Journal of Food Engineering 112 (2012) 326–337

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Journal of Food Engineering

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Modeling of cross flow ultrafiltration of stevia extract in a rectangular cell

Sourav Mondal a, Chhaya b, Sirshendu De a,⇑a Department of Chemical Engineering, Indian Institute of Technology, Kharagpur 721302, Indiab Department of Agriculture and Food Engineering, Indian Institute of Technology, Kharagpur 721302, India

a r t i c l e i n f o

Article history:Received 11 January 2012Received in revised form 6 March 2012Accepted 2 May 2012Available online 14 May 2012

Keywords:SteviosideUltrafiltrationGel layerDifferential-algebraic equation (DAE)Optimization

0260-8774/$ - see front matter � 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.jfoodeng.2012.05.002

⇑ Corresponding author. Tel.: +91 3222 283926; faxE-mail address: sde@che.iitkgp.ernet.in (S. De).

a b s t r a c t

Prediction of ultrafiltration performance during clarification of pre-treated stevia extract by cross flowultrafiltration in a rectangular cell is presented in this work. The steady state performance is modeledby using classical film theory. The transient state behaviour is quantified by using a model available inliterature. In the model, higher molecular weight solutes are clubbed in one gel-forming componentand Stevioside is assumed to be other component. In the process of modeling, the gel characteristicsare estimated. Both total recycle and batch concentration mode of operations are modeled. The modelresults are in good agreement with the experimental data.

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1. Introduction

Stevioside, a natural sweetener, obtained from stevia plants hasanti-diabetic, anti-cancerous, anti-hyperglycemic effects (Geuns,2004; Yamada et al., 1985; Jeppesen et al., 2003). Other glycosides,like, Rebaudioside A, B, D, E, Dulcoside A and B are also available insmall quantities in stevia leaves (Leung and Foster, 1996). Mem-brane based processing of stevia extract is becoming important,due to various advantages over other processes like ion-exchange,adsorption, use of chelating agents, etc. (Giovanetto, 1990; Payzantet al., 1999; Shi et al., 2002; Moraes and Machado, 1999; Montova-neli et al., 2004). Advantages of membrane processes are many,namely, (i) operation at room temperature; (ii) no phase change;(iii) no additives or external chemicals; (iv) cold sterilization, etc.(Cheryan, 1998). Few membrane based studies are available fortreatment of stevia extract. Various process steps were adoptedfor clarification and concentration. These were: ultrafiltration fol-lowed by reverse osmosis (Fuh and Chiang, 1990), microfiltrationfollowed by ultrafiltration and nanofiltration (Zhang et al., 2000),pretreatment by modified zeolite followed by ultrafiltration (Silvaet al., 2007). However, these works were mainly for technologydemonstration and the effects of operating conditions on the sys-tem performance were not reported. In a recent study, potentialof commercial and tailor-make PES membrane was evaluated forseparation and purification of stevioside. These membranes werefound to be effective considering the flux as well as the selectivity(Vanneste et al., 2011).

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Decline in permeate flux i.e., throughput of the process is a ma-jor limitation in membrane filtration. This is due to membranefouling. Fouling occurs due to two possible causes, reversible andirreversible. Reversible fouling corresponds to a phenomenonwhere the membrane permeability is regained after appropriatewashing. On the other hand, irreversible fouling cannot be re-moved completely and the membrane permeability is lost to someextent. Concentration polarization is one of the main causes ofreversible fouling. It is accumulation of solute particles over themembrane surface leading to decline in throughput of the filtrationand it is a major limitation. Concentration polarization can occurby increase in osmotic pressure at membrane-solution interfaceor formation of gel type layer over the membrane surface. Forma-tion of gel type layer is quite common during filtration of fruit juiceor plant extract, because the feed contains high molecular weightsolutes, like cell debris, proteins, pectins, etc. (Rai et al., 2007;Mondal et al., 2011a,b). During ultrafiltration of such natural prod-uct, the aim of filtration is removal of pectin, protein, microbes andhaze forming materials and maximum permeation of nutrients,like total soluble sugar, ascorbic acid, minerals, etc. (Conidi et al.,2011; Cassano et al., 2007, 2011; Vladisavljevic et al., 2003; Raiet al., 2006a; Chhaya et al., 2008; Jayanti et al., 2010). As time offiltration progresses, more solutes are deposited over the mem-brane surface, thereby, increasing the thickness of gel layer anddecreasing the permeate flux. At the same time, transport of desir-able solutes through the gel layer to the permeate side becomesquite significant to maintain the permeate quality. Therefore, acomprehensive modeling of the process is warranted to have anefficient design and subsequent scaling up. The salient feature ofthis modeling would be growth kinetics of the gel layer with a

Nomenclature

Am membrane area, m2

ab coefficient in Eq. (24)atr coefficient in Eq. (3)bb coefficient in Eq. (24), Pa�1

btr coefficient in Eq. (3), Pa�1

C01 initial concentration of component 1, kg/m3

C1 concentration of component 1, kg/m3

C1b bulk concentration of component 1, kg/m3

C1g gel layer concentration of component 1, kg/m3

C2 concentration of component 2, kg/m3

C2b bulk concentration of component 2, kg/m3

C2m concentration of component at membrane surface, kg/m3

C2p average concentration of component 2 in permeate, kg/m3

C2p permeate concentration of component 2, kg/m3

D1 diffusivity of component 1, m/s2

D2 diffusivity of component 2, m/s2

de equivalent channel diameter, mH gel layer thickness, m

kb0 mass transfer coefficient without pressure correction in

batch mode (of high molecular weight components),m/s

kR0 mass transfer coefficient without pressure correction in

total recycle mode (of high molecular weight compo-nents), m/s

kb1 mass transfer coefficient in batch mode, m/s

kR1 mass transfer coefficient in total recycle mode, m/s

k2 mass transfer coefficient of component 2, m/sL length of the channel, mM2 molecular weight of component 2, g/molNexp number of experimentsR universal gas constant, J/mol.KRbl boundary layer resistance, m�1

