·m−3) in 5 wt% sugar solution; anolyte: 830 mL/min with HCl (100 mol·m−3); catholyte: 830 mL/min with Na2EDTA (50 mol·m−3) + AA (50 mol·m−3); applied voltage: 4 V, 8 V and 12 V.


## 5.4. Effect of Flow Rate on Ion Removal Rate

Change in ion removal rate with variation in feed flow rate, without disturbing catholyte and anolyte streams conditions (flow rate, components, concentration, etc.), was analyzed and reported in Figure8. Feed flow rates were varied as 80, 130, and 180 mL/min and change in ion removal rate was noted after nearly 60 min of ED operation. A slow rise in removal rate with increased flow rate was observed. Increased flow rate possibly increased turbulence which reduced thickness of stationary boundary film over membrane surface. This lowered the overall ion transfer resistance and increased ion removal rate.Figure 8
Effect of feed flow rate on CaCl2 removal from sugar solution. Process conditions of feed: 80 mL/min, 130 mL/min and 180 mL/min with CaCl2 (50 mol·m−3) in 5% sugar solution; anolyte: 830 mL/min with HCl (100 mol·m−3); catholyte: 830 mL/min with Na2EDTA (50 mol·m−3) + AA (50 mol·m−3); applied voltage: 8 V.


## 5.5. Model Prediction of Experimental “i” and Ca2+ Ion Concentration

The batch mode of electrodialysis with continuous recirculation under an applied potential becomes an unsteady state process. The electrolyte concentrations of diluate (feed tank) and concentrate streams, solution resistance (conductivity), concentration profile around membrane, and bulk physical properties of the solution become time dependent. The cumulative effects of all these parameters are reflected in diluate (feed tank) concentration and overall current density of the ED cell. Therefore, the mathematical model emphasizes two crucial parameters: (i) electrolyte (CaCl2) concentration of the diluate stream (feed tank) and (ii) overall current density of the cell. Unsteady state mass balance around the diluate channel/tank is written in terms of important process variables, for example, vessel volume, flow rate, concentration, current density, current efficiency, and membrane area. Nernst Planck equation and irreversible thermodynamics are used to estimate the ionic flux through the boundary layer over the membrane. The model proposed closely predicts experimental data between the chosen range of process condition of Ca2+ ion (Figures 9 and 10) and current density with time (Figure 9) in the ED cell.Figure 9
Plot of limiting current density,i
lim
⁡
⁡ (A·m−2), experimental current density, i (A·m−2), and molar concentration of diluate tank, C
expt
dil
T (mol·m−3) (shown as discrete data points), versus time for a given set of operating condition: experiment 1 (feed flow rate = 130 mL·min−1; anolyte = 100 mol·m−3 HCl; catholyte = 100 mol·m−3 NaOH; applied voltage = 4 V) [13]. Theoretically predicted values of current and concentration variation with time are shown by continuous line.Figure 10
Close resemblance of theory (continuous line) with experimental molar concentration of CaCl2 of the diluate tank (mol·m−3) (discrete data points) versus time (min) for specified ED operating conditions: (i) experiment 2 (feed flow rate = 130 mL·min−1; anolyte = 100 mol·m−3 HCl; catholyte = 25 mol·m−3 Na2EDTA + 25 mol·m−3 AA; applied voltage = 4 V). (ii) Experiment 3 (feed flow rate = 130 mL·min−1; anolyte = 100 mol·m−3 HCl; catholyte = 50 mol·m−3 Na2EDTA + 50 mol·m−3 AA; applied voltage = 4 V) [13].Molar concentration of the recirculating feed solution was obtained by solving coupled differential equations. Equations (1) and (3) and physical process parameters values are listed in Table 3. Solution steps (using MATLAB code) are discussed in Figure 3. The concentration estimates so obtained were used to estimate current density, i(17). The theoretical model could closely predict the experimental data (Experiments 1, 2, and 3) of concentration variation (Figures 9 and 10). Experiments 2 and 3, performed with two different concentrations of CaCl2 (25 and 50 mol·m−3) in feed solution, behaved in the same manner (Figure 10). This supports the fact that the method adopted in concentration estimation was correct and reproducible.Initially solute concentration (25 mol·m−3) of the feed solution drops steadily in experiment 1, the rate of which slows down after nearly 200 min (Figure 9). The experimental current density also follows same trend (Figure 9). A steady drop in current density from 120 A·m−2 to 40 A·m−2 during first 200 min was recorded possibly due to rapid lowering in ionic concentration in the diluate under applied potential of 4 V.


