2+ Ion Using Electrodialysis from Sugar Solution

Research ArticleSelection of the Best Process Stream to Remove Ca2+ Ion UsingElectrodialysis from Sugar Solution

Jogi Ganesh Dattatreya Tadimeti1 Shilpi Jain1

Sujay Chattopadhyay1 and Prashant Kumar Bhattacharya2

1Polymer and Process Engineering Department IIT Roorkee Saharanpur Campus Saharanpur 247 001 India2Chemical Engineering Department Indian Institute of Technology Kanpur 208 016 India

Correspondence should be addressed to Sujay Chattopadhyay sujay1999gmailcom

Received 30 July 2014 Revised 3 November 2014 Accepted 14 November 2014 Published 14 December 2014

Academic Editor Sergio Ferro

Copyright copy 2014 Jogi Ganesh Dattatreya Tadimeti et al This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Electrodialytic removal of calcium chloride (CaCl2 25ndash50molsdotmminus3) from 5 sugar solution was executed in batch recirculation

mode Calcium ion removal rate wasmonitoredwith (i) applied potential (ii) feed flow rate (iii) solution viscosity and conductivityand (iv) catholyte streams (NaOH or sodium salt of ethylene diamine tetraacetic acid-acetic acid Na

2EDTA-AA) Unsteady state

model for ion concentration change was written for the ED cell used Linearized Nernst-Planck equation instead of Ohmrsquos law wasapplied to closely obtain the current density and concentration change theoreticallyThemodel developed could closely predict theexperimental observation Mass transfer coefficients and specific energy densities were estimated for each combination of catholytestream used NaOH showed better performance for a short duration over Na

2EDTA-acetic acid combination

1 Introduction

In cane based sugar industry the sugar concentration inthe extracted juice after lime (CaO + H

2O) treatment and

color removal (clarification step) usually reaches around 5(mass basis) This stream subsequently enters into series ofevaporators to get concentrated Presence of excess calciumin the postfloculation and precipitation stage of clarifiedsugar juice creates series of nuisance [1] to the subsequentstages (evaporators etc) in sugar industries affecting productquality 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 drasticallyreduce operation and maintenance (evaporator scaling) costand improve product quality Electrodialysis (ED)was chosento remove CaCl

2from its sugar solution ED was applied

earlier in sugar industry to recover tartrate and malate fromgrape sugar [2] and in demineralisation of beet sugar syrupjuice and molasses [3 4] The technological difficulties arisedue to fouling of ion exchange membranes mainly due todeposition of organicinorganic molecules (sugars proteinsCa2+ Mg2+ etc) With increase in solution viscosity foulingbecomes even severe and affects the current efficiency and ionremoval rate The concentration polarization occurs aroundmembrane surface leading to increase in ion resistance andthis is minimized with the help of suitable spacer designtemperature pH and flow rates applied [5ndash11]

A batch recirculation ED process having a single diluatechannel was performed to remove the CaCl

2from sugar solu-

tion As reported elsewhere [5] during ED process concentra-tion polarization arises around the membrane which limits

Hindawi Publishing CorporationInternational Journal of ElectrochemistryVolume 2014 Article ID 304296 12 pageshttpdxdoiorg1011552014304296

2 International Journal of Electrochemistry

the net salt transport This issue was taken up and sorted outusing different combination of anolyte and catholyte streamsDifferent electrolyte streams (NaOH acetic acid-Na

2EDTA

mixture) were selected as catholyte keeping anolyte as HClsolution

In a batch mode electrodialysis with continuous recircu-lation of feed stream properties like electrolyte concentrationof diluate (feed tank) concentration profiles around thatmembrane and all physical properties of the solution changewith timeThe effect of all these parameters is reflected in ionremoval rate and current density of the ED cell Therefore anunsteady state model that can closely predict the ion removalrate and overall current density will be quite relevant in appli-cation point of view Nernst-Planck equation (purely basedon first principles) and irreversible thermodynamics wereused to estimate current density and ion concentration [12]

2 Materials and Methods

21 Equipment

211 Electrodialysis Setup The experimental setup used forED application is shown in the Figure 1 [13] The ED cell andsetup were from Berghof Germany The electric field wasapplied across the cell stack by a built-in DC source Voltageand current between the two electrodes were measured by abuilt-in digital voltmeter and ammeter respectively The EDcell consisted of three compartments as shown in the figureMembranes used were obtained from Permionics Gujaratand cross-linked styrene and di-vinyl benzene gel was used asbase material Cation exchange membrane (CEM) separatesthe cathode compartment and anion exchange membrane(AEM) separates the anode compartment from the feedchamber The effective membrane area for the cell 119860

119898

was 00037m2 and the feed compartment thickness ℎ was0002m

212 Power Supply The power supply was provided througha voltage stabilizer of 110220V AC with 50ndash80Hz fre-quency The same gave an output voltage 0ndash499V DC andcurrent 0ndash399A Four centrifugal pumps were inbuilt withthe system for pumping the solution

213 Conductivity Meter Solution conductivity was noted atregular interval through an offline conductivity meter (Sys-tronics India) of 200mMho with 5 ranges (accuracy plusmn1)

214 ED Cell Compartments and Solutions Used 1000mLsolutions of each stream (feed catholyte and anolyte) weretaken in three chambers (Figure 1) respectively Each cham-ber was connected with the respective three compartmentsof the ED cell through flexi tubing Solutions were circulatedat a constant rate by three centrifugal pumps and the solutionflow rates were measured using rotameters connected to eachstream Table 1 indicates membrane parameters obtainedfrom Permionics India Ltd The composition and flow ratesof three streams used are reported in Table 2

Synthetic solution of 5 sugar and calcium chloride(CaCl

2) was prepared in distilled water The concentration of

FeedAnolytetank

Catholytetank

V

A

CEM

AEM

DC source

R

R R

Solution flow linesCurrent lines

A AmmeterV Voltmeter

R RotameterAEM Anion exchange membraneCEM Cation exchange membrane

tank

+ minus

minus

+

Figure 1 Batch recirculation electrodialysis process showing thestorage tanks pumps manual control valves various chambers ofthe ED cell electrodes DC supply source voltmeter ammeter andflow meters used in the experiment [13]

Table 1 Membrane parameters as obtained from Permionics IndiaLtd

Physical parameters Cation exchangemembrane

Anion exchangemembrane

Transport number 091 09Experimental resistance(ohm cmminus2) 20ndash35 mdash

Max pressure allowed(kgcmminus2) 30 30

Thickness (mm) 011 to 015 009ndash011Max temperature (∘C) 60 60

sugar was kept unchanged but that of CaCl2was varied The

synthetic solution having CaCl2with initial concentrations of

25molsdotmminus3 and 50molsdotmminus3 were used in the diluate channelof ED cell Dilute solution of HCl (100molsdotmminus3) was usedas anolyte in all experiments while NaOH (100molsdotmminus3) wasused as catholyte in experiment 1 and equimolar mixtures ofacetic acid (AA) andNa

2EDTA (25molsdotmminus3 and 50molsdotmminus3)

were respectively used as catholyte in experiments 2 and 3(Table 2)

215 Viscosity Measurement Viscosity measurement wascarried out using Ubbelhood viscometer always fitted in aconstant temperature bath to nullify any temperature effecton capillary flow

22 Procedure The chambers of the ED cell and membraneswere washed thoroughly before each experiment was carriedout Initially the feed solution containing 5 sugar andCaCl

2

International Journal of Electrochemistry 3

Table 2 Different process variables chosen during ED experimentation [13]

Exptnumber Feed solution

Feed flowrate

(mLsdotminminus1)Anolyte solution

Anolyte flowrate

(mLsdotminminus1)Catholyte solution

Catholyteflow rate

(mLsdotminminus1)

Voltageapplied (V)

Time(min)

125molsdotmminus3 CaCl2

in 5 sugarsolution

130 100molsdotmminus3HClsolution 830 100molsdotmminus3NaOH

solution 830 4 685


in 5 sugarsolution

130 100molsdotmminus3HClsolution 830

25molsdotmminus3Na2EDTA+ 25molsdotmminus3 AA

solution830 4 240


in 5 sugarsolution



solution830 4 240

was used and was circulated at a constant rate (130mLmin)through the feed compartment The feed solution anolyteand catholyte were continuously recycled through the ED celland that caused a continuous change in salt concentrationof feed solution The concentration was measured at regularintervals For a fixed applied voltage (119881) variation of current(ldquo119868rdquo through the membrane stack) and concentration of salt(Ca2+ ions) was estimated from conductivity measurementand using standard calibration chart (mass concentrationversus conductance) and was recorded with time (119905)

ED cell was dismantled membranes were taken outchecked visually to find any deposition over the surfaces aftereach experimentMembraneswere thenwashedwith distilledwater and oven dried at 100∘C for 24 hours and weighed tofind any gain or loss in mass of membrane

3 Modeling of Ion Transport

Current density and limiting current density (LCD) of anED cell is a function of a series of parameters for exam-ple physical (cell geometry flow dynamics spacer spacingsolution density and viscosity) and chemical (ion concen-tration transport number and diffusivity) for a given setof membrane pairs Precise estimate of these parametersand application of Nernst-Planck equation (assuming zeroion concentration on the membrane surface) would give atheoretical estimate of LCD which can also be determinedexperimentally from plot of 119868 versus 119881 characteristics of theelectrolyte in the ED cell [7 9]

31 Determination of Bulk Concentration of Diluate Compart-ment Concentration of ions was obtained through unsteadymass balance over diluate catholyte and anolyte compart-ments The following assumptions were made [18]

(i) The ED cell and the feed tank are approximated to bea perfectly mixed flow reactor

(ii) Back diffusion of ions was ignored(iii) Electroneutrality condition is always maintained

Themass balance equation of diluate compartment in the EDcell can be expressed as

119881dilC119889119862

dil

119889119905

= 119876

dil(119862

dil119879

minus 119862

dil) minus

120578119894119860

119898

119911119865

(1)

where 119881dilC is the volume of the diluate compartment (m3)and 119905 is time (s)119862dil

119879and119862dil represent diluate concentrations

leaving feed tank and leaving cell compartment (molsdotmminus3)119876

dil is the diluate volumetric flow rate (m3s) 120578 is the currentefficiency 119894 is the current density (Asdotmminus2) and 119860

119898is the

effective membrane area (m2)120578 can be obtained from the following equation [18 19]

120578 = 119905

+CEM + 119905

minusAEM minus 1 (2)

where 119905

+CEM is the transport number of cation in cationexchange membranes and 119905

minusAEM is the transport number ofanion in anion exchange membrane

Similarly unsteady state mass balance around feed tankcan be written as

119889 (119881

119879119862

dil119879)

119889119905

= 119876

dil(119862

dilminus 119862

dil119879)