Re reynolds numberRg gel layer resistance, m�1

Rm membrane resistance, m�1

Rr2 real retention of component 2 by the membrane

Rbbl boundary layer resistance in batch mode, m�1

RRbl boundary layer resistance in total recycle mode, m�1

RT total resistance, m�1

RbT total resistance in batch mode, m-1

RRT total resistance in total recycle mode, m-1

S0 sum of squares in Eq. (4)S1 sum of square of errors in Eq. (14)S2 sum of square of errors in Eq. (16)Sc schmidt numberSh sherwood numberT temperature, Kt time of filtration, su cross flow velocity, m/sV volume, m3

V0 initial volume in batch mode, m3

vw permeate flow, m3/m2.sv i

w;cal calculated permeate flux of the ith experiment, m3/m2.s

v iw;exp experimental permeate flux of the ith experiment, m3/

m2.sw width of the channel, my co-ordinate normal to membrane surface, m

Greek symbolsb parameter in Eq. (13), m�2

cg partition coefficientd mass transfer boundary layer thickness, mDP transmembrane pressure drop, kPaDp osmotic pressure difference, kPaeg gel porositypm osmotic pressure at the membrane surface, kPapp osmotic pressure at the permeate side, kPaq density, kg/m3

qg gel layer density, kg/m3

l viscosity of the bulk solution, Pa s

S. Mondal et al. / Journal of Food Engineering 112 (2012) 326–337 327

moving (increasing) boundary under the system hydrodynamicsand permeation of desirable solutes through it. Combination ofthese two aspects would result prediction of permeate flux andpermeate quality. In most of the models, prediction of only gellayer controlled flux decline is quantified (Rai et al., 2007; Mondalet al., 2011). Addressing both these issues under a unified modelingapproach is rare in literature. De et al. (1997) developed a modelfor ultrafiltration of a solution, containing two components, oneis gel forming (hence completely retained by the membrane) andthe other is permeable through the membrane. This model wasvalidated using a synthetic solution of polyvinyl alcohol (gel form-ing) and sucrose (permeable). Therefore, all the transport coeffi-cients were known a priori. In an actual fruit juice or plantextract, it is a complex mixture of gel forming materials (severalhigh molecular weight solutes) and other permeable (low molecu-lar weight) solutes. Thus, independent determination of systemand model parameters is extremely difficult. One such attemptwas made in case of ultrafiltration of mosambi juice (Rai et al.,2006b). But the whole model was extremely simple as the model-ing was carried out in an unstirred batch cell and it was comparedwith the batch experimental data. In a recent work, Mondal et al.(2012), have reported a modeling work of clarification of stevia ex-tract using ultrafiltration in a stirred cell. However, the stirred cellis not an industrially relevant module. The stirred cell experiments

are generally conducted to identify the fouling mechanism, to ob-tain physico-chemical data, etc. The system behavior and informa-tion obtained from stirred cell may not be directly used for designcalculations of actual plant scale operation. On the other hand, acontinuous cross flow configuration is more realistic for practicalindustrial application. Simultaneous solution of permeate fluxand permeate quality in a gel layer controlling filtration duringcross flow ultrafiltration of a real life fruit juice/plant extract isnot available.

To fill this gap the present study has been undertaken to formu-late a suitable mathematical model during continuous cross flowultrafiltration of stevia extract in a rectangular channel. The modelis based on the work of De et al. (1997). Modeling of both total re-cycle and batch concentration mode of operation are attempted.The proposed model can be useful for appropriate scaling up of thissystem.

2. Theoretical development

Stevia extract contains a mixture of solutes of which some arehigh molecular weight (HMW), like, proteins, polysaccharides, etc.,and others are low molecular weight (LMW), like Stevioside andothers. It is assumed that HMW solutes are completely retained bythe membrane and forms a gel type of layer over the membrane

Fig. 1. Schematic of the transport of molecules during ultrafiltration of the mixture.

328 S. Mondal et al. / Journal of Food Engineering 112 (2012) 326–337

surface. Among LMW solutes, Stevioside is selectively rejected bythe membrane as well as partially retained by the gel layer ofHMW solutes that acts like a dynamic membrane. Solutes havingmolecular weight less than Stevioside (molecular weight 804.87g/mol) are assumed to be freely permeable through UF membraneand their hindered transport through gel layer is neglected. Theschematic of the transport phenomena is illustrated in Fig. 1.

Therefore, the permeate flux decline and Stevioside retentionduring ultrafiltration (UF) is a consequence of complex phenomenaarising out of growing gel layer thickness and selective transport ofStevioside through it along with the osmotic pressure difference ofStevioside across the membrane. Subscripts 1 and 2 in the text re-fer to the gel forming solutes (HMW) and Stevioside, respectively.Quantification of the gel layer thickness in both the total recycleand batch concentration mode has been estimated considering thatthe permeate contains only Stevioside and lower molecular weightcomponents.

2.1. Total recycle mode

2.1.1. Steady state modelThe experiments were performed in continuous crossflow mode

with total recycle. Thus, the concentration in feed tank is main-tained constant and a steady state is attained for every set of oper-ating conditions. Since, HMW solutes are assumed to form a gellayer over the membrane surface, the steady state permeate fluxis expressed by classical film theory (Blatt et al., 1970).

vw ¼ kR0 ln

C1g

C1b

� �ð1Þ

where, kR0 is the mass transfer coefficient for HMW solutes in total

recycle mode; C1b and C1gare bulk and gel concentration of thesesolutes, respectively. Mass transfer coefficient for crossflow setupcan be estimated from the following expression of Sherwood num-ber (Wijmans, 1984),

