Modeling of gel layer transport during ultrafiltration of fruit juice with non-Newtonian fluid rheology

food and bioproducts processing 1 0 0 ( 2 0 1 6 ) 72–84

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Food and Bioproducts Processing journal homepage: www.elsevier.com/locate/fbp

Modeling of gel layer transport during ultrafiltration of fruit juice with non-Newtonian fluid rheology Sourav Mondal a,b , Alfredo Cassano c , Carmela Conidi c , Sirshendu De a,∗ a

Department of Chemical Engineering, Indian Institute of Technology Kharagpur, Kharagpur 721302, India Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK c Institute on Membrane Technology, ITM-CNR, c/o University of Calabria, via P. Bucci, 17/C, I-87030 Rende, Cosenza, Italy b

a r t i c l e

i n f o

a b s t r a c t

Article history:

The rheology of fruit juice mixtures generally follows non-Newtonian behavior of power

Received 14 December 2015

law form. The clarification of fruit juices by membrane separation illustrates an example

Received in revised form 30 April

of enhancing the shelf life of a real fruit juice by removing degradable components. How-

2016

ever, the presence of high molecular weight proteins, pectins, polysaccharides, fibers, etc.,

Accepted 27 June 2016

tends to form gel over the membrane during filtration causing fouling and affecting its per-

Available online 2 July 2016

formance. The proposed model developed from the first principle boundary layer analysis, describes the physical mass transport phenomena and quantifies the various extents of

Keywords:

fouling using different membrane materials and operating conditions. The model results

Ultrafiltration

are useful in understanding the complex solute–membrane interplay in fouling and can

Transport

predict the effect of gel layer thickness on the process throughput. In this work, the model results were validated experimentally in clarification of blood

Gel layer Non-Newtonian

orange juice in batch mode using two polysulphone (PS) membranes and polyacryloni-

Mass transfer boundary layer

trile (PAN) membrane in hollow fiber configuration, with different molecular-weight-cut-off

Diffusion

(MWCO). The results clearly indicated that PS membranes are more prone to fouling at higher

Hollow fiber

pressures compared to PAN membrane. An increase in the feed flow rate had a significant effect in reducing the growth of gel layer mainly in PS membranes. © 2016 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

1.

Introduction

Cross flow membrane filtration processes are widely used in food processing industries (Girard and Fukumoto, 2000), biotechnology (Cheryan, 1998), the pharmaceutical sector (Wang and Chung, 2006), clarification and concentration of fruit juice (Rai et al., 2010; Mondal et al., 2011a; Thomas et al., 1987; Mohammad et al., 2012). In most of the filtration processes, batch mode is often used, since the permeate is the preferred product. For efficient design of large scale systems, prediction and detailed understanding of the mass transfer phenomena with coupled fluid flow is important. The relevant flow configuration and flow regimes are significant in modeling the process performance.

∗

The mass transfer coefficient is generally calculated from the Sherwood number correlations using Leveque relation, derived from heat and mass transfer analogies. However, these correlations fail to take into account the effects of non-Newtonian rheology of the fluid and changes due to developing mass transfer boundary layer on the hydrodynamics of the flow regime and consequently on the mass transfer coefficient. The available mass transfer correlations for membrane separation processes along with their shortcomings have been already reviewed in detail (van Den Berg et al., 1989; Gekas and Hallstrom, 1987). Generally, citrus fruit juice containing pectins are non-Newtonian indicating that they do not exhibit a direct proportionality between shear stress and shear rate. The Ostwald–de Waele model (also known

Corresponding author. Tel.: +91 3222 283936; fax: +91 3222 255303. E-mail address: [email protected] (S. De). http://dx.doi.org/10.1016/j.fbp.2016.06.012 0960-3085/© 2016 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

food and bioproducts processing 1 0 0 ( 2 0 1 6 ) 72–84

as the power-law model) is used to describe this rheological behavior for most fruit juice solutions (Rao et al., 1984),

73

debris, cellulose, etc. (Rai et al., 2010; Sarkar et al., 2008; Mondal and Chhaya De, 2012a).

(1)

The present theoretical analysis is focused on developing mass transfer analysis of ultrafiltration of fruit juice considering nonNewtonian power law rheology in a hollow fiber module. Solution of the convective-diffusive species transport equation is performed under

where  is the shear stress, ˙ is the shear rate, K is the consistency index and n is the flow behavior index. There are several reports of carrot (Vandresen et al., 2009), blueberry (Nindo et al., 2005), mango

the framework of the boundary layer analysis. The model includes the developing mass transfer boundary layer over the gel layer, effects of concentration dependence on viscosity and non-Newtonian fluid rhe-

(Dak et al., 2007), pummel (Chin et al., 2009), pineapple (Dak et al., 2008),

ology. The present model quantifies the flux decline as well as the volume reduction factor (VRF) during batch mode of operation from the first principles by solving the overall material balance, overall solute