(3)

where 119881

119879is the volume of feed tank (m3) During electro-

dialysis water transport occurs across the membranes dueto electroosmosis and osmosis [19] Volume change (due towater transport) was ignored as there was no net volumechange noted experimentally

32 Determination of the Current Density

321 Overall Flux Equation A pictorial representation ofdifferent concentration profiles possibly developed aroundthe membrane is described in Figure 2 The flux of ions pass-ing through the membrane can be expressed by generalizedNernst Planck equation as [7]

119873

119895= minus119863

119895

120597119862

119895

120597119909

minus

119911

119895119862

119895119865119863

119895

119877119879

120597120595

120597119909

(4)

where 119909 is the distance measured from boundary layer incontact with the bulk solution in diluate channel towardsthe membrane 119863

119895is the diffusivity of ion (m2sdotsminus1) 119862

119895is

the concentration of ion 119895 (molsdotmminus3) 119877 is the universal gasconstant (8314 Jsdotmolminus1sdotkminus1) 119879 is the temperature (K) 119911

119895is

the charge of diffusing species 119895 and 120597120595120597119909 is the potentialgradient (Vsdotmminus1) and 119865 is the Faraday constant (Csdotgeqvminus1)


Diffusion boundary layer

Concentrate Diluate

Cation exchange membrane

++

minus

Cconcjm

Cconcjb

Cdiljm

Cdiljb

120575 120575

Figure 2 Depiction of ion transport and hypothetical linear con-centration boundary layer formed across either side of the mem-brane in ED cell

The total molar flux of ion ldquo119895rdquo through the ion exchangemembrane 119873

119895119898 can be related to the current density 119894 as

[7]

119873

119895119898=

119905

119895119898119894

119911

119895119865

(5)

where 119905119895119898

is the transport number of ion 119895 in the membrane119894 is current per unit area of membrane or current density(Asdotmminus2) and 119911

119895is the charge of the ion

At steady state119873119895and119873

119895119898are equal that is

119905

119895119898119894

119911

119895119865

= minus119863

119895

120597119862

119895

120597119909

minus

119911

119895119862

119895119865119863

119895

119877119879

120597120595

120597119909

(6)

Assuming that a linear profile of the concentration distribu-tion exists along the boundary layer the linearized Nernst-Planck equation could be used instead of (6) Expression forthe linearized Nernst-Planck equation when applied in thediluate chamber is [7]

119905

119895119898119894

119911

119895119865

=

119863

119895(119862

dil119895119887

minus 119862

dil119895119898

)

120575

minus

119911

119895119863

119895119865120585119862

dil119895119898

119877119879

(7)

where 120575 is the boundary layer thickness (m)119862dil119895119887

and119862dil119895119898

areconcentrations of ions in bulk and at the membrane surfacerespectively of the diluate compartment and 120585 is the potentialgradient (Vsdotmminus1) and is expressed as

120585 =

120595

120575

(8)

In (7) the first part that is119863119895(119862

dil119895119887

minus119862

dil119895119898

)120575 denotes flux duetomolecular diffusion flux of ion arising out of concentrationvariation between solution bulk and boundary layer overmembrane surface The second part that is 119911

119895119863

119895119865120585119862

dil119895119898

119877119879shows flux due to externally applied potential over themembrane

322 Boundary LayerThickness 120575 Estimation 120575 is estimatedusing film theory (equation (9)) and salt mass-transfercoefficient [7 20] Salt mass-transfer coefficient is usuallydetermined based on salt diffusivity and suitable mass-transfer correlation which in-turn is dependent on flowprofile andphysical properties of the fluids cell geometry andsurface morphology of membranes used in ED cell [7 9 2122]

120575 =

119863

119895

119896

(9)

where 119863119895and 119896 are diffusivity and mass transfer coefficient

of diffusing species in solution Each of these parameters wasseparately estimated using standard correlations The masstransfer coefficient was obtained from Sherwood number[7 20 21] as

Sh =

119896 sdot 119897

119863

119895

(10)

where 119897 is the characteristic length (m) Sherwood numberSh is expressed as a function of Reynolds number Re andSchmidt number Sc [7 20] The empirical expression ofSherwood number is based on cell geometry and spacerconfiguration chosen for the present cell as indicated in thefollowing [17 20 23]

Sh = 119886 sdot Re119887 sdot Sc119888 (11)

where Sc (Schmidt number 120583120588119863119895) is estimated from phys-

ical properties (viscosity and density) of the medium whileReynolds number (120588V119897120583) indicates flow characteristics ofthe medium and channel spacing as ldquo119897rdquo and 119886 119887 119888 are theempirical constants which are determined by fitting the data(ShScc versus Re) for experiments where flow rate is variedIn this work the values of 119886 119887 and 119888 are taken from literature[17] and are given in Table 3

Ionic diffusivity is entirely dependent on the size ofhydrodynamic diameter of ions Assuming infinite dilutionthis ionic diffusivity is estimated using the Nernst-Haskelequation (12) [14] as

119863

∘=

119877119879 [(1119911

+) + (1119911

minus)]

119865

2[(1120582

+) + (1120582

minus)]

(12)

where 119911+and 119911

minusdenote charges of cation and anion respec-

tively while 120582+and 120582

minusdenote limiting ionic conductance in

the solvent Other parameters bearing meaning and units areas reported in the nomenclature


Table 3 Values of different physical parameters used in the model

Parameter Value ReferenceTemperature 119879 298K This workTransport number of the cation in CEM 119905

+CEM 091 Table 1Transport number of the anion in AEM 119905

minusAEM 09 Table 1Transport number of cation in the solution 119905Ca2+ 119904 04387 This work [7]Transport number of anion in the solution 119905Clminus 119904 05613 This work [7]Diffusivity of CaCl2 in 5 sugar solution at 25∘C119863CaCl2 1198 times 10minus9m2

sdotsminus1 This work [14 15]Diffusivity of Ca2+ ions at infinite dilution and at 25∘C119863∘Ca2+ 792 times 10minus10m2

sdotsminus1 This work [14]Diffusivity of Ca2+ ions in 5 sugar solutions at 25∘C119863Ca2+ 711 times 10minus10m2

sdotsminus1 This work [14 15]Diffusivity of Clminus ions in 5 sugar solutions at 25∘C119863Clminus 182 times 10minus10m2

sdotsminus1 This work [14 15]Distance between adjacent membranes 119897 2 times 10minus3m This workArea of the membrane 119860

11989837 times 10minus3m2 This work

Charge on the calcium ion 119911Ca2+ +2 This workViscosity of 5 sugar solution 120583 992 times 10minus4 Pasdots [16]Velocity of the feed stream V 31 times 10minus2msdotsminus1 This workApplied voltage 119864tot 4 V This workCurrent density initial value 119894(0) 122Asdotmminus2 This workCurrent efficiency 120578 081 This work

Sh number empirical equation constant 119886 046 for catholyte NaOH [17]025 plusmn 003 for catholyte AA-Na2EDTA This work

Sh number empirical equation constant 119887 063 for any anolyte and catholyte [17]Sh number empirical equation constant 119888 033 for any anolyte and catholyte [17]

Diffusivity is a strong function of viscosity which wascorrected using equation proposed by Yuan-Hui andGregory[15]

119863

119863

∘=

120583

∘

120583

(13)

323 Estimation of Membrane Surface Concentration Themembrane surface concentration of ions is dependent oncurrent density under an applied voltage As long as the EDoperation is executed below limiting current (surface con-centration becomes zero) the surface concentration on eitherside can be estimated from bulk concentration measurement(diluateconcentrate) current density and limiting currentdensity using (14) and (15) [19 24]

119862

conc119895119898

= 119862

conc119895119887

(1 +

119894

119894

119895lim) (14)

119862

dil119895119898

= 119862

dil119895119887

(1 minus

119894

119894

119895lim) (15)

where 119862

conc119895119898

and 119862

conc119895119887

are the concentrations of ion 119895on the membrane surface and in bulk of the concentratecompartment respectively in the ED cell 119862dil

119895119898and 119862

dil119895119887

arethe concentrations of ion 119895 on the membrane surface and inthe bulk of the diluate side respectively in the ED cell

324 Estimation of Current Density and Limiting CurrentDensity (119894 and 119894

119895119897119894119898) LCD(of a single electrolyte) is estimated

using the following equation [5 9]

119894

119895lim =

119862

dil119895119887119863

119895119911

119895119865

120575 (119905

119895119898minus 119905

119895119887)

(16)

where 119905

119895119898and 119905

119895119887are transport numbers of ion 119895 in

membrane and electrolyte solution respectivelyConsidering ion flux in the diluate side of the IEM (15)

is used to calculate concentration of ion 119895 at the membranesurface of diluate side 119862dil

119895119898

The current density can be expressed by (17) after substi-tution of (15) and (16) in (6)

119894 = (119862

dil119895119887119863

119895119911

119895120585

119865

119877119879

)

times (

119905

119895119898minus 119905

119895119887

119911

119895119865

+

120585120575 (119905

119895119898minus 119905

119895119887)

119877119879

minus

119905

119895119898119911

119895

119865

)

minus1

(17)

where 120585 the potential gradient can be estimated from Nernstequation given as follows [18 19]

120585 = minus (2119905

119895119898minus 1)

119877119879

120575119865

ln(

120574

dil119887119862

dil119895119887

120574

dil119898119862

dil119895119898

) (18)

where 120574

dil119898

and 120574

dil119887

are the mean ionic activity coefficientscorresponding to the ions at the wall of IEM and in the bulk


of solution respectively within the diluate channel and theycan be estimated using Debye-Huckel limiting law [25]

4 Numerical Estimation of Parameters

The sequence of steps followed to obtain theoretical estimateof concentration variation is described using flow chart(Figure 3) The differential equations (1) and (3) were inte-grated using Euler method with 1 s time step Few crucialparameters and their evaluationmethod are presented below

41 Determination of Transport Number of Ion in SolutionBulk transport number 119905

119895119887is the fraction of total current

carried by the ion type which is a function of diffusioncoefficient and ionic mobility of hydrated species Ions insolution get hydrated with solvent molecules and differencein hydration ability causes variation in size diffusivity andmobility of such species Thus ions do not transport currentequally in solution The transport number was estimatedusing following equation [7]

119905

119895119887=

1003816

1003816

1003816

1003816

1003816

119911

119895

1003816

1003816

1003816

1003816

1003816

119863

119895

sum

119899

119895=1

1003816

1003816

1003816

1003816

1003816

119911

119895

1003816

1003816

1003816

1003816

1003816

119863

119895

(19)

For a binary-ion salt solution 119899 = 2 119895 = 1 for cation and119895 = 2 for anion respectively

42 Determination of Current from Resistance MeasurementInitial current density estimation is essential to obtain saltconcentration at membrane surface and start numericalintegration which may be evaluated either experimentally orfrom applied potential and solution resistance using Ohmrsquoslaw The potential applied may be expressed as