Sh ¼ kR0de

D1¼ 1:86

�Re:Sc:

de

L

�13

ð2Þ

where, de is the equivalent diameter of the channel cross section,equal to 4h; h is the channel half height, D1 is diffusivity of gelforming solutes, Sc is Schmidt number for HMW components(Sc = l/qD1) and Reynolds number, Re is defined as Re ¼ qude

l , where,u is the crossflow velocity, q and l are effective solution density andviscosity, respectively. It is assumed that solution density and vis-cosity are same as those of aqueous solution.In an ideal gel control-ling filtration model, the mass transfer coefficient is independent oftransmembrane pressure drop (Trettin and Doshi, 1980). But sev-eral earlier literature studies report that mass transfer coefficientexhibits a weak dependence on transmembrane pressure drop(Rai et al., 2007; Mondal et al., 2011; Johnston and Deen, 1999;Banerjee and De, 2012). It is therefore, assumed that mass transfercoefficient is a linear function of transmembrane pressure dropwithin the range of operating pressure studied herein (Johnstonand Deen, 1999). Thus, the following expression of permeate fluxis proposed.

vw ¼ kR1 ln

�C1g

C1b

�ð3Þ

where, kR1 ¼ kR

0ðatr þ btrDPÞ. Since, the HMW solutes are a complexmixture of various components, its effective diffusivity (D1) andgel concentration C1g are difficult to estimate. These values areadopted from an earlier analysis of Stevioside ultrafiltration fromstevia extract in stirred continuous cell (Mondal et al., 2012). Theparameters atr and btr are determined using the optimization rou-tine of interior point algorithm following a trust region method(Byrd et al., 2000), by minimizing the sum of square of errors ofthe steady state permeate flux of all the experiments. Sum of squareerror is defined as,

S0 ¼XNexp

i¼1

�v iw;exp � v i

w;cal

v iw;exp

�2

ð4Þ

where, Nexp is the number of experiments conducted.

2.1.2. Transient modelConsidering, the mass balance of HMW solutes in the mass

transfer boundary layer (0 < y < d) results, (De and Bhattacharyya,1997).

S. Mondal et al. / Journal of Food Engineering 112 (2012) 326–337 329

qgdHdt¼ vwC1 � D1

dC1

dyð5Þ

where, qg is gel layer density and H is the gel layer thickness. Inte-grating the above equation within the mass transfer boundary layerwith the conditions, at y = 0, C1 = C1b and at y = d, C1 = C1g, the fol-lowing equation is resulted

qgdHdt¼ vw

C1g � C1b

exp

�vw=kR

1

�1� exp

�vw=kR

1

�ð6Þ

The initial condition of the above equation is at t = 0, H = 0. It maybe noted that at steady state, Eq. (6) is reduced to Eq. (3).

Next, a mass balance of stevioside in mass transfer boundarylayer and gel layer has been carried out. Following the derivationof De and Bhattacharyya (1997), the final expression of Steviosideat the membrane surface is given as

C2m¼C2b exp vw

1k2þ H

eg D2

� �h icgRr2þð1�Rr2Þðcg�1Þexp vwH

eg D2

� �þð1�Rr2Þexp vwð 1

k2þ H

eg D2Þ

h ið7Þ

where, cg is partition coefficient of Stevioside across the gel layerand mass transfer boundary layer. It is defined as, C2(d�) = cgC2(d+).Rr2 is real retention of Stevioside by the membrane, k2 is its masstransfer coefficient, D2 is diffusivity and eg is the gel layer porosity.Real retention of Stevioside is defined as,

Rr2 ¼ 1� C2p

C2m

� �ð8Þ

The osmotic pressure difference of solution due to concentrationof Stevioside across the membrane is given as,

Dp ¼ pm � pp ð9Þ

where, pm and pp are osmotic pressure of the solution at the mem-brane surface and permeate side, respectively. The osmotic pressureof solutes due to Stevioside is expressed is expressed according tovan’t Hoff’s relation,

p ¼ RTM2

C2b ð10Þ

where, R is universal gas constant, T is temperature, M2 is molecularweight of Stevioside. Thus, the osmotic pressure difference acrossthe membrane is obtained.

Dp ¼ RTM2

C2mRr2 ð11Þ

Permeate flux at any point of time can be written as,

vwðtÞ ¼DP � Dp

lðRm þ RgÞð12Þ

where, Rg is the gel layer thickness and is expressed as,

Rg ¼ bH ð13Þ

b = a(1 � eg)qg and is constant as it is a characteristic of gel layer.Eqs. (6)–(8), (11), (12), and (13) constitute a set of differential–algebraic equation (DAE). In this set, the parameters are b, cg andeg. Real retention of Stevioside (Rr2) is independently estimated asdescribed in experimental section. Gel layer density qg is takenfrom an earlier analysis (Mondal et al., 2012). Three parameters,namely, b, cg and eg are estimated by comparing the sum of squareerrors between the calculated and experimental data. Two separatesum of squares are defined in the solution algorithm. One of them isbased on permeate flux.

S1 ¼XN2

j¼1

XNj

i¼1

v ijw;cal � v ij

w;exp

v ijw;exp

" #2

ð14Þ

where, j represents the number experiment, i represents number ofexperimentally measured data points, Nj is number of data at var-ious time points in jth experiment.

As described in experimental section, Stevioside concentrationwas measured at the end of the experiment, containing the cumu-lative permeate. Thus, the Stevioside concentration in the perme-ate is calculated as, a time averaged value,

C2p ¼1tð1� Rr2Þ

Z t

0C2mdt ð15Þ

Based on the above definition, the sum of squares S2 is defined as,

S2 ¼XNp

k¼1

Ck2p;cal � Ck

2p;exp

Ck2p;exp

" #2

ð16Þ

where, Np is number of experiments at a particular transmembranepressure drop. The detailed constrained optimization is presentedin Fig. 2. Using this procedure, three parameters (as mentioned ear-lier) are estimated using the optimization routine of interior pointalgorithm following a trust region method (Byrd et al., 2000), min-imizing S1 and S2, simultaneously. With these parameter values, theprofiles of gel layer thickness, permeate flux, Stevioside concentra-tion in permeate, gel layer resistance are calculated, using Eqs. (6),(7), (8), (11), (12), and (13).