 = K˙

n

pomegranate (Yildiz et al., 2009), sugarcane juice (Filho et al., 2011), passion fruit (Jiraratananon and Chanachai, 1996), mandarin (Falguera et al., 2010), date (Gabsi et al., 2013), guava (Sánchez et al., 2009) and blood orange juice (Mizrahi and Berk, 1972), that confirm the power law model is the most appropriate in all cases. The knowledge of the fluid rheology is important for design and optimization of unit operations. A significant phenomenon leading to the decline in flux is concentration polarization (Porter, 2005; Sablani et al., 2001). A simple description of concentration polarization is obtained from a stagnant film model, used by Sherwood et al. (1965) to analyze reverse osmosis. Many researchers (Opong and Zydney, 1991; Zydney, 1997; Johnston and Deen, 1999) have used stagnant film model that considers a thin layer of solute adhered to the membrane surface, leading to one-dimensional problem in which the solute concentration depends only on distance from the membrane surface. To overcome this problem, a detailed numerical solution of the governing momentum and solute mass balance equation with pertinent boundary conditions may be used (Kleinstreuer and Paller, 1983; Bouchard et al., 1994; De and Bhattacharya, 1997). However, these studies do not incorporate the effects of fluid rheology and involves inherent complexities and rigorous computational requirements, rendering it unattractive and not useful for fruit juice clarification applications. Detailed studies related to two-dimensional concentration fields for laminar cross flow ultrafiltration in tubes or parallel-plate channels have been reported in literature (Shen and Probstein, 1977; Gill et al., 1988; Denisov, 1999; Bhattacharjee et al., 1999; Madireddi et al., 1999), spiral-wound membrane modules (Kozinski and Lightfoot, 1971). Field and Aimar (1993) have modified Leveque’s correlation for laminar flow in rectangular channel by using a viscosity correction factor. However, the effects of suction were not considered in their study which has been incorporated later by De and Bhattacharya (1997). Sherwood number relationship incorporating the effects of suction (in presence of a membrane) for laminar flow in rectangular, radial, and tubular geometries, have been formulated starting from first principles (De and Bhattacharya, 1997). However, that study includes the osmotic pressure controlled filtration only and the effect of developing mass transfer boundary layer. It has been shown that due to concentration polarization, the variation of the physical properties with concentration is significant in the performance of the ultrafiltration and subsequent development of the boundary layer, specially a gel layer controlling case (Gill et al., 1988; De and Bhattacharya, 1999; Bowen and Williams, 2001). During filtration of high molecular weight proteins, polymer, paint, clay, etc., a highly viscous solid-like layer is formed over the membrane surface above its solubility limit (commonly known as gel concentration) and it obeys the classical gel filtration theory. The primitive gel layer model is derived

balance and solute balance within the mass transfer boundary layer. A numerical solution of these balance equations leads to the flux decline and VRF profile. Therefore, the present model is a comprehensive one including various fundamental aspects of transport phenomena involved. The extensive analytical treatment makes the model easy to estimate the throughput in either of the operation modes by simple computational techniques. Some of the key and distinguishable features of the present modeling approach are summarized here:

1. The present model is completely predictive and does not require any knowledge of the experimental flux values to model the system, which is unlike the case with other fouling models. The steady state flux value is often provided as an input to other existing models. 2. The values of the physical properties and process constants are completely realistic and are not fitting parameters which are obtained by regression in other black box models. 3. The present model captures the essential underlying physics of the species transport in the concentration boundary layer and gel formation, which is not described well by many semi-empirical fouling models. 4. Most fouling models are based on the Hermia’s (1982) and Field et al. (1995) description of the constant pressure filtration, which does not take into account of the increase in feed concentration during batch mode of filtration and the effects of the channel narrowing due to gel formation. 5. The results of the model can be directly interpreted on the effect of the process parameters (transmembrane pressure drop, flow rate, etc.) and thus useful in understanding the interplay of the operating conditions and controlling such systems in practice. 6. Finally, many existing fouling models are not suitable in incorporating the fluid rheological effects on the overall mass transport phenomena.

Gel layer thickness is very difficult to measure experimentally during filtration. There have been very few literature studies on the in situ measurements of the gel layer during unstirred batch membrane filtration (Chen et al., 2004; Guell et al., 2009). In the present study, the experiments are carried out in crossflow mode in hollow fiber configuration. To the best of our knowledge, there is no analytical or instrumentation facility available till date to measure directly the thickness of gel layer inside the hollow fiber during filtration. There have been few literature reports in the past regarding estimation of the gel layer thickness. The classical gel layer theory used to pre-

from conventional film theory (Blatt et al., 1970), considering a uniform

dict the gel thickness was based on a single mass balance at the

mass transfer boundary layer thickness instead of developing boundary layer which is more fundamentally correct. Moreover, the viscosity

membrane interface and require the knowledge of the gel layer concentration and permeate flux together (Blatt et al., 1970; Belfort et al.,

of the solution is a strong function of the solute concentration and

1994; Porter, 1972). Thus, it is impossible to predict the permeate flux

it varies significantly within the mass transfer boundary layer, as the increase in solute concentration from bulk to gel layer concentration is not considered. Gel layer concentration is quite often three to seven

or the gel concentration from this theory, and are often used as input from the experiments to calculate the gel thickness. Also, this is based

times of bulk concentration. This variation of viscosity as a function

on the assumption of constant concentration boundary layer developed over the membrane surface. There has been attempt to include

of concentration was not included in the film model. Probstein et al. (1978) developed a two-dimensional model, developing mass transfer boundary layer under laminar flow condition in a rectangular channel,

the shear-induced-diffusion of the particulate suspension (Davis, 1992) and solving the transient 1D species transport equation (Karode, 2001)

overcoming one of the limitations of the constant thickness boundary layer. Clarification of fruit juice by ultrafiltration has been found to be gel controlling in many occasions due to presence of protein, cell

theories in this regard is the application of the Happel cell model (1965) based on particle flux conservation (Song and Elimelech, 1995). The gel is considered to be a concentrated particulate suspension of

as an improvement to the existing models. One of the prevalent

74

food and bioproducts processing 1 0 0 ( 2 0 1 6 ) 72–84

non-interacting uniform hard spheres. However, this is a 1D model and does not include the effects of the forced convection due to cross flow. Also, the time dependent growth of the gel layer is not accounted for.

(determined from Darcy’s equation) at the wall (De et al., 1997). Therefore, the y-component velocity becomes (refer to Fig. 1),

The present model is fundamentally based on the 2D concentration boundary layer analysis and considers the gel as a continuum domain. This highlights the applicability and strength of the model, as it can pre-

v = −vw

dict the gel layer thickness profile from the knowledge of the operating conditions and physical parameters, which was not possible otherwise.

Using x * = x/L; y * = y/R and C * = C/C0 , where, C0 is the initial feed concentration, L is the length of the module and R is the radius of the hollow fiber, Eq. (3) can be non-dimensionalized as,

The model was successfully applied for the clarification of blood orange juice according to the batch concentration configuration, by using polysulphone (PS), polyacrylonitrile (PAN) and polyetheretherketone (PEEK) ultrafiltration (UF) membranes. Since fruit juice is a complex mixture, some of physical properties are unknown and have never been reported prior to this study. These properties were estimated by minimizing the sum of square errors of the experimental and predicted values. The effects of the operational parameters on the output and the predictive ability of the developed model were also compared.