119864tot minus 119864el = 119877tot sdot 119869 (20)

where 119864el is the potential drop near the electrodes 119877tot isthe overall resistance (ohm) of the ED cell and 119869 is thecurrent (119860) The overall resistance is the sum of resistancesof individual chambers

119877tot = 119877anolyte + 119877diluate + 119877catholyte (21)

where resistance of anolyte catholyte and diluate channel aredetermined either directly from conductivity measurementor from extended Kohlrausch-equation [19 25] The conduc-tivity and the resistance are related as

Resistance = 1

Λ

119871

119860

119898

(22)

where Λ is the conductivity of solution (mhosdotmminus1) 119871 is thegap between membranes or the compartment thickness (m)and 119860

119898is the effective membrane area (m2)

43 Determination of Specific Energy Consumption The spe-cific energy consumption 119864sp (kWhsdotkgminus1) was obtainedusing the following equation

119864sp =

int

1199052

1199051

120576119860

119898119894 (119905) 119889119905

119872CaCl2

Δ119899CaCl2(119905)

(23)

Input data Estimate

Estimate

EstimateNo

Comparison with experimental data

and error calculation

Yes

PlotsEnd

t1 = t1 + Δt

t1 = t + Δt

t = t0

120585(t) and i(t)

t1 = tend

CdilT (0) Cdil(0)

CconcT (0) Cconc(0)

i(0) EtotQdilVdil t0

Δt tend

CdilT (t1) Cdil(t1)

CconcT (t1) Cconc(t1)

ilim(t) Cconcjm (t)

Cdiljm(t)

ilim versus t i versus tCT

dil versus t

Figure 3 MATLAB program algorithm showing calculation stepsfollowed to estimate process parameters

where 120576 is the applied potential in V 119860119898is the area of the

membrane in m2 119894(119905) is the current density as a functionof time in Asdotmminus2 119872CaCl

2

is the molecular mass of CaCl2

(=11102 gmol) and Δ119899CaCl2

(119905) is the number of moles ofCaCl2removed from the feed solution at various time

intervals

5 Results and Discussions

51 Role of Sugar and CaCl2Concentration on Solution

Viscosity and Influence of Temperature Sugar solution vis-cosity increases nonlinearly (Figure 4) with increase in sugarconcentration (5 to 20wt) Viscosity values range between072 and 15mPasdots with increase in sugar concentrationThese values were very much comparable with the literaturereported data [16] Solution viscosity does not show anyappreciable change with CaCl

2concentration (0ndash50molm3)

(Figure 5) Influence of temperature on CaCl2solution vis-

cosity was recorded at 20 25 32 37 and 42∘C and viscositydecreases between 122 and 07mPasdots Nearly sim43 loweringin solution viscosity with temperature rise between 20 and42∘C is noted in Figure 5

52 Role of Sugar and CaCl2Concentration on Electrical

Conductivity of Electrolyte Figure 6 shows plot of CaCl2con-

centration on the electrical conductivity whichwas estimatedin presence and absence of sugar Electrical conductivityincreases almost linearly with rise in CaCl

2concentration

(5 to 50molsdotmminus3) The CaCl2 being a strong electrolyte

dissociates completely in solution thus increasing numberof ions per unit volume available for ionic conductance Onthe contrary sugar addition dampens the conductivity valueThis is possibly because sugar is a water soluble nonelec-trolyte which does not change the number of ionic speciesresponsible for current carriage thus presence of inert sugarmolecules basically increases crowding in solution

53 Effect of Applied Potential on Ion-Removal Rate Theapplied potential is a crucial parameter to define removal


0 2 4 6 8 10

10

11

12 y = 00209x + 0989756

R2 = 098

Visc

osity

at20

∘ C(m

Pamiddots)

Sugar (wtwt) in 20molmiddotmminus3 CaCl2 solution ()

Figure 4 Effect of wt of sugar on solution viscosity at 20∘C

0 10 20 30 40 5006

08

10

12

14

16

Concentration of CaCl2 in 3)

Visc

osity

(mPamiddots)

20∘C25∘C32∘C

37∘C42∘C

5 wt sugar solution (molm

Figure 5 Effect of concentration of CaCl2in 5wt sugar solution

on solution viscosity at different temperatures

rate and efficiency With increased potential ion removalrate increases causing rapid lowering of batch time [26] In abatch operation with gradual lowering of ion concentrationthe current density keeps dropping Once the concentrationreaches below limiting value the solution resistance becomesvery high and heating starts At this increased temperatureelectrolysis of water starts and a major portion of appliedpotential gets consumed without much gain in ion removalThus overall energy consumption increases affecting processefficiency [5 22]

Three different voltages (4V 8V and 12V) were appliedkeeping other process parameters unchanged Figure 7 showseffect of applied potential on Ca2+ ion removal rate Withhigher potential the ion removal rate increases This isquite obvious because with increased electrical driving force

0 10 20 30 40 500

2

4

6

8

10

12

5 sugar solutionPure aq solution

Conc of CaCl2 (molmiddotmminus3)

Elec

tric

al co

nduc

tivity

at25

∘ C(m

S)

Figure 6 Effect of molar concentration of CaCl2in water with and

without sugar on electrical conductivity of solution

0 30 60 90 120 150 180 210 240

10

20

30

40

50

Time (min)

Con

cent

ratio

n of

CaC

l 2(m

olmiddotm

minus3)

4V8V12V

Figure 7 Effect of applied potential on the feed concen-tration Process conditions are feed 130mLmin with CaCl

2

(50molsdotmminus3) in 5wt sugar solution anolyte 830mLminwithHCl(100molsdotmminus3) catholyte 830mLmin with Na

2EDTA (50molsdotmminus3)

+ AA (50molsdotmminus3) applied voltage 4V 8V and 12V

(potential) more current passes through the solution as longas resistance remains unchanged It is interesting to note thatat lower potential the ion removal rate remains linear fora long duration (gt240min) indicating Ohmrsquos law might beapplicable This is not observed with higher potentials Withminus8V the nonlinearity appears at time sim180min while thesame happens at time sim120min for minus12 V Possibly unwantedelectrode reactions (water splitting) initiate at early stageswith increased potential This certainly influences the ionremoval rate showing variation in slope of the concentration


drop curve This indicates that at higher voltage rapid deple-tion of ions and a nonlinear rise in resistance occurs Rapidnonlinear rise in solution resistance was also observed earlierby different scientists [8 9]

54 Effect of Flow Rate on Ion Removal Rate Change inion removal rate with variation in feed flow rate withoutdisturbing catholyte and anolyte streams conditions (flowrate components concentration etc) was analyzed andreported in Figure 8 Feed flow rates were varied as 80 130and 180mLmin and change in ion removal rate was notedafter nearly 60min of ED operation A slow rise in removalrate with increased flow rate was observed Increased flowrate possibly increased turbulence which reduced thicknessof stationary boundary film over membrane surface Thislowered the overall ion transfer resistance and increased ionremoval rate

55 Model Prediction of Experimental ldquoirdquo and Ca2+ IonConcentration The batch mode of electrodialysis with con-tinuous recirculation under an applied potential becomes anunsteady state processThe electrolyte concentrations of dilu-ate (feed tank) and concentrate streams solution resistance(conductivity) concentration profile around membrane andbulk physical properties of the solution become time depen-dent The cumulative effects of all these parameters arereflected in diluate (feed tank) concentration and overallcurrent density of the ED cell Therefore the mathematicalmodel emphasizes two crucial parameters (i) electrolyte(CaCl

2) concentration of the diluate stream (feed tank) and

(ii) overall current density of the cell Unsteady state massbalance around the diluate channeltank is written in termsof important process variables for example vessel volumeflow rate concentration current density current efficiencyand membrane area Nernst Planck equation and irreversiblethermodynamics are used to estimate the ionic flux throughthe boundary layer over the membraneThe model proposedclosely predicts experimental data between the chosen rangeof process condition of Ca2+ ion (Figures 9 and 10) andcurrent density with time (Figure 9) in the ED cell

Molar concentration of the recirculating feed solutionwasobtained by solving coupled differential equations Equations(1) and (3) and physical process parameters values are listed inTable 3 Solution steps (using MATLAB code) are discussedin Figure 3 The concentration estimates so obtained wereused to estimate current density 119894 (17)The theoretical modelcould closely predict the experimental data (Experiments 1 2and 3) of concentration variation (Figures 9 and 10) Experi-ments 2 and 3 performed with two different concentrationsof CaCl

2(25 and 50molsdotmminus3) in feed solution behaved in

the same manner (Figure 10) This supports the fact that themethod adopted in concentration estimation was correct andreproducible

Initially solute concentration (25molsdotmminus3) of the feedsolution drops steadily in experiment 1 the rate of whichslows down after nearly 200min (Figure 9)The experimentalcurrent density also follows same trend (Figure 9) A steadydrop in current density from 120Asdotmminus2 to 40Asdotmminus2 during

0 50 100 150 200 250

10

20

30

40

50

Time (min)

Feed flow rate

Con

cent

ratio

n of

CaC

l 2(m

olmiddotm

minus3)

80mLmin130mLmin180mLmin

Figure 8 Effect of feed flow rate on CaCl2removal from sugar

solution Process conditions of feed 80mLmin 130mLmin and180mLmin with CaCl

2(50molsdotmminus3) in 5 sugar solution anolyte

830mLmin with HCl (100molsdotmminus3) catholyte 830mLmin withNa2EDTA (50molsdotmminus3) + AA (50molsdotmminus3) applied voltage 8 V

0 100 200 300 400 500 600 7000

20

40

60

80

100

120

140

160

180

200

Time (min)

Cdil tankexpt molmiddotmminus3 in experiment 1

iexpt Amiddotmminus2 in experiment 1ilim Amiddotmminus2 in experiment 1Model prediction

Figure 9 Plot of limiting current density 119894lim (Asdotmminus2) experimentalcurrent density 119894 (Asdotmminus2) and molar concentration of diluate tank119862

dil119879expt (molsdotmminus3) (shown as discrete data points) versus time for a

given set of operating condition experiment 1 (feed flow rate =130mLsdotminminus1 anolyte = 100molsdotmminus3 HCl catholyte = 100molsdotmminus3NaOH applied voltage = 4V) [13] Theoretically predicted valuesof current and concentration variation with time are shown bycontinuous line

first 200min was recorded possibly due to rapid lowering inionic concentration in the diluate under applied potential of4V


0 50 100 150 200 25010

15

20

25

30

35

40

45

50

55

60

Time (min)



Model prediction

Con

cent

ratio

n of

CaC

l 2(m

olmiddotm

minus3)

Figure 10 Close resemblance of theory (continuous line) withexperimental molar concentration of CaCl

2of the diluate tank

(molsdotmminus3) (discrete data points) versus time (min) for specifiedED operating conditions (i) experiment 2 (feed flow rate =130mLsdotminminus1 anolyte = 100molsdotmminus3 HCl catholyte = 25molsdotmminus3Na2EDTA + 25molsdotmminus3 AA applied voltage = 4V) (ii) Experiment