2.2. Batch concentration mode

In this mode of operation, the permeate is not recycled back tothe feed. As a result, the feed concentration of the Stevioside andHMW components increase. The thickness of gel layer dependson the feed concentration of the gel forming solutes and trans-membrane pressure drop across the membrane. Therefore, withtime of operation, the gel layer grows, and it is responsible for sig-nificant decline of permeate flux compared to total recycle mode,as the gel layer resistance increases considerably. It can be notedthat the total resistance to driving force, in the entire process ofultrafiltration, can be constituted as membrane hydraulic resis-tance (Rm), the gel layer resistance (Rg) and resistance due toboundary layer (Rbl),

RT ¼ Rm þ Rg þ Rbl ð17Þ

Thus, the permeate flux is expressed as

vw ¼DPlRT

ð18Þ

The average permeate flux in total recycle mode is greater thanthe batch mode at identical operating conditions. Thus, it can beinterpreted that,

RRT < Rb

T ð19Þ

where, RRT and Rb

T are total resistance in total recycle and batchmode, respectively. Since, Rg in case of total recycle mode is lessthan that of batch mode, it can be concluded,

RRbl < Rb

bl ð20Þ

where, RRbl and Rb

bl are boundary layer resistance in total recycle andbatch mode, respectively. As mass transfer coefficient is inverselyproportional to boundary layer resistance, it assumes a higher valuein the batch concentration mode.

kb1 < kR

1 ð21Þ

The expression of mass transfer coefficient for total recycle modehas already been described in Eq. (2). However, it must be observedthat the effective channel thickness (2h) decreases, due to

Fig. 2. Sequence of the calculations (algorithm) for optimization of transient state modeling.

330 S. Mondal et al. / Journal of Food Engineering 112 (2012) 326–337

deposition of gel layer over the membrane surface. Since, the cross-sectional area to flow is reduced, the crossflow velocity through thechannel (u) increases. Rearranging the expression in Eq. (2), themass transfer coefficient (k0) in batch mode can be represented as,

kb0 ¼

uD21

deL

!13

ð22Þ

As already shown, in batch mode, the ratio ude

increases comparedto total recycle mode. Hence, the following inequality holds

kb0 > kR

0 ð23Þ

Thus, the mass transfer coefficient in batch mode has a differentnumerical value compared to total recycle mode. Now, similar to to-tal recycle mode, a pressure correlation factor has to be incorporatedto account for variation for permeate flux with transmembrane pres-sure drop,

kb1 ¼ kb

0ðab þ bbDPÞ ð24Þ

Considering Eqs. (23) and (24) it can be concluded that the constantparameters ab and bb will be less than atr and btr respectively.

Considering an overall material balance, the following equationis obtained,

S. Mondal et al. / Journal of Food Engineering 112 (2012) 326–337 331

ddtðqf VÞ ¼ �vwAmqp ð25Þ

where, qf and qp are densities in feed and permeate streams; V isthe feed volume and Am is the effective membrane area. Assumingqf ’ qp the above equation is modified as

dVdt¼ �vwAm ð26Þ

Using overall species balance of gel forming component, the fol-lowing equation is obtained,

ddtðC1bVÞ ¼ �vwAmCp1 ð27Þ

Since, concentration of the gel forming material in the permeateis zero (Cp1 = 0) (Cheryan, 1998), the above equation reduces to asimple algebraic equation

C1bV ¼ C01V0 ð28Þ

using initial boundary condition as C = C01and V = V0 at t = 0. Rear-ranging Eq. (28) we get

C1b ¼C01V0

Vð29Þ

Using overall species balance of Stevioside, the following equa-tion is obtained,

C2bdVdtþ V

dC2b

dt¼ �vwAmCp2 ð30Þ

with the initial conditions as C = C02 and V = V0 at t = 0.It may be noted that as time of operation proceeds, the effective

channel thickness decreases by deposition of gel layer and it isquantified as,

dte ¼ de � 2HðtÞ ð31Þ

Consequently, the cross flow velocity ut inside the channelchanges as,

ut ¼ Q

w� ðdte=2Þ

ð32Þ

where, w is the width of the channel.The above expressions of equivalent diameter and cross flow

velocity within the channel have been utilized to evaluate the masstransfer coefficient kb

0. Using Eqs. (6), (7), (8), (11), (12), (13) andcombining Eqs. (26), (29), (30), (31), (32), a system of differentialalgebraic equations (DAE) has been setup involving five state vari-ables, namely, H, C1b, C2b, V and C2m. The system of stiff-coupledDAE involves state dependent mass matrix. The solution is basedon the numerical differentiation formulae with Gears method,through a MATLAB function ode15s (Shampine and Reichelt,1997; Shampine et al., 1999).

Similar to the total recycle mode, two separate nonlinear con-strained multi-objective optimization functions have been imple-mented to minimize the square of error of the permeate flux andpermeate Stevioside concentration. The parameters ab and bb aredetermined by the flux optimization routine, while the parametercg is determined by the permeate concentration optimizationroutine.

3. Experimental

3.1. Materials

Dry stevia leaves powder was obtained from M/s, RAS AgroAssociates, Maharashtra, India. Distilled water was used as solventfor extraction process. M/s, Merck India Limited, Mumbai, India,

supplied high performance liquid chromatography (HPLC) gradeacetonitrile and water. Standard stevioside of 98% purity was ob-tained from M/s, Sigma–Aldrich, USA.

3.2. Membranes

For ultrafiltration, a 30 kDa membrane of polyethersulfone (PES)with permeability 4.4 � 10�11 m/Pa s has been used. This mem-brane was selected after investigating the performance of 5, 10, 30and 100 kDa membranes for extraction of stevia. 30 kDa membranewas found to result the highest permeate flux and maximum recov-ery of stevioside in the permeate (Chhaya et al., 2012a). These mem-branes were supplied by M/s, Permionics Membranes Pvt. Ltd.,Gorwa, Vadodara, India. The permeability of ultrafiltration mem-brane was 5.4 � 10�11 m/Pa s. Clarification and purification ofsweeteners from stevia extract has also been performed using PESmembranes (Vanneste et al., 2011), which shows that commercialPES membrane has high selectivity and permeability for steviosideseparation and purification.