2.

Theoretical development

During ultrafiltration of fruit juice, high molecular weight solutes are transported toward the membrane wall, forming a deposition known as gel layer over the membrane wall, as shown in Fig. 1. During batch mode of filtration, the retentate stream is recycled back to the feed but the permeate is continuously taken out. This results in reduction of the feed volume and corresponding increase in feed concentration with time of operation. The following assumptions were considered in the model: 1. The diffusivity and viscosity does not depend on the concentration of the suspended particles. 2. There are no particle–wall and particle–particle interactions. 3. The gel concentration is below the solubility limit, so that the continuum equations are still valid. 4. The density of the feed and permeate are same, and the fluid is incompressible in nature. 5. The fluid flow is in the laminar zone and fully developed. The gel layer formed is considered to be of constant concentration in the layer. As a result, there exists a concentration boundary layer for a hollow fiber membrane system given as,

 ∂c  ∂

∂c ∂c ∂c +u +v = ∂t ∂x ∂r ∂r

D

∂r

(2)

where c is the concentration of the gel forming solute, t is the time of filtration, u is the axial velocity, v is the transverse velocity in the concentration boundary layer and D is the effective diffusivity of the gel forming solutes. Since the thickness of the concentration boundary layer is much less than the radius of the hollow fiber, the curvature effect of the membrane surface can be neglected. Thus, Eq. (2) is reduced to a planar coordinate with origin fixed at the membrane surface and defining, y = R − r, where y is the distance from the membrane surface. Thus, Eq. (1) can be written as, ∂c ∂c ∂c ∂2 c +u +v =D 2 ∂t ∂x ∂y ∂y

(3)

Since concentration boundary layer is extremely small, the transverse velocity is equal to the permeation velocity vw

∂C∗ + ∂



(4)

ud2 4DL



∂C∗ − ∂x∗

 v d  ∂C w 2D

∂y∗

=

∂2 C∗ ∂y∗2

(5)

where  = tD/d2 and d = 2R. Considering an order of magnitude analysis of Eq. (5) is carried out term wise. O(x*) is 1; order of y is same as that of thickness of concentration boundary layer, ı ≈ D/k = 10−11 /10−6 = 10−5 . Thus, O(y*) is 10−5 /10−3 = 10−2 . O(ud2 /DL) is 10−6 /(10−11 × 10−1 ) = 106 . O(vw d/D) = 10−6 × 10−3 /10−11 = 102 . Therefore, the order of the second, third and last term is at least 104 or higher. It may be noted that the first term has significant magnitude compared to the remaining terms up to a time of operation of 100 s (around 2 min). Beyond 100 s, it is reduced by order of magnitudes. Hence, comparing the full operation time in this experiment, the first term is small enough to be ignored. Therefore, we can take recourse to a quasi steady state analysis for further calculations. It may be noted that the fluid velocity inside the channel is order of magnitude higher than the permeation velocity, therefore, the fully developed velocity profile inside the channel remains undisturbed due to permeation. It has been widely reported that fruit juice mixture exhibits non-Newtonian rheology (Mizrahi and Berk, 1972; Romero et al., 1999; Falguera and Ibarz, 2010). The fully developed laminar velocity profile for a power law fluid is expressed as (Bird et al., 2007),



u = u0

(3n + 1) 1− (n + 1)



= u0

 r n+1/n  R



(3n + 1) y 1− 1− R (n + 1)

n+1/n  (6)

where u0 is the maximum fluid velocity (centerline velocity). Since, the thickness of the concentration boundary layer is very small, i.e., y/R  1, the velocity profile can be approximated as (expanding the polynomial powers on the right hand side in Eq. (6), and thus ignoring higher order terms of (y/R)2 ),



u = u0 3 +

1 n

y

(7)

R

Substituting the velocity profile into Eq. (5) and ignoring the first term as explained, the following equation is obtained, 1 4



3+

1 n

 u d2 0 DL

y∗

∂C∗ vw d ∂C ∂2 C∗ − = ∂x∗ 2D ∂y∗ ∂y∗2

(8)

The concentration profile can be approximated as a quadratic polynomial (De et al., 1997; Mondal et al., 2011b; Mondal and Chhaya De, 2012a, 2012b), C∗ =

C = a1 + a2 y ∗ +a3 y∗2 C0

(9)

75

food and bioproducts processing 1 0 0 ( 2 0 1 6 ) 72–84

where a1 , a2 and a3 are the coefficients evaluated from the boundary conditions C∗ = C∗g

at y∗ = 0,

(10a)

 ∗

at y∗ = ı∗,

C∗ = C∗b

(10b)

at y∗ = ı∗,

∂C∗ =0 ∂y∗

(10c)

where ı* = ı/R is the non-dimensional thickness of the concentration boundary layer, C∗g = Cg /C0 is the non-dimensional gel layer concentration and C∗b = Cb /C0 is the non-dimensional bulk concentration. Using the boundary conditions (Eqs. (10a)–(10c)), the constants a1 , a2 and a3 are evaluated and the concentration profile in Eq. (9) is rewritten as, C∗ = C∗g − 2(C∗g − C∗b )

where Pew = vw d/D is the wall Peclet number. ∂C */∂y * |y*=0 is evaluated from Eqs. (11a)–(11c) and is substituted in the above equation to obtain

 y∗ 

 y∗ 2

+ (C∗g − C∗b )

Pew ı = 2

1 48



2.1.

