Limiting Flux and Critical Transmembrane Pressure Determination

Article pubs.acs.org/IECR

Limiting Flux and Critical Transmembrane Pressure Determination Using an Exponential Model: The Effect of Concentration Factor, Temperature, and Cross-Flow Velocity during Casein Micelle Concentration by Microfiltration Carolina L. Astudillo-Castro* Escuela de Alimentos, Pontificia Universidad Católica de Valparaíso, Waddington 716, Valparaíso, Chile ABSTRACT: During microfiltration, limiting (JL) and critical flux (JC) are essential. Using these concepts, the operational zones, have been established for flux (J) versus transmembrane pressure (ΔPT). However, the resistance model cannot be used for an accurate description of these operational zones. The aim of this work was to evaluate the application of an equation for process parameters’ determination during skim milk microfiltration. The exponential model, J = JL(1 − exp(−ΔPT/(ΔPT)C), allowed a direct determination of JL and the critical ΔPT ((ΔPT)C) and allowed the calculation of JC and the limiting ΔPT ((ΔPT)L). The effect of temperature, concentration factor, and cross-flow velocity over JL and (ΔPT)C were evaluated. For JL and (ΔPT)C, a good fitting was obtained (Radj2 = 98.12%; Radj2 = 97.83%, respectively). These results allow to predict the limiting and critical points for given values of the concentration factor, cross-flow velocity and temperature. Moreover, determination of the operational zones could be established. Zone 1, for low ΔPT values, only the concentration polarization phenomenon exists, and it is known as a subcritical zone, where the permeate flux is lower than the critical flux (JC). Zone 2 is where cake formation and consolidation occur, as well as pore blocking or protein adsorption onto the membrane. Finally, Zone 3 is where the cake compacts, which is an undesirable phenomenon, because this irreversible fouling type is difficult to remove even using chemical membrane cleaning. The operational curves show two important points: the critical point and the limiting point. The critical point [(ΔPT)C, JC] is where the linear relationship with the transmembrane pressure is lost,16 and the limiting point [(ΔPT)L, JL] is where the maximum flux value is obtained under some process condition sets;17 it cannot be increased by varying ΔPT. Several studies for the prediction of the maximum limiting flux (JL) have been conducted using back-transport models.18−20 The limiting flux depends on the shear stress applied, the feeding stream properties and the module geometry. The critical flux theory (JC) was introduced for the first time by Field et al.,16 and it describes the flux for which an irreversible fouling does not form on the membrane. This fouling type is a consequence of the dispersed phase transition, from the concentration polarization to a condensed phase, cake formation, or pore blocking.18,21 If the system is operated under a J < JC condition, the possibility of generating irreversible fouling of the membrane can be eliminated or at least reduced.22 When a module is operated under subcritical conditions, a continuous process can persist for several hours without a

1. INTRODUCTION During the last decades, the industry has shown great interest in membrane separation technology, for example, in the dairy industry with the use of microfiltration (MF) for macromolecules from milk and whey concentration and separation1 and in water treatment processes due to its high rate of rejection of particles and bacteria.2 Milk as a process fluid is interesting in membrane processing. Its multicomponent and complex nature with high concentration of several components with different particle sizes, such as microorganisms, fat, casein micelles, soluble proteins, lactose, makes its fractioning a challenge.3 MF with ceramic membranes has been used for fat separation,4 casein concentration,3,5,6 and microorganism removal from milk7−12 and sweet whey,13 because it is a milder technique in comparison to thermal processing, such as pasteurization or evaporative concentration, which both cause protein denaturation.14 Nevertheless, fouling of the membrane, which can be reversible or irreversible in nature,1,14 has been the main limiting factor for enhancing the productivity of the membrane processes. Short-time reversible fouling, that is, pore blocking or cake formation,3 occurs by the deposition of milk protein and colloids, and concentration polarization in nanofiltration and reverse osmosis membranes.14 Reversible fouling can be removed through effective membrane cleaning, but there are some costs involved related to labor, energy, and the use of chemicals and water. In the case of milk microfiltration for casein concentration and native whey production, fouling is mainly produced by milk proteins such as casein micelles and serum proteins. For operational curves of permeate flux (J) versus transmembrane pressure (ΔPT), three areas or zones related with membrane fouling have been described.3,15 Each has a different flux behavior as a function of the transmembrane pressure. In © 2014 American Chemical Society

Received: Revised: Accepted: Published: 414

August 21, 2014 December 3, 2014 December 4, 2014 December 4, 2014 dx.doi.org/10.1021/ie5033292 | Ind. Eng. Chem. Res. 2015, 54, 414−425

Industrial & Engineering Chemistry Research

Article

zone be determined? And, for each condition, what is the flux value? In this context, the aim of this work was to propose the use of an analytical equation to describe the whole curve of the flux versus transmembrane pressure and to describe its use for the determination of the limiting flux. A case of study skim milk microfiltration was carried out for casein micelle concentration, which had, in average, a particle size over the membrane cut off tested.