3.3. Experimental set up

A cross flow ultrafiltration set up was used for clarification ofstevia extract using ultrafiltration. The effective dimension of themembrane was 14.5 cm in length, 5.5 cm in width and 3.0 � 10�3

m channel height. The cell consisted of two rectangular matchingstainless steel flanges. The inner surface of the top flange was mir-ror polished. The bottom flange was grooved, forming the channelsfor the permeate flow. A porous stainless steel plate was placed onthe lower flange that provides mechanical support to the mem-brane. Two flanges were tightened to create a leak proof channelfor conducting experiments in cross flow mode. Permeate sampleswere collected from the bottom of the cell and were analyzed forcolor, clarity, total solids and stevioside concentration. The detailsof the set up are available (Prabhavathy and De, 2010).

3.4. Methods

3.4.1. Extraction processDry stevia leaves powder was mixed with hot distilled water at

a ratio of 1:14 (g:ml). Temperature was fixed at 78 ± 1 �C for56 min (Chhaya et al., 2012b). Constant temperature water bathwas used for hot water extraction. Next, the aqueous stevia extractwas cooled to room temperature and cloth filtered. The filtered ex-tract was analyzed for their color, clarity, stevioside concentrationand total solid content.

3.4.2. Primary clarificationPrimary clarification of the extract was carried out in a labora-

tory centrifuge (Model number R-24, supplied by M/s, Remi Inter-national Ltd., Mumbai, India). The centrifugation capacity was200 ml per batch. The operating conditions were stirrer speed5334 g and centrifugation time 26 min (Chhaya et al., 2012c).

3.4.3. Cross flow ultrafiltrationA fresh membrane was compacted at a pressure higher than the

maximum operating pressure for 3 h using distilled water and thenits permeability was measured. The extract was placed in a stain-less steel feed tank of 3 l capacity. A high pressure reciprocatingpump was used to feed the effluent into the cross-flow membranecell. Cumulative volumes of permeate were collected during theexperiment. Permeate samples were collected at different timeintervals for analysis. A bypass line was provided from the pumpdelivery to the feed tank. Retentate and bypass control valves wereused to vary the pressure and flow rate accordingly. Values of per-meate flux were determined from the slopes of cumulative volume

332 S. Mondal et al. / Journal of Food Engineering 112 (2012) 326–337

versus time plot. The precision of flux measurement was in theorder of ±5%. The permeate stream after collecting requiredamount of sample was recycled to the feed tank to maintain a con-stant concentration in the feed tank under total recycle mode. Thepermeate was not recycled under batch concentration mode ofoperation. Duration of the cross-flow experiments was forty-fiveminutes for total recycle mode of operation and it was 10 h forbatch concentration mode. The feed volumes were 2 l for total re-cycle mode and the initial feed volume was 1.8 l for batch concen-tration mode.

Once an experimental run was over, the membrane was thor-oughly washed, in situ, with distilled water for 30 min applying amaximum pressure of 200 kPa. The cell was dismantled and themembrane was rinsed with distilled water and was dipped in 2%sodium dodecyl sulphate solution overnight. Next, the membranewas washed carefully with distilled water to remove traces of sur-factant. The cell was reassembled and the membrane permeabilitywas again measured using distilled water. After that, the set upwas ready for the next experiment with centrifuged stevia extract.All the experiments were conducted at a room temperature of32 ± 2 �C.

3.5. Experimental design

Cross flow ultrafiltration experiments under total recycle modewere performed using the operating pressure difference as 276,414, 552 and 690 kPa. The cross flow rates were 60, 80, 100 and120 l/h. Experiments under batch concentration mode were under-taken at 276, 414 and 552 kPa pressure and 100 l/h cross flow rate.

3.6. Determination of real retention of Stevioside

A solution of 1 kg/m3 concentration of Stevioside (obtainedfrom M/s, Sigma–Aldrich, USA) was prepared and a stirred experi-ment was conducted at high stirring speed, 2000 rpm and lowtransmembrane pressure drop 128 kPa. These conditions main-tained a low polarized condition, where, the permeate concentra-tion of Stevioside was measured. The observed retention underthis situation is a reasonably good estimate of real retention ofthe membrane (De and Bhattacharyya, 1997). The value of realretention for Stevioside (Rr2) was determined to be 0.1. This param-eter is generally constant for a particular membrane-solute–sol-vent system (Opong and Zydney, 1991). Many studies involvingmodeling of the membrane process in the literature have been per-formed considering real retention as a constant inherent mem-brane-solute–solvent property (Bouchard et al., 1994; Trettin andDoshi, 1981; De et al., 1997).

3.7. Analysis

The original, centrifuged and ultrafiltered stevia extract wereanalyzed for their color, clarity, total solid content and stevioside con-centration. Color of the extract was measured in terms of opticalabsorbance (A) at a wavelength of 420 nm using a spectrophotometer(BIORAD Smart Spec 3000, USA). Clarity of the extract was measuredin terms of percentage of transmittance (%T) using a spectrophoto-metrically. This is given by the equation, %T = 100 � 10�A, where, Ais optical absorbance at a wavelength of 660 nm.

Total solid of the sample was measured gravimetrically by heat-ing the extract in hot air oven at 104 ± 2 �C until the difference inthe weight of the extract becomes constant at successive intervals(Ranganna, 1986). Total solid was represented in terms of gram per100 ml of stevia extract.