∂C∗ = 2(C∗g − C∗b ) ∂y∗





y∗2 y∗ − ∗3 ı∗2 ı

 y∗ ı∗2

1 − ∗ ı

dı∗ dx∗

(11a)

 (11b)

∂C∗ 1 = 2(C∗g − C∗b ) ∗2 ∂y∗ ı

(11c)

These partial derivatives are inserted back in Eq. (8) and after simplification the following equation is obtained, 1 4



1 3+ n

 u d2  y∗2 0 ı∗2

DL



y∗3 − ∗3 ı

Pew dı∗ − dx∗ 2

 y∗ ı∗2

−

1 ı∗



=

1 ı∗2

1 n

3+

4 −

3+

n

Pew 2

DL



ı∗

dx∗

 y∗ ı∗2

0

−

ı∗



ı∗2

0

 1 ı∗

y∗2

dy∗ =

1 ı∗2

−

y∗3



ı∗3





3+

1 n

 u d2 0 DL

ı∗2

 dı∗  dx∗

+

dy ∗

=0

x∗1/3

(19)

k(Cg − Cb ) = − D



∂C ∂y y=0

(20)

Non-dimensionalizing the above equation and substituting ∂C */∂y * |y*=0 from Eqs. (11a)–(11c) leads to the following expression of Sherwood number, Sh =

4 ı∗

(21)

Sh(x∗) =

  4 9

3+

1 n

 u0 d2 C∗ 1/3 g

DLC∗b

x∗−1/3

(22)

The length averaged Sherwood number thus, becomes



1



1 Sh(x∗)dx∗ = 1.145 3 + n

1/3 

d Re · Sc · L

1/3  C∗ 1/3 g

C∗b (23)

dy∗

(13)

0

Pew ı∗ =1 4

(14)

(15)

The non-dimensional version of the above equation is,

y∗=0

1/3

The definition of the mass transfer coefficient (k) can be written as (Cussler, 1997),

where Re is the Reynolds number and Sc is the Schmidt number. It can be noted that for Newtonian fluid (n = 1), the leading coefficient of the expression of length average Sherwood number becomes 1.816 (Mondal et al., 2011b). Since, the gel layer concentration is several order of magnitude higher than the bulk concentration it is obvious that the viscosity variation within concentration boundary layer is significant. The viscosity effects are included in Sherwood number expression following the derivation as elaborated in another study (Mondal et al., 2011b), which was developed for a tubular geometry. Therefore, the final expression of Sherwood number is presented below:

 Sh = 1.145 3 +

∂C∗ Pew C∗g + ∂y∗

(18)

C∗g

ı∗



∂C =0 ∂y y=0

dx∗

C∗b

Estimation of mass transfer co-efficient

0

Now considering a steady-state mass balance over the membrane surface (y = 0), the following equation is obtained. vw Cg + D

=

(3 + (1/n))u0 d2 C∗g

Sh =

On solving the above integral the following equation is arrived 1 48

 dı∗ 

Substituting the profile of ı* from Eq. (19) in Eq. (21), the expression of Sherwood number becomes,

where Pew = vw d/D is the wall Peclet number. Taking the zeroth moment of Eq. (12) by multiplying both sides by dy* and integrating across the boundary layer thickness from 0 to ı*, the following equation is obtained,

   1 u0 d2 dı∗

DL

ı∗2

144DLC∗b

(12)

 1

 u d2 0



Now the terms: ∂C*/∂x *, ∂C*/∂y * and ∂2 C */∂y * 2 in Eq. (8) are evaluated from Eqs. (11a)–(11c) as, ∂C∗ = 2(C∗g − C∗b ) ∂x∗

(17)

C∗g

Integration of the above equation leads to the profile of concentration boundary layer thickness with x* as,

ı∗ =

ı∗



Replacing this value of Pew ı∗ in Eq. (17), results to the following governing equation of concentration boundary layer thickness,

(11)

ı∗

C∗g − C∗b

(16)

1 n

1/3  Re · Sc ·

d L

1/3 

∗ (−2/3)˛C0 (C∗ g −Cb )

e

0.14  C∗ 1/3 g

C∗b

(24)

Combining Eqs. (17) and (22), the length averaged permeate flux becomes,

76

food and bioproducts processing 1 0 0 ( 2 0 1 6 ) 72–84

Fig. 1 – Schematic of the transport process inside the hollow fibers.



Pew = 1.145 3 +

 ×

C∗g

1 n

1/3 

1/3

 −

C∗b

Re · Sc C∗g



 × ln

C∗g

1 n

1/3 



C∗b

1/3 

(−2/3)˛C0 (C∗g −C∗ )

e

0.14

Now, following the material balance for the gel-forming component in the concentration boundary layer results in the following equation (Mondal and Chhaya De, 2012b):

b

−2/3  (25)

C∗b

For C∗g /C∗b  e3 , [(C∗g /C∗b ) ln(C∗g /C∗b ), thus Pew = 1.145 3 +

d L

for 0 < y < ı, 1/3

Re · Sc

− (C∗g /C∗b )

d L

1/3 

−2/3

where g and εg are the gel layer density and porosity, respectively. The pertinent boundary conditions are,

0.14

b

(26)

Considering an overall material balance, the following equation is obtained, d ( V) = −vw Am p dt f

(27)

where f and p are densities in feed and permeate streams; V is the feed volume and Am is the effective membrane area. Assuming f = p (density is a weak function of concentration and both feed and permeate are diluted solutions) the above equation is modified as, dV = −vw Am dt

(28)

Using overall species balance of gel forming component, the following equation is obtained, d (C V) = −vw Am Cp dt b

(29)

Since the concentration of the gel forming material in the permeate is zero (Cp = 0) (Cheryan, 1998), the above equation reduces to a simple algebraic equation Cb V = C0 V0

dH dC1 = vw C1 − D dt dy (31)

], is reduced to

(−2/3)˛C0 (C∗g −C∗ )

e

j1 = mass = g (1 − εg )

(30)

with initial boundary condition as C = C0 and V = V0 at t = 0

C1 = Cb (t) at y = 0

(32a)

C1 = Cg

(32b)

at y = ı

The solution of Eqs. (32a) and (32b) using the above stated boundary conditions represents the variation of the gel layer thickness (H) with time (Mondal et al., 2011b), g (1 − εg )

Cg − Cb exp(vw /k) dH = vw dt 1 − exp(vw /k)

(33)

where k is the mass transfer coefficient defined as D/ı. In this case, the expression of mass transfer coefficient is different from Eq. (20). This is because the boundary condition of the concentration profile within concentration boundary layer at the edge is no longer initial feed concentration (C0 ). It becomes bulk concentration that is a function of time, Cb (t). The expression of length averaged permeate flux, is already presented in Eq. (26). The flux vw can be expressed using the phenomenological equation, vw =