3 (feed flow rate = 130mLsdotminminus1 anolyte = 100molsdotmminus3 HClcatholyte = 50molsdotmminus3 Na

2EDTA + 50molsdotmminus3 AA applied voltage

= 4V) [13]

56 Role of Catholyte Composition and a Probable Mechanismfor Smooth Operation of ED CaCl

2is a strong electrolyte

and preferentially exists in ionized (Ca2+ and 2Clminus1) state inthe aqueous solution containing sugar (5)Water moleculesform a hydration sphere around each dissociated ion and sta-bilize it On application of external potential these hydratedspecies start crossing polar membranes charged with counterions and cause concentration polarization buildup across thepolar membrane

The approach adopted here is to minimize the concen-tration polarization Ca2+ ion crosses the cation exchangemembrane This was accomplished by either (i) precipitatingout the ions or by (ii) complexing out before a back diffusionsets in Two different catholyte streams were chosen with adefinite purpose for example (i) 01 N NaOH (which formsan insoluble precipitate of Ca2+ ion (23)) and (ii) a mixtureof acetic acid and di-sodium salt of EDTA (Na

2EDTA a

well-known complexing agent for bivalent cation (Ca2+)after it crosses the CEM (24)) Hydrated Ca2+ ions crosscation exchange membrane (CEM) and reaches catholytecompartment where it may precipitate or dissolve based onthe electrolyte (s) and pH of the catholyte stream Ca2+ ionsreact with theNaOHof catholyte stream and formsCa(OH)

2

As the solubility product of Ca(OH)2in water is very low

(sim10minus6) it experiences high probability of precipitation overmembrane surface facing higher pH Once this precipitatecomes in contact with electrolyte containing Na

2EDTA it

reacts and forms a stable complex CaNa2EDTA which

washes out the precipitate formed and cleans the membranesurfaceThe schemeof overall reaction is presented as follows

Ca2+ + 2 (OHminus) 997888rarr Ca (OH)

2

CO2

997888rarr CaCO3+H2O (24)

Ca2+ +Na2EDTA 997888rarr CaNa

2EDTA + 2H+ (25)

Bivalent cation are well known for their low solubility at highpH and often precipitate out as metal hydroxides [27] Thisprecipitation problem was also observed with calcium ionreported here when NaOH was used in catholyte streamFigure 11 shows NaOH (100molsdotmminus3) as catholyte streamsalthough increases ion removal rate initially but vigorousfouling prevented the process from running for long dura-tion With NaOH as catholyte Ca(OH)

2precipitation was

extensive which turned the membrane color from brownishyellow to white and probably blocked the swollen membranepores on the rare side Although this approach completelyarrested the reverse transport of Ca2+ ions but continuousoperation was limited due to membrane fouling increasedresistance and drop in current density Frequent acid washhelped in improving the membrane performance but contin-uous operation was not feasible

Formation of white solid powder was noted over themembrane (CEM) surface facing catholyte stream (NaOHhigher pH) in experiment 1 and experiment 3 The whitepowder over membrane was investigated further to havebetter understanding of the problem which arose after EDoperation for specified duration Quantitative estimations ofthe fouledmembrane weremade by gravimetric methodTheCEM membrane after ED experimentation was taken outwashed and weighed after drying and equilibration Theused membrane (equilibrated 24 hours at 100∘C) was foundto increase in mass over its initial mass (equilibrated) beforeED Gain of mass in used membrane is reported in Table 4

The white deposit on the membrane surface could beremoved by immersing the membrane in a dilute HCl (10in water) solution Immediately after immersion bubblingfrom the fouled surface of the membrane was observed Forcomplete dissolution of the white deposit the membrane wasleft immersed in the solution for sim30 minutes until bubblingstopped Subsequently the membrane was removed washedrepeatedly with deionized water and dried in oven (100∘Cfor 24 hours) and weighed A blank test was simultaneouslyperformed using a fresh membrane to record the differencebetween used and fresh membrane For an applied potentialthe dry mass of the used membrane was found to be depen-dent on its duration of application electrolyte concentrationand electrolyte stream pH

Multiple samples of the used membrane were tested andformation of bubbles was confirmed Once the bubblingstopped after immersing the membrane in dilute HCl solu-tion the piece was taken out washed dried and equilibratedbefore weighing Mass of the membrane did not deviatemuch from its initial value This indicated possibility of CO

2

evolution from the reaction of HCl with CaCO3 The most

probable sequence of the overall reaction occurring over the


Table 4 Specific energy consumption mass transfer coefficient average running cost estimated and gravimetric analysis

ExptSpecific energy

consumption for CaCl2removal 119864sp (kWhsdotkgminus1)

Average running cost(INRg of CaCl2 removed)

Mass transfer coefficient119896 (msdotsminus1) times 105

weight gained by CEMdue to fouling

1 24023 47 1928 222 24027 34 1174 33 24027 19 1173 17

0 50 100 150 200 2500

10

20

30

40

50

60

70

80

90

100

Rem

oval

()

Time (min)

Anolyte = 100molmiddotmminus3 HClCatholyte = 25 molmiddotmminus3 Na2EDTA

+ 25molmiddotmminus3 AA

Anolyte = 100molmiddotmminus3 HClCatholyte = 100molmiddotmminus3 NaOH

Figure 11 Comparison of Ca2+ ions (feed solution 25molsdotmminus3)removal rate between two different techniques adopted Case 1anolyte = 100molsdotmminus3 HCl catholyte = 100molsdotmminus3NaOH Case2 anolyte = 100molsdotmminus3 HCl catholyte = 25molsdotmminus3 Na

2EDTA +

25molsdotmminus3 AA [13]

membrane surface and its subsequent cleaning with diluteHCl may be explained by the following scheme

CO2(air) + 2OHminus 997888rarr CO

3

2minus+H2O (26)

Ca(OH)

2+ CO2997888rarr CaCO

3(s) +H

2O (27)

CaCO3(s) +HCl 997888rarr CaCl

2+ CO2(g) +H

2O (28)

At higher pH solubility of CO2(air) increases in NaOH

solution (catholyte stream) which results in formation ofHCO3

minus1CO3

2minusThese ions subsequently react withNaOH toform Na

2CO3providing the source for CaCO

3precipitation

from Ca(OH)2 Conversion of Ca(OH)

2to CO

3

minus2 is (27)is thermodynamically favorable and moves forward Nearly1000 times higher value of solubility product of Ca(OH)

2

[55 times 10

minus6] over CaCO3[339 times 10

minus9] [28] drives the processfaster

Formation of CaCO3not only increasedmembrane resis-

tance to ion transport but alsomade the EDoperation discon-tinuous The process was made uninterrupted by changing

the electrolyte composition of the catholyte stream Herewe report application of Na

2EDTA-acetic acid solution as

catholyte stream the chelating agent continuously complexeswith the precipitated CaCO

3and formed corresponding

salt CaNa2EDTA The pH of catholyte stream was adjusted

between 35ndash50 (Table 2) and the anolyte was maintainedas HCl (100molsdotmminus3) This combination showed negligiblefouling even after long (240min) operation time (Table 4)

The mass transfer coefficients estimated from Sherwoodnumber correlation (11) showed higher values while NaOH(100molsdotmminus3) was used as catholyte stream compared toNa2EDTA-acetic acid (AA) combination (Table 4) Reduced

mass transfer coefficient with Na2EDTA-acetic acid stream

may be attributed to higher solution resistance arising possi-bly due to weak dissociation of acetic acid of Na

2EDTA + AA

combination than that of NaOH The dissociation constantcan get further affected due to Na

2EDTA (a bulky diffusing

species) Thus reduction in mass transfer coefficient loweredCa2+ ion removal rate

As of now we have understood that chemical compo-sition and concentration of anolytecatholyte streams playcrucial role in controlling overall resistance and ion removalrate The specific energy consumption 119864sp estimated from(23) (Table 4) shows lower value with NaOH compared to thestreams containing Na

2EDTA + AA

The average running cost to remove unit mass of CaCl2is

reported in Table 4 The cost is dependent on concentrationof the electrolyte stream and time of ED operation Cost isinversely proportional to initial concentration of the streamand directly proportional to operation time Energy dueto pumping is the major contribution to the overall costsestimate in a batch ED operation for a given time

6 Conclusions

Calcium ion (CaCl2 25molsdotmminus3) removal rate depends on

feed flow rates electrolyte (anolytecatholyte) componentsconcentrations applied potential and so forth NaOH ascatholyte showed higher removal rate and increased masstransfer coefficient over mixed electrolyte (AA-Na

2EDTA)

Specific energy consumption (119864sp kWhsdotkgminus1) estimates forthree typical set of experiments (Table 4) also support theabove observation of easy ion removal rate Based on thisit may be concluded that although NaOH shows betterperformance for the duration chosen in this report but anuninterrupted mode ED operation would be feasible withmixed electrolyte only but of course energy consumption willbe partly increasing The unsteady state model used could


0 5 10 15 20 25

1018

1020

1022

1024

1026

Conc of CaCl2 in 5 wt sugar solution (molmiddotmminus3)

Den

sity

(kgmiddot

mminus3)

y = 0323x + 10175

R2 = 0984

Figure 12 Calibration chart used to estimate solution density(kgsdotmminus3) from molar concentration of CaCl

2(molsdotmminus3) in 5wt

sugar solution

effectively predict the current density and concentrationchange with an accuracy of 95

Appendix

Density values of 5 sugar solution with varying concen-tration of CaCl

2were estimated from the fitted equation

(Density (kgsdotmminus3) = 0323 times Concentration (molsdotmminus3) +10175 1198772 = 98) obtained from the experimental data ofdensity versus concentration of CaCl

2in 5 sugar solution

(Figure 12)

Nomenclature

List of Symbols

119886 Sh number empirical equation constant119860

119898 Area of the membrane m2

119887 Sh number empirical equation constant119888 Sh number empirical equation constant119862 Concentration molsdotmminus3119863 Diffusivity of the salt or ion in the solution

at temperature 119879119863

∘ Diffusivity of the salt or ion at infinitedilution at temperature 119879

119863

119895 Diffusivity of ion ldquo119895rdquo

119864el Electrode potential V119864tot Total electric potential applied V119864sp Specific energy consumption kWhsdotkgminus1

119865 Faraday constant Csdotgm-eqminus1119894 Current density Asdotmminus2119894

119895lim Limiting current density of ion ldquo119895rdquo119868 Ionic strength119869 Current 119860119896 Mass transfer coefficient ms119871 Characteristic length m