Amount of stevioside present in the stevia extract (before andafter clarification) was analyzed by HPLC (M/s, Perkin Elmer Co.,Shelton, Connecticut, USA). Initially a calibration curve was pre-

pared using standard stevioside of 98% purity. Then, for eachanalysis, a sample volume of 30 lL was injected into an AgilentZorbax SB C-18 reverse phase HPLC column (4.6 mm I.D.,250 mm length and 5 lm particle size). Mobile phase was a mix-ture of acetonitrile and water at a ratio of 80:20 (volume basis)and the flow rate was 1 mL/min. UV detector (Perkin Elmer series200) was used for detection of stevioside present in the sampleat a wavelength of 210 nm. Stevioside concentration was repre-sented in terms of percentage (%) of stevioside recovered in theclarified extract as:

%Stevioside¼ðstevioside retained in clarified extract=stevioside present in feedÞ�100:

2.7. Statistical Analysis

All membrane filtration experiments were carried out in tripli-cate. The permeate flux data were within ±3% variation and thesewere presented as error bars in the figures. The permeability valueshad ±5% variation.

4. Results and discussion

4.1. Total recycle mode

In this study, there are altogether ten parameters (Rr2, D1, C1g, D2,qg, atr, btr, cg ; eg and b). The first one is independently determinedas described in Section 3.6. The values of D1, C1g, qg and D2 are ob-tained from the previous study (Mondal et al., 2012). These are3.7 � 10�11 m2/s, 51.5 kg/m3, 1550 kg/m3 and 2.0 � 10�10 m2/s,respectively. Both D1 and C1g are obtained by minimizing thesum of square of error of the experimental and predicted steadystate flux values, while the D2 and qg are determined by minimiz-ing the sum of square of error of the experimental and predictedtransient flux values. Both these algorithms employ non-linearconstrained optimization. The parameters atr and btr are estimatedfrom the steady state analysis (as described at the end of Section2.1.1) and other three parameters cg, eg and b are estimated fromthe transient analysis (as described at the end of Section 2.1.2).The value of C1b and C2b are 6.3 and 15.75 g/l, respectively. Thecomplete list of parameters involved in this study has been pre-sented in Table 1.

4.1.1. Steady stateAs discussed in Section 2.1, the steady state permeate flux of

pre-treated stevia extract can be calculated using the modified filmtheory equation. This calculation involves estimation of twoparameters, namely, atr and btr Physically, these two parametersindicate the pressure dependence of mass transfer coefficient andthese are estimated as discussed earlier. These values are:atr = 0.35; btr = 1.22 � 10�6 Pa�1. The comparison between the cal-culated steady state permeate flux values with the experimentaldata is performed and is presented in Fig. 3. It is observed from thisfigure that the agreement between the calculated and the experi-mental data are within ±15%.

4.1.2. Transient stateAs discussed in Section 2.1.2 the profiles of transient flux decline

and concentration of Stevioside in the permeate have been calcu-lated by the procedure illustrated in Section 2.1.2. It may be men-tioned that this optimization procedure was adopted for differenttransmembrane pressure drop, separately. It is observed that theparameter b and eg vary in a narrow range over DP and the averagevalues are reported. These are (4.55 ± 0.47) � 1019 m�2 and 0.56 ±

4 5 6 7 8 9 10 11 124

5

6

7

8

9

10

11

12

Pred

icte

d fl

ux (

l/m2 h)

Experimental flux (l/m2h)

+15%

-15%

Fig. 3. Comparison of the predicted and experimental steady state flux in continuous mode.

Table 1Details of the parameters estimated in this study.

Parameter Type Value Method of determination Reference

D1 Physical property of the solution mixture 3.7 � 10�11 m2/s Minimizing the sum of square of error of the experimentaland predicted steady state flux values

Mondal et al.,2012

D2 2.0 � 10�11 m2/s Constrained non-linear optimization by minimizing the sumof square of error of the experimental and predicted transientflux values

C1g Gel layer characteristics 51.5 kg/m3 Minimizing the sum of square of error of the experimentaland predicted steady state flux values

eg 0.56 Simultaneous optimization of the experimental flux andstevioside permeate concentration values with the predictedones

Present study

qg 1550 kg/m3 Constrained non-linear optimization by minimizing the sumof square of error of the experimental and predicted transientflux values

Mondal et al.,2012

b Gel layer resistance model parameter 4.55 � 1019 m�2

(average value in totalrecycle mode)

Simultaneous optimization of the experimental flux andstevioside permeate concentration values with the predictedones

Present study

cg Partition coefficient specific to operatingconditions, solute-solution system

Reported in Table 2

Rr2 Membrane feature 0.1 Measured experimentally Present studyand Mondalet al., 2012

atr Adjustable parameter to relate the effectof pressure in gel layer controllingultrafiltration

0.35 Optimization of the experimental flux profile with change inpressure drop

Present study

ab 0.22btr 1.22 � 10�6 Pa�1

bb 2.22 � 10�7 Pa�1

Table 2Values of the partition coefficient with pressure in total recycle as well as in batchmode.

TMP (kPa) cg

Total recycle mode Batch concentration mode

276 2.25 ± 0.11 3.51 ± 0.17414 3.14 ± 0.16 4.53 ± 0.27552 3.88 ± 0.20 5.53 ± 0.28690 6.13 ± 0.35 –

S. Mondal et al. / Journal of Food Engineering 112 (2012) 326–337 333

0.03, respectively. The distribution coefficient cg is observed to bevarying with transmembrane drop and is presented in Table 2.As discussed earlier, cg represents the partition coefficient of Stevi-oside concentration in the bulk-gel layer interface and the gel layer.So, at higher transmembrane pressure drop, gel layer retains more

Stevioside as is evident from this figure. Thus, it is expected thatpermeation of Stevioside is lower at higher transmembrane pres-sure drop.

With the estimated parameter values, as outlined in Section2.1.2, Eqs. (6), (7), (11), (12), and (13) are solved to obtain theprofiles of permeate flux, Stevioside concentration, gel layer thick-ness and gel layer resistances.

Fig. 4 represents the permeate flux decline for various operatingconditions. As the time of filtration progresses, the gel layer thick-ness increases, leading to increase in gel layer resistance and hencethe permeate flux decreases. Finally, due to forced convection im-posed by the cross flow of the feed, the growth of gel layerthickness is arrested and a steady state is attained. For example,it is observed from Fig. 4(a) and (b) that the steady state is attainedafter 10 min. At higher cross flow rate, the thickness of gel layer atthe steady state is less due to enhanced forced convection,

Table 3Comparison of the stevioside recovery (in percentage) values.