P (Rm + Rg )

(34)

where Rm is the hydraulic membrane resistance determined experimentally and Rg is the gel layer resistance in batch concentration mode. It may be added here that additional resistance can be present due to the pore blocking phenomena. Blocking models are typically characterized by dJ/dt =− k˛ J3−n where n = 2: represents complete pore blocking, n = 1.5 for standard blocking and n = 1 for intermediate pore

77

food and bioproducts processing 1 0 0 ( 2 0 1 6 ) 72–84

blocking. However, in case of gel formation, external cross flow restricts arrests the growth and is therefore represented by the modified equation (Field et al., 1995), dJ/dt =− kc (J − Jss )J2 . The blocking mechanisms are generally present in the initial period of filtration (the region up to which the theoretical prediction is not accurate with experiments) before the onset of the gel formation. With the presence of large concentration of suspended materials (e.g., fruit juice, wastewater, etc.), gel formation is more prevalent and starts quickly. The corresponding resistance due to the individual pore blocking effects can be quantified from the above equation and are represented by additional resistance components in Eq. (34). However, it may be noted that with higher flux decline ratios and low porous membranes (ultrafiltration instead of microfiltration), the gel formation is more dominant and favorable filtration mechanism compared to complete (Mondal and De, 2009) or intermediate blocking (Mondal and De, 2010). The gel layer resistance and its characteristics are described with the platform of traditional gel filtration theory (Bhattacharjee et al., 1996). So, Rg is expressed as, Rg = ˇ(1 − εg )g H

(35)

where ˇ is the specific gel resistance. Since εg , g are all constants during the experiment, the product ˇ(1 − εg )g is clubbed together into a single parameter and is treated as another constant ( ) during the course of the simulation. Thus, Rg = H

(36)

Combining Eqs. (33) and (34), the governing equation of gel layer thickness becomes (Mondal et al., 2011b), g (1 − εg )

Cg − Cb exp(P/(k (Rm + Rg ))) dH = vw dt 1 − exp(P/(k (Rm + Rg )))

(37)

Eq. (37) is a first order ordinary differential equation of H(t) which gives the gel layer thickness (H) when solved numerically in conjunction with Eqs. (24), (28), (30), (34), (36) and (39), using the initial condition H = 0 at t = 0. It may be noted that as time of operation proceeds, the effective channel height narrows by deposition of gel layer and it is quantified as, d(t) = d(t = 0) − 2 × H(t)

(38)

Consequently, the cross flow velocity u0 (t) inside the hollow fiber as, u(t) =

4Q 2

2

d(t = 0) [1 − (d(t)/(d(t = 0))) ]

(39)

The above expressions of channel height and cross flow velocity within the hollow fibers have been utilized to evaluate the non-dimensional permeate flux in Eq. (34). The governing equation of volume and bulk concentration at any time point is given by Eqs. (28) and (30), respectively. Thus, Eqs. (24), (28), (30), (34), (36), (37) and (39) present a case of coupled equations which is solved numerically. The parameters , D, Cg and ˛ are determined by unconstrained optimization of the experimental flux profiles with model results for cross flow ultrafiltration of the blood orange juice in batch mode under various operating conditions. This is done by minimizing the sum of the square of the

relative error between the experimental and simulated data at the same time point using an interior point optimization algorithm (Byrd et al., 2000). The optimality of the optimization constraint takes into account the Karush–Kuhn–Tucker condition, that the gradient must be zero at a minimum (Coleman and Li, 1996). The objective function, defined as the sum of square of error (Err) between the experimental and predicted flux values for all operating conditions and time points is given as,

Err =

nexp N

i,j

i,j

vw,cal − vw,exp

2

i,j

i=1 j=1

(40)

vw,exp

where i is number of experiments nexp and j is number of time points N in the ith experiment.

3.

Materials and methods

3.1.

Juice preparation

Blood orange juice was prepared from fresh fruits of Tarocco variety cultivated in the area of Corigliano Calabro (Cosenza, Italy). Orange juice was obtained by cutting crosswise and squeezing, using a household electric extractor, about 20 kg of oranges immediately after their harvest and after a preliminary operation of washing and drying. The squeezed juice was treated with 1% (w/w) of pectolytic enzyme (Pectinex Ultra SPL, Sigma–Aldrich, Milan) and then incubated for 4 h at room temperature in plastic tanks. The juice was finally filtered through a 200 ␮m cotton fabric filter. This method gave an average juice yield of 54.6% (w/w). The depectinized juice was characterized by a pH of 3.5, a total soluble solids content of about 10.2◦ Brix, a suspended solid concentration (C0 ) of 10.0% (w/w) and an electrical conductivity of 7410 ␮S/cm. It was stored at −20 ◦ C and defrosted to room temperature before the UF treatment.

3.2.

UF experimental set-up

UF experiments were performed by using a bench scale cross flow membrane system. The plant consists of a feed tank with a capacity of 3 L, a magnetic drive gear pump (Micropump Mod. GC-M25 JF5 SA), a hollow fiber membrane module with an effective membrane surface area of 0.16 m2 and a permeate tank. Two manometers before and after the membrane module were used to measure the inlet and the outlet pressure and, consequently, the transmembrane pressure. The feed flow rate was measured by a digital flowmeter, while the feed temperature was measured by using a digital thermometer placed inside the feed tank. Transmembrane pressure (TMP) values were regulated by a pressure control valve, on the retentate side, and by regulating the velocity of the gear pump. The feed temperature was adjusted by circulating water in a cooling coil. A schematic representation of the UF plant is depicted in Fig. 2. Three UF membrane modules with different membrane material (polysulphone and polyacrylonitrile) and molecular weight cut-off (MWCO) were used in this study. The module length is 330 mm. Their characteristics are reported in Table 1. Experimental runs were performed in selected operating conditions according to the batch concentration configuration, in which the retentate is continuously recycled back to the feed tank while the permeate stream is collected separately. In all experiments the temperature of the juice was