119898

119895 Molality of ion ldquo119895rdquo

119876 Volumetric flow rate m3sdotsminus1119877 Gas constant Jsdotkgminus1sdotKminus1119877anolyte Resistance of anolyte chamber119877catholyte Resistance of catholyte chamber119877diluate Resistance of diluate chamber119877tot Total Resistance of the electrodialysis cellRe Reynolds numberSc Schmidt numberSh Sherwood number119905 Time s119879 Temperature 119870119905

+CEM Transport number of cation in cationexchange membrane

119905

minusAEM Transport number of anion in anionexchange membrane

119905

119895119898 Transport number of ion ldquo119895rdquo in the

membrane119905

119895119887 Transport number of ion ldquo119895rdquo in the bulk

solutionV Velocity ms119881 Volume m3119911 Ion charge

Subscripts

AEM Anion exchange membrane119887 Bulk solutionCEM Cation exchange membraneC Compartment119895 Ion ldquo119895rdquo119879 Feed tankplusmn Cation or anion

Superscripts

Conc Concentratedil Diluatelim Limiting

Greek Symbols

120578 Current efficiency120576 Applied voltage V120583 Viscosity of the solution at the same

temperature 119879 Pasdots120583

∘ Viscosity of the pure water at atemperature 119879 Pasdots

Λ Conductivity 119878120582

+ 120582

minus Limiting (zero concentration) ionicconductance(Asdotcmminus2)sdot(Vsdotcmminus1)(g-eqvsdotcmminus3)

120588 Density kgsdotmminus3120575 Diffusion boundary layer thickness m120585 Potential gradient Vsdotmminus1120595 Potential drop in the diffusion boundary

layer V120574

plusmn Mean ionic activity coefficient


Conflict of Interests

The authors declare that there is no conflict of interestsregarding to the publication of this paper

Acknowledgment

Financial support to execute the experimental work is grate-fully acknowledged to IIT Roorkee (no IITRSRIC244FIG-Sch-A)

References

[1] R B L Mathur Handbook of Cane Sugar Technology Oxfordand IBH Publishing New Delhi India 1978

[2] F Smagghe JMourgues J L Escudier T Conte JMolinier andC Malmary ldquoRecovery of calcium tartrate and calcium malatein effluents from grape sugar production by electrodialysisrdquoBioresource Technology vol 39 no 2 pp 185ndash189 1992

[3] A Elmidaoui L Chay M Tahaikt et al ldquoDemineralisation ofbeet sugar syrup juice and molasses using an electrodialysispilot plant to reduce melassigenic ionsrdquo Desalination vol 165p 435 2004

[4] G Tragardh and V Gekas ldquoMembrane technology in the sugarindustryrdquo Desalination vol 69 no 1 pp 9ndash17 1988

[5] H Strathmann Ion-Exchange Membrane Separation ProcessesElsevier 2004

[6] J J Krol M Wessling and H Strathmann ldquoConcentra-tion polarization with monopolar ion exchange membranescurrent-voltage curves and water dissociationrdquo Journal of Mem-brane Science vol 162 no 1-2 pp 145ndash154 1999

[7] V Geraldes and M D Afonso ldquoLimiting current density in theelectrodialysis of multi-ionic solutionsrdquo Journal of MembraneScience vol 360 no 1-2 pp 499ndash508 2010

[8] H Strathmann J J Krol H-J Rapp and G EigenbergerldquoLimiting current density and water dissociation in bipolarmembranesrdquo Journal of Membrane Science vol 125 no 1 pp123ndash142 1997

[9] H-J Lee H Strathmann and S-H Moon ldquoDetermination ofthe limiting current density in electrodialysis desalination as anempirical function of linear velocityrdquo Desalination vol 190 no1ndash3 pp 43ndash50 2006

[10] Y Tanaka ldquoLimiting current density of an ion-exchange mem-brane and of an electrodialyzerrdquo Journal of Membrane Sciencevol 266 no 1-2 pp 6ndash17 2005

[11] A Elmidaoui F Lutin L Chay M Taky M Tahaikt and M RA Hafidi ldquoRemoval of melassigenic ions for beet sugar syrupsby electrodialysis using a new anion-exchange membranerdquoDesalination vol 148 no 1ndash3 pp 143ndash148 2002

[12] Y Tanaka ldquoIrreversible thermodynamics and overall masstransport in ion-exchangemembrane electrodialysisrdquo Journal ofMembrane Science vol 281 no 1-2 pp 517ndash531 2006

[13] S Chattopadhyay Removal of Calcium Ion from Sugar Solutionthrough Electrodialysis Department of Chemical EngineeringIndian Institute of Technology Kanpur Kanpur India 1994

[14] B E Poling J M Prausnitz and J P OrsquoConnellThe Propertiesof Gases and Liquids McGraw-Hill New York NY USA 5thedition 2000

[15] L Yuan-Hui and S Gregory ldquoDiffusion of ions in sea water andin deep-sea sedimentsrdquo Geochimica et Cosmochimica Acta vol38 no 5 pp 703ndash714 1974

[16] httpwwwsugartechcozaviscosityindexphp[17] M S Isaacson andA A Sonin ldquoSherwood number and friction

factor correlations for electrodialysis systems with applicationto process optimizationrdquo Industrial amp Engineering ChemistryProcess Design and Development vol 15 no 2 pp 313ndash321 1976

[18] J M Ortiz J A Sotoca E Exposito et al ldquoBrackish waterdesalination by electrodialysis batch recirculation operationmodelingrdquo Journal of Membrane Science vol 252 no 1-2 pp65ndash75 2005

[19] F S Rohman M R Othman and N Aziz ldquoModeling ofbatch electrodialysis for hydrochloric acid recoveryrdquo ChemicalEngineering Journal vol 162 no 2 pp 466ndash479 2010

[20] R E Treybal Mass-Transfer Operations McGraw-Hill NewYork NY USA 3rd edition 1980

[21] R B Bird W E Stewart and E N Lightfoot TransportPhenomenon John Wiley amp Sons 2nd edition 2002

[22] J Balster M H Yildirim D F Stamatialis et al ldquoMorphologyandmicrotopology of cation-exchange polymers and the originof the overlimiting currentrdquo The Journal of Physical ChemistryB vol 111 no 9 pp 2152ndash2165 2007

[23] O V Grigorchuk V I Vasilrsquoeva and V A Shaposhnik ldquoLocalcharacteristics of mass transfer under electrodialysis deminer-alizationrdquo Desalination vol 184 no 1ndash3 pp 431ndash438 2005

[24] V M Barragan and C Ruız-Bauza ldquoCurrent-voltage curves forion-exchange membranes a method for determining the limit-ing current densityrdquo Journal of Colloid and Interface Science vol205 no 2 pp 365ndash373 1998

[25] J Koryta J Dvorak and L KavanPrinciples of ElectrochemistryJohn Wiley amp Sons New York NY USA 2nd edition 1993

[26] N Kabay M Demircioglu E Ersoz and I KurucaovalildquoRemoval of calcium and magnesium hardness of electrodial-ysisrdquo Desalination vol 149 no 1ndash3 pp 343ndash349 2002

[27] M Araya-Farias and L Bazinet ldquoElectrodialysis of calciumand carbonate high-concentration solutions and impact onmembrane foulingrdquoDesalination vol 200 no 1ndash3 p 624 2006

[28] httpwww4ncsuedusimfranzenpublic htmlCH201dataSol-ubility Product Constantspdf

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy


Carbohydrate Chemistry

International Journal of


Journal of

Chemistry


Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of


Chromatography Research International


Applied ChemistryJournal of



Theoretical ChemistryJournal of


Journal of

Spectroscopy

Analytical ChemistryInternational Journal of


Journal of


Quantum Chemistry


Organic Chemistry International

ElectrochemistryInternational Journal of



CatalystsJournal of


the net salt transport This issue was taken up and sorted outusing different combination of anolyte and catholyte streamsDifferent electrolyte streams (NaOH acetic acid-Na

2EDTA

mixture) were selected as catholyte keeping anolyte as HClsolution

In a batch mode electrodialysis with continuous recircu-lation of feed stream properties like electrolyte concentrationof diluate (feed tank) concentration profiles around thatmembrane and all physical properties of the solution changewith timeThe effect of all these parameters is reflected in ionremoval rate and current density of the ED cell Therefore anunsteady state model that can closely predict the ion removalrate and overall current density will be quite relevant in appli-cation point of view Nernst-Planck equation (purely basedon first principles) and irreversible thermodynamics wereused to estimate current density and ion concentration [12]

2 Materials and Methods

21 Equipment

211 Electrodialysis Setup The experimental setup used forED application is shown in the Figure 1 [13] The ED cell andsetup were from Berghof Germany The electric field wasapplied across the cell stack by a built-in DC source Voltageand current between the two electrodes were measured by abuilt-in digital voltmeter and ammeter respectively The EDcell consisted of three compartments as shown in the figureMembranes used were obtained from Permionics Gujaratand cross-linked styrene and di-vinyl benzene gel was used asbase material Cation exchange membrane (CEM) separatesthe cathode compartment and anion exchange membrane(AEM) separates the anode compartment from the feedchamber The effective membrane area for the cell 119860

119898

was 00037m2 and the feed compartment thickness ℎ was0002m

212 Power Supply The power supply was provided througha voltage stabilizer of 110220V AC with 50ndash80Hz fre-quency The same gave an output voltage 0ndash499V DC andcurrent 0ndash399A Four centrifugal pumps were inbuilt withthe system for pumping the solution

213 Conductivity Meter Solution conductivity was noted atregular interval through an offline conductivity meter (Sys-tronics India) of 200mMho with 5 ranges (accuracy plusmn1)

214 ED Cell Compartments and Solutions Used 1000mLsolutions of each stream (feed catholyte and anolyte) weretaken in three chambers (Figure 1) respectively Each cham-ber was connected with the respective three compartmentsof the ED cell through flexi tubing Solutions were circulatedat a constant rate by three centrifugal pumps and the solutionflow rates were measured using rotameters connected to eachstream Table 1 indicates membrane parameters obtainedfrom Permionics India Ltd The composition and flow ratesof three streams used are reported in Table 2

Synthetic solution of 5 sugar and calcium chloride(CaCl

2) was prepared in distilled water The concentration of

FeedAnolytetank

Catholytetank

V

A

CEM

AEM

DC source

R

R R

Solution flow linesCurrent lines

A AmmeterV Voltmeter

R RotameterAEM Anion exchange membraneCEM Cation exchange membrane

tank

+ minus

minus

+

Figure 1 Batch recirculation electrodialysis process showing thestorage tanks pumps manual control valves various chambers ofthe ED cell electrodes DC supply source voltmeter ammeter andflow meters used in the experiment [13]