TMP (kPa) 80 LPH 100 LPH 120 LPHPredicted Experiment Predicted Experiment Predicted Experiment

276 51.6 58.0 51.4 49.0 51.3 49.0414 43.0 45.0 42.7 43.3 42.5 40.4552 39.3 40.5 39.0 39.7 38.9 37.3690 29.5 29.7 29.3 31.1 29.1 27.5

0 10 20 30 40 504

6

8

10

12

14

16

Error bar: ±5%

Perm

eate

flu

x (l

/m2 h)

Time (min)

80 l/h 100 l/h

symbols - Experiemtalsolid line - Calculated

(a) ΔP = 552 kPa

0 10 20 30 40 508

10

12

14

16

18

20

Error bar: ±5%symbols - Experiemtalsolid line - Calculated

Perm

eate

Flu

x (L

/m2 h)

Time (min)

100 l/h 120 l/h

(b) ΔP = 690 kPa

Fig. 4. Transient flux profile of the experimental as well as the predicted fluxes atdifferent transmembrane pressure drop and crossflow rates. (a) DP = 552 kPa; (b)DP = 690 kPa.

0 10 20 30 40 505

6

7

8

9

10

Perm

eate

Ste

vios

ide

conc

entr

atio

n (k

g/m

3 )

Time (min)

1

23

ΔP (kPa) Flowrate (l/h)1: 276 1002: 552 803: 552 100

Fig. 5. Transient profiles of stevioside at different operating conditions.

0 10 20 30 40 500

1

2

3

4

ΔP (kPa) Flowrate (l/h)1: 690 1002: 690 1203: 276 100

Gel

laye

r th

ickn

ess

( μm

)

Time (min)

1

2

3

Fig. 6. Predicted profiles of gel layer thickness.

334 S. Mondal et al. / Journal of Food Engineering 112 (2012) 326–337

resulting to higher steady state permeate flux. For example, at552 kPa, the permeate flux increases from 8 to 9 l/m2h (12.5% in-crease) as the cross flow rate increases from 80 to 100 l/h. At690 kPa, the permeate flux increases from 10 to 11.5 l/m2h (15% in-crease) with increase in cross flow rate from 100 to 120 l/h.

The profiles of stevioside concentration in the permeate areshown in Fig. 5 for different operating conditions. As representedin Table 1 that the predicted and experimental steady state recov-ery values are in close agreement. A general trend is observed fromthe curves of this figure that the stevioside concentration in thepermeate decreases with time and finally it reaches a steady stateafter about 10 min. This time coincides with that required to attainthe steady state permeate flux. Effect of transmembrane pressuredrop is also observed from curves 1 and 2. The steady state concen-

tration of stevioside in permeate is more at lower operating pres-sure as shown in Table 3 (Chhaya et al., 2012a; Mondal et al.,2012). As discussed earlier, the limiting step of transport of stevi-oside in the permeate is its transport through the gel layer and itis dictated by the partition coefficient cg. As observed earlier, thevalue of this parameter increases with transmembrane pressuredrop. Higher value of this parameter indicates that the gel layer ar-rests more stevioside, leading to lower concentration of it in thepermeate. The value of this parameter is 2.3 and 3.7 at 276 and552 kPa. Thus, stevioside concentration is more in permeate atlower transmembrane pressure drop. Since, partition coefficientis a function of transmembrane pressure drop only, at 552 kPapressure cg is constant and the amount of stevioside in the gel layer

0 10 20 30 40 500

1

2

3

4

5

ΔP (kPa) Flowrate (l/h)1: 690 1002: 690 1203: 276 100

Rg

/ Rm

Time (min)

1

2

3

Fig. 7. Profiles of gel layer to membrane resistance for different operatingconditions.

0 100 200 300 400 500 600 7001.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

Error bar: ± 2%

Flowrate 100 l/h

symbols - Experimentalsolid line - Calculated

276 kPa 414 kPa 552 kPa

VC

F

Time (min)

Fig. 9. Variation of VCF with time.

S. Mondal et al. / Journal of Food Engineering 112 (2012) 326–337 335

remains same. Therefore, its concentration profile in the permeatedoes not change significantly with cross flow rate (from curves 2and 3) at 552 kPa pressure drop.

Fig. 6 shows the profile of gel layer thickness with differentoperating conditions. The effects of transmembrane pressure dropwould be clear from the curves 2 and 3. At higher transmembranepressure drop, the gel layer thickness is more due to enhanced con-vection of gel forming solutes towards the membrane surface.Thus, at the steady state and 100 l/h cross flow rate, the gel layerthickness increases from 2.4 to 3.9 lm as the transmembrane pres-sure drop increases from 276 to 690 kPa. The effect of cross flowrate is observed by comparing the curves 1 and 2. At higher crossflow rate, due to forced convection of the retentate stream, thegrowth of gel layer is arrested and its thickness is less. As the crossflow rate increases from 100 to 120 l/h, the gel layer thickness isreduced from 3.9 to 3.5 lm. Profile of gel layer resistance withoperating conditions is shown in Fig. 7. Since, gel layer resistanceis directly proportional to gel thickness, it shows the similar trendof gel layer thickness. Gel layer resistance is more at higher trans-membrane pressure drop and less at higher cross flow rate. It is ob-served from this figure that the gel layer resistance at the steadystate is about four times of the membrane resistance.

0 100 200 300 400 500 600 7000

4

8

12

16

Error bar: ±5%

Perm

eate

flu

x (l

/m2 h)

Time (min)

276 kPa 414 kPa 552 kPa

symbols - Experimentalsolid line - Calculated

Flowrate 100 l/h

Fig. 8. Profile of permeate flux at different transmembrane pressure drop.