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food and bioproducts processing 1 0 0 ( 2 0 1 6 ) 72–84

11

10

1

4

4

2

6

5

3

7

8 9 Fig. 2 – Schematic of the experimental setup (1 – feed tank; 2 – cooling coil; 3 – feed pump; 4 – manometers; 5 – hollow fiber membrane module; 6,7 – regulating valves; 8 – permeate tank; 9 – digital balance; 10 – digital flowmeter; 11 – thermometer). Table 1 – Properties of the UF membranes and modules. Type

UF HF membrane module DCQ II-006C-PS50

Membrane material Operating temperature (◦ C) Operating pH Internal diameter of fibers (mm) Membrane surface area (m2 ) Total number of fibers MWCO (kDa) Permeability (L/m2 h bar)

DCQ II-006C-PS100

Polysulphone 5–45 2–13 2.1 0.16 103 50 91.0

kept at an average value of 20 ± 1 ◦ C. Experiments were performed at different operating TMP (in the range 0.3–1.2 bar) in fixed conditions of temperature and flow rate (20 ± 1 ◦ C and 100 L/h, respectively) and at different feed flow rate (from 20 to 140 L/h) in fixed conditions of temperature and TMP (20 ± 1 ◦ C and 0.6 bar, respectively). Permeate fluxes were measured at regular intervals by using a digital balance placed under the permeate tank. All the experiments were performed in triplicate and the mean data is presented, within the confidence interval of ±5%.

Polysulphone 5–45 2–13 2.1 0.16 103 100 192.0

Polyacrylonitrile 5–45 2–10 2.1 0.16 103 50 221.0

heated and refrigerated Circulator, Julabo F32 (Houston, USA, error ±0.1 ◦ C). The total phenolic content (TPC) was estimated colorimetrically by using the Folin–Ciocalteu method (Singleton and Rossi, 1965). Results were expressed as mg/L gallic acid (mg GAE/L). The total anthocyanin content (TAC) was assessed by using an HPLC system (Hitachi D-7000 System) equipped with a pump, a UV–vis detector, and a data acquisition system as reported elsewhere (Conidi et al., 2015).

4. 3.3.

DCQ II-006C-PAN50

Results and discussion

Physicochemical analysis

The total soluble solid (TSS) content of the juice samples was measured by an Abbe digital refractometer Bellingham + Stanley 60/DR (Bellingham and Stanley Ltd., Kent, UK) and expressed as Brix. The suspended solids content was determined in relation to the total juice (%, w/w) by centrifuging, at 2000 rpm for 20 min, 45 mL of a pre-weighted sample; the weight of settled solids was determined after removing the supernatant. pH was measured by an Orion Expandable ion analyzer EA 920 pH meter (Allometrics, Inc., Baton Rouge, LA, USA) with automatic temperature compensation. Rheological measurements were performed by means of a controlled strain Rheometer ARES-RFS III (TA Instruments, USA) equipped with concentric cylinder geometry (inner radius 17 mm, gap 1 mm). An evaporation trap was used for avoiding water loss. The temperature was controlled by a

The pH of the juice (3.5) was not affected by the UF process. All clarified samples resulted free of suspended solids. The conductivity of the clarified juice was of about 5550 ␮S/cm. As reported in Table 2, the TSS content of permeates decreased slightly with UF. Most of phenolic compounds and anthocyanins were recovered in the clarified juice. In particular, 50 kDa membranes showed a higher retention of phenolic compounds (about 23%) when compared with the PS 100 kDa membrane (17.7%). The rheology of the blood orange juice was described using the power law model, as presented in Fig. 3. The values of the consistency index (K) and flow behavior index (n) were found to be 1.766 Pa s2−n and 0.93. The gel forming solute (C as defined in the model) is the suspended solid content. The feed suspended solid concentration (C0 ) was found to be 10% (w/w). The optimized values of the parameters (intrinsic

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food and bioproducts processing 1 0 0 ( 2 0 1 6 ) 72–84

Table 2 – Analyses of total soluble solids (TSS), total phenolic content (TPC) and total anthocyanin content (TAC) in samples of blood orange juice clarified with different UF membranes. Sample

TSS (◦ Brix)

TPC (mg GAE/L)

TAC (mg/L)

DCQ II-006C-PS100

Feed Permeate

10.0 ± 0.2 9.8 ± 0.2

835.42 ± 0.43 687.08 ± 0.22

7.33 ± 0.14 6.79 ± 0.13

DCQ II-006C-PS50

Feed Permeate

10.2 ± 0.2 10.0 ± 0.2

920.00 ± 0.47 705.00 ± 0.34

6.83 ± 0.13 6.20 ± 0.12

DCQ II-006C-PAN50

Feed Permeate

10.4 ± 0.2 10.2 ± 0.2

966.25 ± 0.27 738.33 ± 0.19

8.52 ± 0.17 8.03 ± 0.16

UF HF membrane module

Permeate flux (L/m2.h)

(Pa.s)

1.6 1.5 Equation

1.4

= K*

Adj. R-Square

n-1--

0.98965 Value

-- K

1.3

-- n-1

1.2

21.5 L/h 67.9 L/h 100 L/h 139.5 L/h

60

1.7

1

Standard Error

1.76658

0.00911

-0.07068

0.00256

10

. (s-1)

(a)

50

PS 50k

40 30 20 10

100

0 0

Fig. 3 – Variation of viscosity with shear rate for blood orange juice.