Table 1 Membrane parameters as obtained from Permionics IndiaLtd

Physical parameters Cation exchangemembrane

Anion exchangemembrane

Transport number 091 09Experimental resistance(ohm cmminus2) 20ndash35 mdash

Max pressure allowed(kgcmminus2) 30 30

Thickness (mm) 011 to 015 009ndash011Max temperature (∘C) 60 60

sugar was kept unchanged but that of CaCl2was varied The

synthetic solution having CaCl2with initial concentrations of

25molsdotmminus3 and 50molsdotmminus3 were used in the diluate channelof ED cell Dilute solution of HCl (100molsdotmminus3) was usedas anolyte in all experiments while NaOH (100molsdotmminus3) wasused as catholyte in experiment 1 and equimolar mixtures ofacetic acid (AA) andNa

2EDTA (25molsdotmminus3 and 50molsdotmminus3)

were respectively used as catholyte in experiments 2 and 3(Table 2)

215 Viscosity Measurement Viscosity measurement wascarried out using Ubbelhood viscometer always fitted in aconstant temperature bath to nullify any temperature effecton capillary flow

22 Procedure The chambers of the ED cell and membraneswere washed thoroughly before each experiment was carriedout Initially the feed solution containing 5 sugar andCaCl

2




Feed flowrate


Anolyte flowrate


Catholyteflow rate

(mLsdotminminus1)

Voltageapplied (V)

Time(min)


in 5 sugarsolution


solution 830 4 685


in 5 sugarsolution



solution830 4 240


in 5 sugarsolution



solution830 4 240









119881dilC119889119862

dil

119889119905

= 119876

dil(119862

dil119879

minus 119862

dil) minus

120578119894119860

119898

119911119865

(1)





119898is the


120578 = 119905

+CEM + 119905


where 119905




119889 (119881

119879119862

dil119879)

119889119905

= 119876

dil(119862

dilminus 119862

dil119879)

(3)

where 119881





119873

119895= minus119863

119895

120597119862

119895

120597119909

minus

119911

119895119862

119895119865119863

119895

119877119879

120597120595

120597119909

(4)



119895is


119895is




Concentrate Diluate


++

minus

Cconcjm

Cconcjb

Cdiljm

Cdiljb

120575 120575




[7]

119873

119895119898=

119905

119895119898119894

119911

119895119865

(5)

where 119905119895119898





119905

119895119898119894

119911

119895119865

= minus119863

119895

120597119862

119895

120597119909

minus

119911

119895119862

119895119865119863

119895

119877119879

120597120595

120597119909

(6)


119905

119895119898119894

119911

119895119865

=

119863

119895(119862

dil119895119887

minus 119862

dil119895119898

)

120575

minus

119911

119895119863

119895119865120585119862

dil119895119898

119877119879

(7)


and119862dil119895119898


120585 =

120595

120575

(8)


dil119895119887

minus119862

dil119895119898


119895119863

119895119865120585119862

dil119895119898



120575 =

119863

119895

119896

(9)



Sh =

119896 sdot 119897

119863

119895

(10)


Sh = 119886 sdot Re119887 sdot Sc119888 (11)




119863

∘=

119877119879 [(1119911

+) + (1119911

minus)]

119865

2[(1120582

+) + (1120582

minus)]

(12)

where 119911+and 119911



















119863

119863

∘=

120583

∘

120583

(13)


119862

conc119895119898

= 119862

conc119895119887

(1 +

119894

119894

119895lim) (14)

119862

dil119895119898

= 119862

dil119895119887

(1 minus

119894

119894

119895lim) (15)

where 119862

conc119895119898

and 119862

conc119895119887


119895119898and 119862

dil119895119887





119894

119895lim =

119862

dil119895119887119863

119895119911

119895119865

120575 (119905

119895119898minus 119905

119895119887)

(16)

where 119905

119895119898and 119905




119895119898


119894 = (119862

dil119895119887119863

119895119911

119895120585

119865

119877119879

)

times (

119905

119895119898minus 119905

119895119887

119911

119895119865

+

120585120575 (119905

119895119898minus 119905

119895119887)

119877119879

minus

119905

119895119898119911

119895

119865

)

minus1

(17)


120585 = minus (2119905

119895119898minus 1)

119877119879

120575119865

ln(

120574

dil119887119862

dil119895119887

120574

dil119898119862

dil119895119898

) (18)

where 120574

dil119898

and 120574

dil119887









119905

119895119887=

1003816

1003816

1003816

1003816

1003816

119911

119895

1003816

1003816

1003816

1003816

1003816

119863

119895

sum

119899

119895=1

1003816

1003816

1003816

1003816

1003816

119911

119895

1003816

1003816

1003816

1003816

1003816

119863

119895

(19)







Resistance = 1

Λ

119871

119860

119898

(22)




119864sp =

int

1199052

1199051

120576119860

119898119894 (119905) 119889119905

119872CaCl2

Δ119899CaCl2(119905)

(23)

Input data Estimate

Estimate

EstimateNo



Yes

PlotsEnd

t1 = t1 + Δt

t1 = t + Δt

t = t0

120585(t) and i(t)

t1 = tend

CdilT (0) Cdil(0)

CconcT (0) Cconc(0)


Δt tend

CdilT (t1) Cdil(t1)


ilim(t) Cconcjm (t)

Cdiljm(t)


dil versus t




2




intervals










2concentration





0 2 4 6 8 10

10

11

12 y = 00209x + 0989756

R2 = 098

Visc

osity

at20

∘ C(m

Pamiddots)



0 10 20 30 40 5006

08

10

12

14

16


Visc

osity

(mPamiddots)

20∘C25∘C32∘C

37∘C42∘C






0 10 20 30 40 500

2

4

6

8

10

12



Elec

tric

al co

nduc

tivity

at25

∘ C(m

S)



0 30 60 90 120 150 180 210 240

10

20

30

40

50

Time (min)

Con

cent

ratio

n of

CaC

l 2(m

olmiddotm

minus3)

4V8V12V


2















0 50 100 150 200 250

10

20

30

40

50

Time (min)

Feed flow rate

Con

cent

ratio

n of

CaC

l 2(m

olmiddotm

minus3)






0 100 200 300 400 500 600 7000

20

40

60

80

100

120

140

160

180

200

Time (min)








0 50 100 150 200 25010

15

20

25

30

35

40

45

50

55

60

Time (min)



Model prediction

Con

cent

ratio

n of

CaC

l 2(m

olmiddotm

minus3)






= 4V) [13]





2EDTA a


2



2EDTA it




2

CO2



2EDTA + 2H+ (25)


2precipitation was





2





ExptSpecific energy





1 24023 47 1928 222 24027 34 1174 33 24027 19 1173 17

0 50 100 150 200 2500

10

20

30

40

50

60

70

80

90

100

Rem

oval

()

Time (min)





2EDTA +




3

2minus+H2O (26)

Ca(OH)


3(s) +H

2O (27)


2+ CO2(g) +H

2O (28)



minus1CO3



3precipitation


2to CO

3


2

[55 times 10














2EDTA + AA





2EDTA + AA



6 Conclusions



2EDTA)



0 5 10 15 20 25

1018

1020

1022

1024

1026


Den

sity

(kgmiddot

mminus3)

y = 0323x + 10175

R2 = 0984



sugar solution


Appendix





(Figure 12)

Nomenclature

List of Symbols






119863





119898




119905


119905


membrane119905



Subscripts


Superscripts


Greek Symbols





+ 120582



layer V120574





Acknowledgment


References






































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of




Feed flowrate


Anolyte flowrate


Catholyteflow rate

(mLsdotminminus1)

Voltageapplied (V)

Time(min)


in 5 sugarsolution


solution 830 4 685


in 5 sugarsolution



solution830 4 240


in 5 sugarsolution



solution830 4 240









119881dilC119889119862

dil

119889119905

= 119876

dil(119862

dil119879

minus 119862

dil) minus

120578119894119860

119898

119911119865

(1)





119898is the


120578 = 119905

+CEM + 119905


where 119905




119889 (119881

119879119862

dil119879)

119889119905

= 119876

dil(119862

dilminus 119862

dil119879)

(3)

where 119881





119873

119895= minus119863

119895

120597119862

119895

120597119909

minus

119911

119895119862

119895119865119863

119895

119877119879

120597120595

120597119909

(4)



119895is


119895is




Concentrate Diluate


++

minus

Cconcjm

Cconcjb

Cdiljm

Cdiljb

120575 120575




[7]

119873

119895119898=

119905

119895119898119894

119911

119895119865

(5)

where 119905119895119898





119905

119895119898119894

119911

119895119865

= minus119863

119895

120597119862

119895

120597119909

minus

119911

119895119862

119895119865119863

119895

119877119879

120597120595

120597119909

(6)


119905

119895119898119894

119911

119895119865

=

119863

119895(119862

dil119895119887

minus 119862

dil119895119898

)

120575

minus

119911

119895119863

119895119865120585119862

dil119895119898

119877119879

(7)


and119862dil119895119898


120585 =

120595

120575

(8)


dil119895119887

minus119862

dil119895119898


119895119863

119895119865120585119862

dil119895119898



120575 =

119863

119895

119896

(9)



Sh =

119896 sdot 119897

119863

119895

(10)


Sh = 119886 sdot Re119887 sdot Sc119888 (11)




119863

∘=

119877119879 [(1119911

+) + (1119911

minus)]

119865

2[(1120582

+) + (1120582

minus)]

(12)

where 119911+and 119911



















119863

119863

∘=

120583

∘

120583

(13)


119862

conc119895119898

= 119862

conc119895119887

(1 +

119894

119894

119895lim) (14)

119862

dil119895119898

= 119862

dil119895119887

(1 minus

119894

119894

119895lim) (15)

where 119862

conc119895119898

and 119862

conc119895119887


119895119898and 119862

dil119895119887





119894

119895lim =

119862

dil119895119887119863

119895119911

119895119865

120575 (119905

119895119898minus 119905

119895119887)

(16)

where 119905

119895119898and 119905




119895119898


119894 = (119862

dil119895119887119863

119895119911

119895120585

119865

119877119879

)

times (

119905

119895119898minus 119905

119895119887

119911

119895119865

+

120585120575 (119905

119895119898minus 119905

119895119887)

119877119879

minus

119905

119895119898119911

119895

119865

)

minus1

(17)


120585 = minus (2119905

119895119898minus 1)

119877119879

120575119865

ln(

120574

dil119887119862

dil119895119887

120574

dil119898119862

dil119895119898

) (18)

where 120574

dil119898

and 120574

dil119887









119905

119895119887=

1003816

1003816

1003816

1003816

1003816

119911

119895

1003816

1003816

1003816

1003816

1003816

119863

119895

sum

119899

119895=1

1003816

1003816

1003816

1003816

1003816

119911

119895

1003816

1003816

1003816

1003816

1003816

119863

119895

(19)







Resistance = 1

Λ

119871

119860

119898

(22)




119864sp =

int

1199052

1199051

120576119860

119898119894 (119905) 119889119905

119872CaCl2

Δ119899CaCl2(119905)

(23)