## 5.6. Role of Catholyte Composition and a Probable Mechanism for Smooth Operation of ED

CaCl2 is a strong electrolyte and preferentially exists in ionized (Ca2+ and 2Cl−1) state in the aqueous solution containing sugar (5%). Water molecules form a hydration sphere around each dissociated ion and stabilize it. On application of external potential these hydrated species start crossing polar membranes charged with counter ions and cause concentration polarization buildup across the polar membrane.The approach adopted here is to minimize the concentration polarization. Ca2+ ion crosses the cation exchange membrane. This was accomplished by either (i) precipitating out the ions or by (ii) complexing out before a back diffusion sets in. Two different catholyte streams were chosen with a definite purpose, for example, (i) 0.1 N NaOH (which forms an insoluble precipitate of Ca2+ ion (23)) and (ii) a mixture of acetic acid and di-sodium salt of EDTA (Na2EDTA, a well-known complexing agent for bivalent cation (Ca2+) after it crosses the CEM, (24)). Hydrated Ca2+ ions cross cation exchange membrane (CEM) and reaches catholyte compartment where it may precipitate or dissolve based on the electrolyte (s) and pH of the catholyte stream. Ca2+ ions react with the NaOH of catholyte stream and forms Ca(OH)2. As the solubility product of Ca(OH)2 in water is very low (~10−6), it experiences high probability of precipitation over membrane surface facing higher pH. Once this precipitate comes in contact with electrolyte containing Na2EDTA, it reacts and forms a stable complex, CaNa2EDTA, which washes out the precipitate formed and cleans the membrane surface. The scheme of overall reaction is presented as follows:
(24)
Ca
2
+
+
2
(
OH
-
)
⟶
Ca
OH
2
⟶
CO
2
CaC
O
3
+
H
2
O
(25)
Ca
2
+
+
Na
2
EDTA
⟶
Ca
Na
2
EDTA
+
2
H
+
Bivalent cation are well known for their low solubility at high pH and often precipitate out as metal hydroxides [27]. This precipitation problem was also observed with calcium ion reported here when NaOH was used in catholyte stream. Figure 11 shows NaOH (100 mol·m−3) as catholyte streams although increases ion removal rate initially, but vigorous fouling prevented the process from running for long duration. With NaOH as catholyte, Ca(OH)2 precipitation was extensive which turned the membrane color from brownish yellow to white and probably blocked the swollen membrane pores on the rare side. Although this approach completely arrested the reverse transport of Ca2+ ions but continuous operation was limited due to membrane fouling, increased resistance, and drop in current density. Frequent acid wash helped in improving the membrane performance but continuous operation was not feasible.Figure 11
Comparison of Ca2+ ions (feed solution, 25 mol·m−3) removal rate between two different techniques adopted. Case 1: anolyte = 100 mol·m−3 HCl; catholyte = 100 mol·m−3NaOH. Case 2: anolyte = 100 mol·m−3 HCl; catholyte = 25 mol·m−3 Na2EDTA + 25 mol·m−3 AA [13].Formation of white solid powder was noted over the membrane (CEM) surface facing catholyte stream (NaOH, higher pH) in experiment 1 and experiment 3. The white powder over membrane was investigated further to have better understanding of the problem which arose after ED operation for specified duration. Quantitative estimations of the fouled membrane were made by gravimetric method. The CEM membrane after ED experimentation was taken out, washed, and weighed, after drying and equilibration. The used membrane (equilibrated 24 hours at 100°C) was found to increase in mass over its initial mass (equilibrated) before ED. Gain of mass in used membrane is reported in Table4.Table 4
Specific energy consumption, mass transfer coefficient, average running cost estimated, and gravimetric analysis.
Expt.
Specific energy consumption for CaCl2 removal, E
sp (kWh·kg−1)
Average running cost (INR/g of CaCl2 removed)
Mass transfer coefficient,
k (m·s−1) × 105
% weight gained by CEM due to fouling
1
2.4023
4.7
1.928
22
2
2.4027
3.4
1.174
3
3
2.4027
1.9
1.173