40

60 80 100 Time (min)

Permeate flux (L/m2.h)

60 50

120

140

23.1 L/h 65.6 L/h 131.6 L/h

(b)

PAN 50k

40 30 20 10 0 0

20

40

60

80

100

120

140

Time (min)

60 Permeate flux (L/m2.h)

property of the solution) D, Cg /C0 and ˛ were (4.9 ± 0.1) × 10−11 m2 /s, 6.1 ± 0.08 and (5 ± 0.2) × 10−4 m3 /kg, respectively. However, the specific cake resistance (clubbed parameter ) is dependent on the solute-membrane system. It was calculated as [5.65 ± 0.15 9.50 ± 0.29 6.57 ± 0.08] × 10−11 m−2 for [PS-50 PAN-50 PS-100] membranes. The variation of the permeate flux with cross flow velocity for all three types of membrane is presented in Fig. 4. As observed from this figure, the permeate flux increased with cross flow rate. This is because with cross flow velocity, the forced convection increases arresting the growth of the concentration polarization layer. The deviation of the predicted result with actual experimental data is less than ±7% for the case of PS50 kDa and PS100 kDa membranes, and it is ±12% for PAN50 kDa membranes, beyond 20 min of filtration. Toward the start of the filtration, the matching of the experimental results with model was not good, as there may be errors involved with the experimental results along with the occurrence. In the beginning few moments, other blocking mechanisms are also prominent causing the inaccuracy of the present model in its predictions. Moreover, at the start of the experiment, the pump takes some time to get the flow rate to be steady as it adds perturbed unsteady loads to the system. Also, it may be noted that the temporal term in Eq. (5) is ignored as the analysis is predicted over longer time scales. However, this term is significant for the first couple of minutes and thus partially responsible to the discrepancy of the model prediction. It may be observed here that with different membrane modules having different permeabilities, the permeate flux decline was almost within similar range for all the membranes. This suggests that even the membranes have high permeability, once the gel resistance becomes dominant, the membrane permeability have little significance over the throughput. As the operation is in batch mode, steady state was never attained, since the permeate is continuously withdrawn from the system.

20

24.8 L/h 63.1 L/h 99.2 L/h 138.9 L/h

(c)

PS 100k

50 40 30 20 10 0

0

20

40

60 80 100 Time (min)

120

140

Fig. 4 – Permeate flux profiles at a constant TMP of 0.6 bar (a) PS 50 kDa MWCO; (b) PAN 50 kDa MWCO and (c) PS 100 kDa MWCO. Permeate flux profiles at a constant TMP of 0.6 bar (a) PS 50 kDa MWCO; (b) PAN 50 kDa MWCO and (c) PS 100 kDa MWCO. (For interpretation of the references to color in text, the reader is referred to the web version of the article.) The effect of the transmembrane pressure (TMP) on the filtration output, is presented in Fig. 5. The permeate flux increased with TMP and it was almost directly proportional to the magnitude of the TMP, as evident from Eq. (34). Similar to the case of Fig. 4, the model results matched with

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3.0

(a)

50

2.8

0.3 bar 0.6 bar 0.9 bar 1.2 bar

PS 50k

40

21.5 L/h 67.9 L/h 100 L/h 139.5 L/h

2.6 2.4 VRF (V0/V)

Permeate flux (L/m2.h)

60

30 20

2.2 2.0 1.8

PS 50k

(a)

1.6 1.4

10 0

1.2 1.0

0

20

40

60

80

100

120

0

20

40

Time (min)

0.3 bar 0.6 bar 0.9 bar 1.2 bar

(b)

PAN 50k

50 40 30

3.3

100

120

140

21.5 L/h 65.6 L/h 131.6 L/h

3.0 2.7

20

2.4

PAN 50k

(b)

2.1 1.8 1.5

10

1.2

0

0.9

20

40

60 80 Time (min)

60

120

(c)

40

0

20

40

60

80

100

120

140

Time (min)

0.3 bar 0.6 bar 0.9 bar 1.2 bar

PS 100k

50

100

30 20

3.0 24.8 63.1 99.2 L/h

2.8 2.6 2.4 VRF (V0/V)

0

Permeate flux (L/m2.h)

80

Time (min)

VRF (V0/V)

Permeate flux (L/m2.h)

60

60

2.2

PS 100k

(c)

2.0 1.8 1.6 1.4

10

1.2

0

1.0

0

20

40

60 80 Time (min)

100

120

0

20

40

60

80

100

120

140

Time (min) Fig. 5 – Permeate flux profiles at a constant cross flow rate of 100 L/h (a) PS 50 kDa MWCO; (b) PAN 50 kDa MWCO and (c) PS 100 kDa MWCO. (For interpretation of the references to color in text, the reader is referred to the web version of the article.)

Fig. 6 – VRF profiles at a constant TMP of 0.6 bar (a) PS 50 kDa MWCO; (b) PAN 50 kDa MWCO and (c) PS 100 kDa MWCO. (For interpretation of the references to color in text, the reader is referred to the web version of the article.)

experimental data considerably well beyond 15 min of the start of the filtration. The deviation between the model prediction and experimental data was within ±8%. However, for the PAN 50 kDa membrane, data were not well fitted for lower TMP (0.3 bar) and the matching was more than ±15% beyond 1.5 h. The volume reduction factor (VRF) during the batch filtration mode is represented in Figs. 6 and 7. It is evident from the figures that the theoretical prediction was within ±10% of the experimental data. The strength in model results is exhibited by extrapolating the VRF values beyond the actual filtration time. In fact, this is useful in understanding the long term performance output of the system. It may be observed from the figures that the nature of the VRF profile is dependent on the type of membrane used. The permeate flux increased with cross flow rate: consequently the feed (or retentate) volume

also decreased leading to higher VRF values. At a constant TMP and at the lowest flow rate (see Fig. 6a–c), the VRF was higher for the PAN membrane suggesting that the permeate flux is comparable to that of PS membranes. As shown in Fig. 9, the gel layer resistance was higher for the PAN membrane (more fouling resistant) compared to that of PS membranes; therefore, the increase in flux for the PAN membrane can be attributed to its high permeability as reported in Table 1. At a constant cross flow rate, VRF increased with TMP due to the proportional flux enhancement. As observed from Fig. 7, the effect of pressure was not prominent for the PS 50 kDa membrane, at least for 1.5 h. For the PAN 50 kDa membrane, the effect of TMP was prominent at higher pressure (1.2 bar), while an opposite effect was observed for the PS 100 kDa membrane. For a particular pressure (1.2 bar), the VRF was the highest

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food and bioproducts processing 1 0 0 ( 2 0 1 6 ) 72–84

3.0 2.8

210

VRF (V0/V)