4.2. Batch concentration mode

As described in section 2.2, Eqs. (26)–(30) are solvedsimultaneously to obtain the profiles of permeate flux, steviosideconcentration in permeate, volume concentration factor, bulkconcentration of stevioside and HMW solute, gel layer thicknessand gel layer resistance. Three parameters ab, bb and cg are evalu-ated during this calculation as described in Section 2.2, as theseparameters depend on the mode of operation. The values of otherparameters are considered as used in the analysis of total recyclemode. As observed in the case of total recycle mode, cg valuesare mainly function of transmembrane pressure drop and theyare independent of cross flow rate. Variation of cg with transmem-brane pressure drop in this case is shown in Table 2.

Profiles of permeate flux at various transmembrane pressuredrop are presented in Fig. 8. This figure shows that the permeateflux declines sharply within 100 min of operation and slowlythereafter. The permeate flux is more at higher transmembranepressure drop. The model calculations show excellent matchingwith the experimental data. In the batch concentration mode, sincethe filtrate is drawn, the feed volume is reduced. Profiles of volumeconcentration factor are shown in Fig. 9. At higher transmembranepressure drop, as more filtrate is taken out, it leads to higher valueof VCF. At 552 kPa pressure, VCF attains a value of 1.4 after 10 h of

0 100 200 300 400 500 6000

4

8

12

16

20Flowrate 100 l/h 276 kPa

414 kPa 552 kPa

symbols - Experimentalsolid line - Calculated

Stev

iosi

de p

erm

eate

co

ncen

trat

ion

(kg

/ m3 )

Time (min)

Error bar: ±5%

Fig. 10. Variation of the stevioside permeate concentration with time.

0 100 200 300 400 500 600 700

6.0

6.2

6.4

6.6

6.8

7.0

7.2

7.4

7.6

7.8

8.0

8.2

Bul

k co

ncen

trat

ion

of H

MW

(kg

/m3 )

Time (min)

1: ΔP - 276 kPa2: ΔP - 414 kPa3: ΔP - 552 kPa

1

2

3Flowrate 100 l/h

(a)

0 100 200 300 400 500 600

16.0

16.5

17.0

17.5

18.0

18.5

Bul

k co

ncen

trat

ion

of S

tevi

osid

e (k

g/m

3 )

Time (min)

1: ΔP - 276 kPa2: ΔP - 414 kPa3: ΔP - 552 kPa

1

2

3

(b)

Flowrate 100 l/h

Fig. 11. Variation of bulk concentration with time (a) HMW components (b)stevioside.

0 100 200 300 400 500 6000

50

100

150

200

Flowrate 100 l/h

1: ΔP - 276 kPa2: ΔP - 414 kPa3: ΔP - 552 kPa

Gel

laye

r th

ickn

ess

(μm

)

Time (min)

1

2

3

Fig. 12. Variation of the gel layer thickness with time.

0 100 200 300 400 500 600

1

10

100

Flowrate 100 l/h

Rg

/ Rm

Time (min)

1: ΔP - 276 kPa2: ΔP - 414 kPa3: ΔP - 552 kPa

1

2

3

Fig. 13. Variation of the ratio of membrane to gel layer resistance ratio with time.

336 S. Mondal et al. / Journal of Food Engineering 112 (2012) 326–337

operation. It is observed from this figure that the calculated pro-files agree closely with the experimental data.

Recovery of Stevioside in the permeate was calculated for vari-ous operating conditions and the comparison of experimental andcalculated values are presented in Table 2. It is observed from thistable that the calculated values agree well with the experimentalresults. Concentration profile of stevioside in the permeate for dif-ferent pressure is presented in Fig. 10. As observed and explainedin the case of total recycle mode, the Stevioside concentration inthe permeate is more at lower transmembrane pressure drop.Profiles of bulk concentration of HMW solute and stevioside areshown in Fig. 11(a) and (b), respectively. As more solvent is drawnout, bulk concentration of HMW solutes increases due to reductionof volume. Bulk concentration is more at higher operating pressuredue to filtering out of more solvent. Variation of gel layer thicknesswith transmembrane pressure drop is shown in Fig. 12. The curvesshow the usual trends, i.e., gel layer thickness increases withtransmembrane pressure drop. Comparing to corresponding figurein total recycle mode (Fig. 6), it can be observed that gel layerthickness does not attain a steady state in this case, rather it growswith time. Since this mode is a batch operation, the steady state isnever be attained and the gel layer thickness grows slowly asshown in this figure. However, gel layer thickness increases withtransmembrane pressure drop as expected. Gel thickness in thiscase is quite large about 200 lm after 10 h of operation at552 kPa and 100 l/h whereas, that in Fig. 5 is only 4.4 lm. This is

because in total recycle mode, steady state is attained within10 min. Profiles of gel layer resistance for various transmembranepressure drop are shown in Fig. 13. As observed in this figure, gellayer resistance increases with time continuously as it is a batchoperation. Gel layer resistance is more at higher transmembranepressure drop as the gel thickness increases with pressure. It is alsonoted that gel layer resistance can be as high as 100 times of themembrane resistance after 10 h of operation.

5. Conclusion

Gel layer controlling model for UF of stevia extract for both totalrecycle and batch concentration mode was successfully applied in arectangular filtration cell. Prediction of permeate flux and permeateconcentration in both operating mode, steady and transient condi-tions agreed well with the experimental data. In the total recyclemode, the effect of cross flow is prominent due to less concentrationpolarization as the feed concentration remains constant and gellayer thickness was in between 2.5 and 4 lm for various operatingconditions. In batch mode, gel layer thickness was in between 75and 200 lm after 10 h as the bulk concentration increases simulta-neously. The parameter cg dictated the concentration of Stevioside

S. Mondal et al. / Journal of Food Engineering 112 (2012) 326–337 337

in the permeate, which increases with pressure drop. At highertransmembrane pressure drop, the gel holds more Stevioside. Thus,Stevioside recovery is higher at lower transmembrane pressuredrop. The proposed model can be efficiently used to scale up the fil-tration of stevia extract and recovery of Stevioside.

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