17The white deposit on the membrane surface could be removed by immersing the membrane in a dilute HCl (10% in water) solution. Immediately after immersion bubbling from the fouled surface of the membrane was observed. For complete dissolution of the white deposit, the membrane was left immersed in the solution for ~30 minutes until bubbling stopped. Subsequently the membrane was removed, washed repeatedly with deionized water, and dried in oven (100°C for 24 hours) and weighed. A blank test was simultaneously performed using a fresh membrane to record the difference between used and fresh membrane. For an applied potential the dry mass of the used membrane was found to be dependent on its duration of application, electrolyte concentration, and electrolyte stream pH.Multiple samples of the used membrane were tested and formation of bubbles was confirmed. Once the bubbling stopped after immersing the membrane in dilute HCl solution, the piece was taken out, washed, dried, and equilibrated before weighing. Mass of the membrane did not deviate much from its initial value. This indicated possibility of CO2 evolution from the reaction of HCl with CaCO3. The most probable sequence of the overall reaction occurring over the membrane surface and its subsequent cleaning with dilute HCl may be explained by the following scheme:
(26)
CO
2
(
air
)
+
2
O
H
-
⟶
CO
3
2
-
+
H
2
O
(27)
Ca
(
OH
)
2
+
CO
2
⟶
CaC
O
3
(
s
)
+
H
2
O
(28)
CaC
O
3
s
+
HCl
⟶
Ca
Cl
2
+
C
O
2
g
+
H
2
O
At higher pH, solubility of CO2 (air) increases in NaOH solution (catholyte stream) which results in formation of HCO
3
-
1/CO
3
2
-. These ions subsequently react with NaOH to form Na2CO3 providing the source for CaCO3 precipitation from Ca(OH)2. Conversion of Ca(OH)2 to CO
3
-
2 is (27) is thermodynamically favorable and moves forward. Nearly 1000 times higher value of solubility product of Ca(OH)2 [5.5
×
10
-
6] over CaCO3 [3.39
×
10
-
9] [28] drives the process faster.Formation of CaCO3 not only increased membrane resistance to ion transport but also made the ED operation discontinuous. The process was made uninterrupted by changing the electrolyte composition of the catholyte stream. Here we report application of Na2EDTA-acetic acid solution as catholyte stream; the chelating agent continuously complexes with the precipitated CaCO3 and formed corresponding salt CaNa2EDTA. The pH of catholyte stream was adjusted between 3.5–5.0 (Table 2) and the anolyte was maintained as HCl (100 mol·m−3). This combination showed negligible fouling even after long (240 min) operation time (Table 4).The mass transfer coefficients estimated from Sherwood number correlation (11) showed higher values while NaOH (100 mol·m−3) was used as catholyte stream compared to Na2EDTA-acetic acid (AA) combination (Table 4). Reduced mass transfer coefficient with Na2EDTA-acetic acid stream may be attributed to higher solution resistance arising possibly due to weak dissociation of acetic acid of Na2EDTA + AA combination than that of NaOH. The dissociation constant can get further affected due to Na2EDTA (a bulky diffusing species). Thus, reduction in mass transfer coefficient lowered Ca2+ ion removal rate.As of now, we have understood that chemical composition and concentration of anolyte/catholyte streams play crucial role in controlling overall resistance and ion removal rate. The specific energy consumption,E
sp, estimated from (23) (Table 4) shows lower value with NaOH compared to the streams containing Na2EDTA + AA.The average running cost to remove unit mass of CaCl2 is reported in Table 4. The cost is dependent on concentration of the electrolyte stream and time of ED operation. Cost is inversely proportional to initial concentration of the stream and directly proportional to operation time. Energy due to pumping is the major contribution to the overall costs estimate in a batch ED operation for a given time.


## 6. Conclusions

Calcium ion (CaCl2, 25 mol·m−3) removal rate depends on feed flow rates, electrolyte (anolyte/catholyte) components, concentrations, applied potential, and so forth. NaOH as catholyte showed higher removal rate and increased mass transfer coefficient over mixed electrolyte (AA-Na2EDTA). Specific energy consumption (E
sp, kWh·kg−1) estimates for three typical set of experiments (Table 4) also support the above observation of easy ion removal rate. Based on this it may be concluded that although NaOH shows better performance for the duration chosen in this report, but an uninterrupted mode ED operation would be feasible with mixed electrolyte only but of course energy consumption will be partly increasing. The unsteady state model used could effectively predict the current density and concentration change with an accuracy of 95%.



---

*Source: 304296-2014-12-14.xml*