2.6 2.4 2.2 2.0 1.8

Gel layer thickness ( m)

0.3 bar 0.6 bar 0.9 bar 1.2 bar PS 50k

(a)

1.6 1.4 1.2

(a)

21.5 L/h, 0.6 bar 100 L/h, 0.6 bar 100 L/h, 1.2 bar

180 150

PS 50k

120 90 60 30

1.0 0

20

40

60

80

100

120

0

140

0

20

40

Time (min)

60 80 Time (min)

100

120

100

120

100

120

3.0

2.4 2.2 2.0

Gel layer thickness ( m)

2.6 VRF (V0/V)

270

0.3 bar 0.6 bar 0.9 bar 1.2 bar

2.8

PAN 50k

(b)

1.8 1.6 1.4 1.2

23.1 L/h, 0.6 bar 108.5 L/h, 0.6 bar 108.5 L/h, 1.2 bar

240 210 180 150

(b)50k PAN

120 90 60 30

1.0 0

20

40

60

80

100

120

0

140

0

20

40

3.0 2.8 2.6 2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0

0.3 bar 0.6 bar 0.9 bar 1.2 bar PS 100k

(c)

0

20

40

60

80

100

120

140

Time (min)

60 80 Time (min)

24.8 L/h, 0.6 bar 99.2 L/h, 0.6 bar 99.2 L/h, 1.2 bar

150 Gel layer thickness ( m)

VRF (V0/V)

Time (min)

120

(c)

PS 100k 90 60 30 0

0

20

40

60

80

Time (min)

Fig. 7 – VRF profiles at a constant cross flow rate of 100 L/h (a) PS 50 kDa MWCO; (b) PAN 50 kDa MWCO and (c) PS 100 kDa MWCO. (For interpretation of the references to color in text, the reader is referred to the web version of the article.)

Fig. 8 – Gel layer thickness profiles at different operating conditions for (a) PS 50 kDa MWCO; (b) PAN 50 kDa MWCO and (c) PS 100 kDa MWCO. (For interpretation of the references to color in text, the reader is referred to the web version of the article.)

for the PAN 50 kDa membrane, followed by PS 100 kDa and PS 50 kDa membranes. The thickness of the gel layer with time of filtration is presented in Fig. 8. The effect of cross flow rate can be analyzed comparing the red and black curves (Fig. 8a). Due to the higher cross flow rate, the growth of the mass transfer boundary layer is minimized: as a result the gel thickness decreased with higher flow rate. On the other hand, the effect of the TMP can be understood comparing pink and blue curves. The solute convection toward the membrane surface increases with the operating TMP, leading to more solute deposition; as a result the gel resistance and the gel layer thickness increased. For the PAN 50 kDa membrane, the effect of flow rate and TMP was not considerable for quantification up to 80 min, which was

unlike the case of PS 50 kDa or PS 100 kDa. The maximum gel thickness is around 150 ␮m, which is about 30% of the channel diameter. In the case of PAN 50 kDa membrane, the thickness was much higher and almost 40% of the channel diameter. The relative ratio of the gel resistance (Rg /Rm ) follows similar trend as compared to the gel profiles, as shown in Fig. 9. It is may be noted that the PAN 50 kDa membrane exhibited maximum fouling compared to PS membranes. The chemical structure of the membrane material and its morphology is responsible for the increased fouling of PAN membranes. It was also observed that at the beginning of the filtration, for less than 10 min, the gel layer resistance was low (Rg /Rm < 10), which suggests that gel layer formation is not dominant and that the presence of other blocking mechanisms is responsible

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25

21.5 L/h, 0.6 bar 100 L/h, 0.6 bar 100 L/h, 1.2 bar

Rg/Rm

20

PS (a)50k

15 10 5 0

0

20

120

40

60 80 Time (min)

100

120

23.1 L/h, 0.6 bar 108.5 L/h, 0.6 bar 108.5 L/h, 1.2 bar

100

Rg/Rm

80 60 40 20 0

PAN 50k

(b)

0

20

50 Rg/Rm

40

60 80 Time (min)

24.8 L/h, 0.6 bar 99.2 L/h, 0.6 bar 99.2 L/h, 1.2 bar

60

100

References 120

PS 100k

(c)

40 30 20 10 0

0

20

40

60

80

100

120

Time (min)

Fig. 9 – Profiles of the relative gel layer resistance (Rg /Rm ) at different operating conditions for (a) PS 50 kDa MWCO; (b) PAN 50 kDa MWCO and (c) PS 100 kDa MWCO. (For interpretation of the references to color in text, the reader is referred to the web version of the article.) for flux decline. This explains why in the initial few minutes of the filtration process experimental data are not well fitted by the prediction model.

5.

However, the total gel resistance resulted much higher for the PAN membrane (almost 4–5 times for similar operating parameters) in comparison with PS membranes. The increasing in the cross flow velocity produced a reduction of the growth of the gel layer (of about 50% when the flow rate is enhanced by 5 folds) for PS membranes after 1 h of filtration. For PAN membrane, the cross flow rate did not have a significant effect on the growth of the gel layer. The sharp decline in the permeate flux at the beginning of the filtration (within first 20 min), suggests that dynamics of cake formation are really fast and the time after which cake resistance is dominant can be estimated (time after which Rg /Rm > 10). A further improvement on the predictive ability of the present model can be achieved by including the viscoelastic behavior in the fluid rheology (as many fruit juices exhibit such rheological properties) and the concentration dependence on mixture diffusivity of the polydisperse solution. There is also a possibility to include particle–wall interactions due to adsorption and sticking of solute particles on the membrane surface (Bhattacharjee et al., 1999, 2000).

Conclusions

A mathematical model has been developed to describe the physical mass transport phenomena and quantify the various extents of fouling using different membrane materials and operating conditions in the clarification of blood orange juice. The model results have been validated in close agreement with the experimental data. The generalized theory formulated in this work will be useful in predicting and analyzing the flux profile for ultra- or microfiltration of various fruit juice mixtures using different polymeric membranes. The results have shown that PS membranes are more prone to fouling at higher pressures, compared to PAN membrane.

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