Input data Estimate

Estimate

EstimateNo



Yes

PlotsEnd

t1 = t1 + Δt

t1 = t + Δt

t = t0

120585(t) and i(t)

t1 = tend

CdilT (0) Cdil(0)

CconcT (0) Cconc(0)


Δt tend

CdilT (t1) Cdil(t1)


ilim(t) Cconcjm (t)

Cdiljm(t)


dil versus t




2




intervals










2concentration





0 2 4 6 8 10

10

11

12 y = 00209x + 0989756

R2 = 098

Visc

osity

at20

∘ C(m

Pamiddots)



0 10 20 30 40 5006

08

10

12

14

16


Visc

osity

(mPamiddots)

20∘C25∘C32∘C

37∘C42∘C






0 10 20 30 40 500

2

4

6

8

10

12



Elec

tric

al co

nduc

tivity

at25

∘ C(m

S)



0 30 60 90 120 150 180 210 240

10

20

30

40

50

Time (min)

Con

cent

ratio

n of

CaC

l 2(m

olmiddotm

minus3)

4V8V12V


2















0 50 100 150 200 250

10

20

30

40

50

Time (min)

Feed flow rate

Con

cent

ratio

n of

CaC

l 2(m

olmiddotm

minus3)






0 100 200 300 400 500 600 7000

20

40

60

80

100

120

140

160

180

200

Time (min)








0 50 100 150 200 25010

15

20

25

30

35

40

45

50

55

60

Time (min)



Model prediction

Con

cent

ratio

n of

CaC

l 2(m

olmiddotm

minus3)






= 4V) [13]





2EDTA a


2



2EDTA it




2

CO2



2EDTA + 2H+ (25)


2precipitation was





2





ExptSpecific energy





1 24023 47 1928 222 24027 34 1174 33 24027 19 1173 17

0 50 100 150 200 2500

10

20

30

40

50

60

70

80

90

100

Rem

oval

()

Time (min)





2EDTA +




3

2minus+H2O (26)

Ca(OH)


3(s) +H

2O (27)


2+ CO2(g) +H

2O (28)



minus1CO3



3precipitation


2to CO

3


2

[55 times 10














2EDTA + AA





2EDTA + AA



6 Conclusions



2EDTA)



0 5 10 15 20 25

1018

1020

1022

1024

1026


Den

sity

(kgmiddot

mminus3)

y = 0323x + 10175

R2 = 0984



sugar solution


Appendix





(Figure 12)

Nomenclature

List of Symbols






119863





119898




119905


119905


membrane119905



Subscripts


Superscripts


Greek Symbols





+ 120582



layer V120574





Acknowledgment


References






































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



Concentrate Diluate


++

minus

Cconcjm

Cconcjb

Cdiljm

Cdiljb

120575 120575




[7]

119873

119895119898=

119905

119895119898119894

119911

119895119865

(5)

where 119905119895119898





119905

119895119898119894

119911

119895119865

= minus119863

119895

120597119862

119895

120597119909

minus

119911

119895119862

119895119865119863

119895

119877119879

120597120595

120597119909

(6)


119905

119895119898119894

119911

119895119865

=

119863

119895(119862

dil119895119887

minus 119862

dil119895119898

)

120575

minus

119911

119895119863

119895119865120585119862

dil119895119898

119877119879

(7)


and119862dil119895119898


120585 =

120595

120575

(8)


dil119895119887

minus119862

dil119895119898


119895119863

119895119865120585119862

dil119895119898



120575 =

119863

119895

119896

(9)



Sh =

119896 sdot 119897

119863

119895

(10)


Sh = 119886 sdot Re119887 sdot Sc119888 (11)




119863

∘=

119877119879 [(1119911

+) + (1119911

minus)]

119865

2[(1120582

+) + (1120582

minus)]

(12)

where 119911+and 119911



















119863

119863

∘=

120583

∘

120583

(13)


119862

conc119895119898

= 119862

conc119895119887

(1 +

119894

119894

119895lim) (14)

119862

dil119895119898

= 119862

dil119895119887

(1 minus

119894

119894

119895lim) (15)

where 119862

conc119895119898

and 119862

conc119895119887


119895119898and 119862

dil119895119887





119894

119895lim =

119862

dil119895119887119863

119895119911

119895119865

120575 (119905

119895119898minus 119905

119895119887)

(16)

where 119905

119895119898and 119905




119895119898


119894 = (119862

dil119895119887119863

119895119911

119895120585

119865

119877119879

)

times (

119905

119895119898minus 119905

119895119887

119911

119895119865

+

120585120575 (119905

119895119898minus 119905

119895119887)

119877119879

minus

119905

119895119898119911

119895

119865

)

minus1

(17)


120585 = minus (2119905

119895119898minus 1)

119877119879

120575119865

ln(

120574

dil119887119862

dil119895119887

120574

dil119898119862

dil119895119898

) (18)

where 120574

dil119898

and 120574

dil119887









119905

119895119887=

1003816

1003816

1003816

1003816

1003816

119911

119895

1003816

1003816

1003816

1003816

1003816

119863

119895

sum

119899

119895=1

1003816

1003816

1003816

1003816

1003816

119911

119895

1003816

1003816

1003816

1003816

1003816

119863

119895

(19)







Resistance = 1

Λ

119871

119860

119898

(22)




119864sp =

int

1199052

1199051

120576119860

119898119894 (119905) 119889119905

119872CaCl2

Δ119899CaCl2(119905)

(23)

Input data Estimate

Estimate

EstimateNo



Yes

PlotsEnd

t1 = t1 + Δt

t1 = t + Δt

t = t0

120585(t) and i(t)

t1 = tend

CdilT (0) Cdil(0)

CconcT (0) Cconc(0)


Δt tend

CdilT (t1) Cdil(t1)


ilim(t) Cconcjm (t)

Cdiljm(t)


dil versus t




2




intervals










2concentration





0 2 4 6 8 10

10

11

12 y = 00209x + 0989756

R2 = 098

Visc

osity

at20

∘ C(m

Pamiddots)



0 10 20 30 40 5006

08

10

12

14

16


Visc

osity

(mPamiddots)

20∘C25∘C32∘C

37∘C42∘C






0 10 20 30 40 500

2

4

6

8

10

12



Elec

tric

al co

nduc

tivity

at25

∘ C(m

S)



0 30 60 90 120 150 180 210 240

10

20

30

40

50

Time (min)

Con

cent

ratio

n of

CaC

l 2(m

olmiddotm

minus3)

4V8V12V


2















0 50 100 150 200 250

10

20

30

40

50

Time (min)

Feed flow rate

Con

cent

ratio

n of

CaC

l 2(m

olmiddotm

minus3)






0 100 200 300 400 500 600 7000

20

40

60

80

100

120

140

160

180

200

Time (min)








0 50 100 150 200 25010

15

20

25

30

35

40

45

50

55

60

Time (min)



Model prediction

Con

cent

ratio

n of

CaC

l 2(m

olmiddotm

minus3)






= 4V) [13]





2EDTA a


2



2EDTA it




2

CO2



2EDTA + 2H+ (25)


2precipitation was





2





ExptSpecific energy





1 24023 47 1928 222 24027 34 1174 33 24027 19 1173 17

0 50 100 150 200 2500

10

20

30

40

50

60

70

80

90

100

Rem

oval

()

Time (min)





2EDTA +




3

2minus+H2O (26)

Ca(OH)


3(s) +H

2O (27)


2+ CO2(g) +H

2O (28)



minus1CO3



3precipitation


2to CO

3


2

[55 times 10














2EDTA + AA





2EDTA + AA



6 Conclusions



2EDTA)



0 5 10 15 20 25

1018

1020

1022

1024

1026


Den

sity

(kgmiddot

mminus3)

y = 0323x + 10175

R2 = 0984



sugar solution


Appendix





(Figure 12)

Nomenclature

List of Symbols






119863





119898




119905


119905


membrane119905



Subscripts


Superscripts


Greek Symbols





+ 120582



layer V120574





Acknowledgment


References






































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of















119863

119863

∘=

120583

∘

120583

(13)


119862

conc119895119898

= 119862

conc119895119887

(1 +

119894

119894

119895lim) (14)

119862

dil119895119898

= 119862

dil119895119887

(1 minus

119894

119894

119895lim) (15)

where 119862

conc119895119898

and 119862

conc119895119887


119895119898and 119862

dil119895119887





119894

119895lim =

119862

dil119895119887119863

119895119911

119895119865

120575 (119905

119895119898minus 119905

119895119887)

(16)

where 119905

119895119898and 119905




119895119898


119894 = (119862

dil119895119887119863

119895119911

119895120585

119865

119877119879

)

times (

119905

119895119898minus 119905

119895119887

119911

119895119865

+

120585120575 (119905

119895119898minus 119905

119895119887)

119877119879

minus

119905

119895119898119911

119895

119865

)

minus1

(17)


120585 = minus (2119905

119895119898minus 1)

119877119879

120575119865

ln(

120574

dil119887119862

dil119895119887

120574

dil119898119862

dil119895119898

) (18)

where 120574

dil119898

and 120574

dil119887









119905

119895119887=

1003816

1003816

1003816

1003816

1003816

119911

119895

1003816

1003816

1003816

1003816

1003816

119863

119895

sum

119899

119895=1

1003816

1003816

1003816

1003816

1003816

119911

119895

1003816

1003816

1003816

1003816

1003816

119863

119895

(19)







Resistance = 1

Λ

119871

119860

119898

(22)




119864sp =

int

1199052

1199051

120576119860

119898119894 (119905) 119889119905

119872CaCl2

Δ119899CaCl2(119905)

(23)

Input data Estimate

Estimate

EstimateNo



Yes

PlotsEnd

t1 = t1 + Δt

t1 = t + Δt

t = t0

120585(t) and i(t)

t1 = tend

CdilT (0) Cdil(0)

CconcT (0) Cconc(0)


Δt tend

CdilT (t1) Cdil(t1)


ilim(t) Cconcjm (t)

Cdiljm(t)


dil versus t




2




intervals










2concentration





0 2 4 6 8 10

10

11

12 y = 00209x + 0989756

R2 = 098

Visc

osity

at20

∘ C(m

Pamiddots)



0 10 20 30 40 5006

08

10

12

14

16


Visc

osity

(mPamiddots)

20∘C25∘C32∘C

37∘C42∘C






0 10 20 30 40 500

2

4

6

8

10

12



Elec

tric

al co

nduc

tivity

at25

∘ C(m

S)



0 30 60 90 120 150 180 210 240

10

20

30

40

50

Time (min)

Con

cent

ratio

n of

CaC

l 2(m

olmiddotm

minus3)

4V8V12V


2















0 50 100 150 200 250

10

20

30

40

50

Time (min)

Feed flow rate

Con

cent

ratio

n of

CaC

l 2(m

olmiddotm

minus3)






0 100 200 300 400 500 600 7000

20

40

60

80

100

120

140

160

180

200

Time (min)








0 50 100 150 200 25010

15

20

25

30

35

40

45

50

55

60

Time (min)



Model prediction

Con

cent

ratio

n of

CaC

l 2(m

olmiddotm

minus3)






= 4V) [13]





2EDTA a


2



2EDTA it




2

CO2



2EDTA + 2H+ (25)


2precipitation was





2





ExptSpecific energy





1 24023 47 1928 222 24027 34 1174 33 24027 19 1173 17

0 50 100 150 200 2500

10

20

30

40

50

60

70

80

90

100

Rem

oval

()

Time (min)





2EDTA +




3

2minus+H2O (26)

Ca(OH)


3(s) +H

2O (27)


2+ CO2(g) +H

2O (28)



minus1CO3



3precipitation


2to CO

3


2

[55 times 10














2EDTA + AA





2EDTA + AA



6 Conclusions



2EDTA)



0 5 10 15 20 25

1018

1020

1022

1024

1026


Den

sity

(kgmiddot

mminus3)

y = 0323x + 10175

R2 = 0984



sugar solution


Appendix





(Figure 12)

Nomenclature

List of Symbols






119863





119898




119905


119905


membrane119905



Subscripts


Superscripts


Greek Symbols





+ 120582



layer V120574





Acknowledgment


References






































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of








119905

119895119887=

1003816

1003816

1003816

1003816

1003816

119911

119895

1003816

1003816

1003816

1003816

1003816

119863

119895

sum

119899

119895=1

1003816

1003816

1003816

1003816

1003816

119911

119895

1003816

1003816

1003816

1003816

1003816

119863

119895

(19)







Resistance = 1

Λ

119871

119860

119898

(22)




119864sp =

int

1199052

1199051

120576119860

119898119894 (119905) 119889119905

119872CaCl2

Δ119899CaCl2(119905)

(23)

Input data Estimate

Estimate

EstimateNo



Yes

PlotsEnd

t1 = t1 + Δt

t1 = t + Δt

t = t0

120585(t) and i(t)

t1 = tend

CdilT (0) Cdil(0)

CconcT (0) Cconc(0)


Δt tend

CdilT (t1) Cdil(t1)


ilim(t) Cconcjm (t)

Cdiljm(t)


dil versus t




2




intervals










2concentration





0 2 4 6 8 10

10

11

12 y = 00209x + 0989756

R2 = 098

Visc

osity

at20

∘ C(m

Pamiddots)



0 10 20 30 40 5006

08

10

12

14

16


Visc

osity

(mPamiddots)

20∘C25∘C32∘C

37∘C42∘C






0 10 20 30 40 500

2

4

6

8

10

12



Elec

tric

al co

nduc

tivity

at25

∘ C(m

S)



0 30 60 90 120 150 180 210 240

10

20

30

40

50

Time (min)

Con

cent

ratio

n of

CaC

l 2(m

olmiddotm

minus3)

4V8V12V


2















0 50 100 150 200 250

10

20

30

40

50

Time (min)

Feed flow rate

Con

cent

ratio

n of

CaC

l 2(m

olmiddotm

minus3)






0 100 200 300 400 500 600 7000

20

40

60

80

100

120

140

160

180

200

Time (min)








0 50 100 150 200 25010

15

20

25

30

35

40

45

50

55

60

Time (min)



Model prediction

Con

cent

ratio

n of

CaC

l 2(m

olmiddotm

minus3)






= 4V) [13]





2EDTA a


2



2EDTA it




2

CO2



2EDTA + 2H+ (25)


2precipitation was





2





ExptSpecific energy





1 24023 47 1928 222 24027 34 1174 33 24027 19 1173 17

0 50 100 150 200 2500

10

20

30

40

50

60

70

80

90

100

Rem

oval

()

Time (min)





2EDTA +




3

2minus+H2O (26)

Ca(OH)


3(s) +H

2O (27)


2+ CO2(g) +H

2O (28)



minus1CO3



3precipitation


2to CO

3


2

[55 times 10














2EDTA + AA





2EDTA + AA



6 Conclusions



2EDTA)



0 5 10 15 20 25

1018

1020

1022

1024

1026


Den

sity

(kgmiddot

mminus3)

y = 0323x + 10175

R2 = 0984



sugar solution


Appendix





(Figure 12)

Nomenclature

List of Symbols






119863





119898




119905


119905


membrane119905



Subscripts


Superscripts


Greek Symbols





+ 120582



layer V120574





Acknowledgment


References






































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


0 2 4 6 8 10

10

11

12 y = 00209x + 0989756

R2 = 098

Visc

osity

at20

∘ C(m

Pamiddots)



0 10 20 30 40 5006

08

10

12

14

16


Visc

osity

(mPamiddots)

20∘C25∘C32∘C

37∘C42∘C






0 10 20 30 40 500

2

4

6

8

10

12



Elec

tric

al co

nduc

tivity

at25

∘ C(m

S)



0 30 60 90 120 150 180 210 240

10

20

30

40

50

Time (min)

Con

cent

ratio

n of

CaC

l 2(m

olmiddotm

minus3)

4V8V12V


2















0 50 100 150 200 250

10

20

30

40

50

Time (min)

Feed flow rate

Con

cent

ratio

n of

CaC

l 2(m

olmiddotm

minus3)






0 100 200 300 400 500 600 7000

20

40

60

80

100

120

140

160

180

200

Time (min)








0 50 100 150 200 25010

15

20

25

30

35

40

45

50

55

60

Time (min)



Model prediction

Con

cent

ratio

n of

CaC

l 2(m

olmiddotm

minus3)






= 4V) [13]





2EDTA a


2



2EDTA it




2

CO2



2EDTA + 2H+ (25)


2precipitation was





2





ExptSpecific energy





1 24023 47 1928 222 24027 34 1174 33 24027 19 1173 17

0 50 100 150 200 2500

10

20

30

40

50

60

70

80

90

100

Rem

oval

()

Time (min)





2EDTA +




3

2minus+H2O (26)

Ca(OH)


3(s) +H

2O (27)


2+ CO2(g) +H

2O (28)



minus1CO3



3precipitation


2to CO

3


2

[55 times 10














2EDTA + AA





2EDTA + AA



6 Conclusions



2EDTA)



0 5 10 15 20 25

1018

1020

1022

1024

1026


Den

sity

(kgmiddot

mminus3)

y = 0323x + 10175

R2 = 0984



sugar solution


Appendix





(Figure 12)

Nomenclature

List of Symbols






119863





119898




119905


119905


membrane119905



Subscripts


Superscripts


Greek Symbols





+ 120582



layer V120574





Acknowledgment


References






































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of











0 50 100 150 200 250

10

20

30

40

50

Time (min)

Feed flow rate

Con

cent

ratio

n of

CaC

l 2(m

olmiddotm

minus3)






0 100 200 300 400 500 600 7000

20

40

60

80

100

120

140

160

180

200

Time (min)








0 50 100 150 200 25010

15

20

25

30

35

40

45

50

55

60

Time (min)



Model prediction

Con

cent

ratio

n of

CaC

l 2(m

olmiddotm

minus3)






= 4V) [13]





2EDTA a


2



2EDTA it




2

CO2



2EDTA + 2H+ (25)


2precipitation was





2





ExptSpecific energy





1 24023 47 1928 222 24027 34 1174 33 24027 19 1173 17

0 50 100 150 200 2500

10

20

30

40

50

60

70

80

90

100

Rem

oval

()

Time (min)





2EDTA +




3

2minus+H2O (26)

Ca(OH)


3(s) +H

2O (27)


2+ CO2(g) +H

2O (28)



minus1CO3



3precipitation


2to CO

3


2

[55 times 10














2EDTA + AA





2EDTA + AA



6 Conclusions



2EDTA)



0 5 10 15 20 25

1018

1020

1022

1024

1026


Den

sity

(kgmiddot

mminus3)

y = 0323x + 10175

R2 = 0984



sugar solution


Appendix





(Figure 12)

Nomenclature

List of Symbols






119863





119898




119905


119905


membrane119905



Subscripts


Superscripts


Greek Symbols





+ 120582



layer V120574





Acknowledgment


References






































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


0 50 100 150 200 25010

15

20

25

30

35

40

45

50

55

60

Time (min)



Model prediction

Con

cent

ratio

n of

CaC

l 2(m

olmiddotm

minus3)






= 4V) [13]





2EDTA a


2



2EDTA it




2

CO2



2EDTA + 2H+ (25)


2precipitation was





2





ExptSpecific energy





1 24023 47 1928 222 24027 34 1174 33 24027 19 1173 17

0 50 100 150 200 2500

10

20

30

40

50

60

70

80

90

100

Rem

oval

()

Time (min)





2EDTA +




3

2minus+H2O (26)

Ca(OH)


3(s) +H

2O (27)


2+ CO2(g) +H

2O (28)



minus1CO3



3precipitation


2to CO

3


2

[55 times 10














2EDTA + AA





2EDTA + AA



6 Conclusions



2EDTA)



0 5 10 15 20 25

1018

1020

1022

1024

1026


Den

sity

(kgmiddot

mminus3)

y = 0323x + 10175

R2 = 0984



sugar solution


Appendix





(Figure 12)

Nomenclature

List of Symbols






119863





119898




119905


119905


membrane119905



Subscripts


Superscripts


Greek Symbols





+ 120582



layer V120574





Acknowledgment


References






































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



ExptSpecific energy





1 24023 47 1928 222 24027 34 1174 33 24027 19 1173 17

0 50 100 150 200 2500

10

20

30

40

50

60

70

80

90

100

Rem

oval

()

Time (min)





2EDTA +




3

2minus+H2O (26)

Ca(OH)


3(s) +H

2O (27)


2+ CO2(g) +H

2O (28)



minus1CO3



3precipitation


2to CO

3


2

[55 times 10














2EDTA + AA





2EDTA + AA



6 Conclusions



2EDTA)



0 5 10 15 20 25

1018

1020

1022

1024

1026


Den

sity

(kgmiddot

mminus3)

y = 0323x + 10175

R2 = 0984



sugar solution


Appendix





(Figure 12)

Nomenclature

List of Symbols






119863





119898




119905


119905


membrane119905



Subscripts


Superscripts


Greek Symbols





+ 120582



layer V120574





Acknowledgment


References






































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


0 5 10 15 20 25

1018

1020

1022

1024

1026


Den

sity

(kgmiddot

mminus3)

y = 0323x + 10175

R2 = 0984



sugar solution


Appendix





(Figure 12)

Nomenclature

List of Symbols






119863





119898




119905


119905


membrane119905



Subscripts


Superscripts


Greek Symbols





+ 120582



layer V120574





Acknowledgment


References






































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of




Acknowledgment


References






































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of










Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of

2+ Ion Using Electrodialysis from Sugar Solution

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Transcript of 2+ Ion Using Electrodialysis from Sugar Solution