decrease in the permeate flux.23 However, experimental evidence of low fouling formation during subcritical operation conditions of a membrane bioreactor have been observed.24 This shows that when the term subcritical operation is used, it usually refers to “low fouling” rather than “zero fouling”. Even if the operation of a system under a J < JC condition diminishes the fouling of a membrane, it is not feasible to eliminate it entirely.25 The subcritical operation zone means decreased production costs26 due to the energy savings during operation, and it requires fewer membrane cleaning cycles.21,23,27,28 The highest cost in membrane systems operation is related to membrane fouling,23 and it is the limiting step in the development of current membrane technology.29 To obtain the same flow process at J = JC, a larger than J = JL membrane surface is required,30 an element that is related to the plant investment cost. However, during the last several years, a decrease in the cost of membrane devices has been observed, and hence, the operation costs now deserve greater attention.29 For this reason, the subcritical operation zone is considered a valid option for the industry, and it is used as a valid tool for process optimization in terms of fouling control.31 When the critical flux hypothesis is used with the production cost optimization, it is possible to obtain a sustainable flux that represents the lower flux value where the fouling generation is economically acceptable for the plant operation.31 This is the reason why a subcritical operation, that is, low constant flux, low transmembrane pressure, low resistance and low fouling, seems to be the key for sustainable membrane operation.26,30 When cake formation is lower, operating the system within Zone 2 optimizes the process capacity and minimizes the membrane area used. However, in this zone, the selectivity is not optimal, due a cake layer formation,3 usually called “dynamic membrane”, which can reject more molecules than the original membrane. Until now, the industry has opted to operate at the critical flux level to concentrate whey protein, for bacteria and spore removal and to operate at limiting flux conditions for casein concentration.3 The classical model for membrane resistance14,32 based in the Darcy’s law33 is used for the determination of the total resistance of any membrane process. This model is shown in eq 1:

J=

ΔPT μRT

2. MATERIAL AND METHODS 2.1. Reagents. As a raw material, powdered skim milk from a Chilean milk factory (Colún) was used. This powdered milk all belonged to the same batch (315/69) and was dissolved in warm water (40 °C) by mild stirring for 30 min. Then, it was left standing for 30 min to reach an adequate hydration level of the casein micelles. The reconstituted skim milk showed an average particle diameter (D[3,2]) of 0.41 μm; the analysis was performed by the Centro Chileno de Energiá Nuclear (CCHEN) using laser diffraction equipment (Mastersizer X, Malvern Instruments, 0.63 μm laser wavelength, MSX1, U.K.). Several reconstitutions of powdered skim milk were performed with different solids contents to evaluate the concentration factor (CF) effect during the skim milk microfiltration process. Whereas CF = 0.5 represents diluted skim milk with half of the normal solids and casein concentration, CF = 1.0 represents regular skim milk, with the typical solids and casein content. CF = 1.5 represents a concentrated skim milk with an extra 50% of solids and casein contents when compared to regular milk. The skim milk and cleaning solutions were prepared with deionized water (conductivity ≤ 10 μS/cm). Ultrasil11 was supplied by Henkel-Ecolab (U.S.A.). 2.2. Experimental Setup. Figure 1 shows the experimental setup used for all the trials. A Membralox module (Pall, U.S.A.)

(1)

where μ is the permeate viscosity and RT is the total membrane resistance. RT depends on the resistance offered by the membrane (RM) and by the irreversible (RIF) and reversible fouling (RRF), as shown in eq 2. RT = RM + RIF + RRF

Figure 1. Full recirculation mode setup.

was used with a tubular ceramic membrane of 0.14 μm (pore size), 3.6 mm diameter, and 0.0094 m2 area (Tami, France). Stainless stell manometers (Wika, Chile) coupled to the membrane module and rotatory pumps (Fluid-o-Tech, U.S.A.) were included. The pumps were connected to a 0.5 HP engine for all the trials. The pump characteristic curve describes the flow in L/ min (Q) that is capable to impulse the fluid, and the inlet pressure to the module (Pi) is in bars. All the equations of the pump characteristic curves were performed with deionized water at 20 °C, and they are shown in Table 1. The milk temperature was kept in a narrow range (±0.1 °C) using an immersion bath circulator (LabTech, Iran), and the process fluid temperature was maintained with a precision of ±0.5 °C.

(2)

from where the total fouling term stems and is summarized in eq 3: RTF = RIF + RRF

(3)

Normally, RTF is higher than RM because of a layer deposited onto the membrane.34,35 Equation 1 is unable to describe the flux versus transmembrane pressure behavior when the linear correlation between the flux and transmembrane pressure is lost due to the concentration polarization and fouling effects. The correlation is valid only for low transmembrane pressures. However, what would happen in the case of a transmembrane pressure close to the limiting value? How can the transmembrane pressure required for the operation of each specific 415

dx.doi.org/10.1021/ie5033292 | Ind. Eng. Chem. Res. 2015, 54, 414−425


Article

large enough volume for the determination and concentration of protein. Then, as ΔPT was increased for a following trial, the procedure was repeated, until the entire working range for the transmembrane pressure given for each process condition was analyzed. 2.5. Membrane Cleaning. After the skim milk microfiltration processes, the leftover milk was removed from the system using water rinsing at 50 °C. This was performed in 2 cycles: (i) first 5 min with the permeate valve closed for rinsing the membrane surface and (ii) 5 min with the permeate valve open for rinsing the pores of the membrane. After the rinsing procedure, cleaning was performed using 0.5% w/v Ultrasil11 at 50 °C and 1.3 bar inlet pressure in 2 cycles: (i) 20 min with the permeate valve closed and, (ii) 20 min with the permeate valve opened. The Ultrasil11 pH value was 12.9. After cleaning, the membrane was rinsed several times using water at 50 °C until the water was clear and its conductivity was lower than 10 μS/cm. Using this methodology for each case, the membrane performance recovery (MPR) was higher than 90%;37 therefore, the cleaning procedure was considered successful. Also, the new membrane was conditioned using a shorter Ultrasil11 cleaning procedure, that is, using 10 min in each step instead 20 min. Then, the curve J vs ΔPT was measured and was used as starting point for cleaning assessment. 2.6. Protein Determination. The proteins were classified into two types: casein micelles and soluble proteins. For that reason, before protein quantification, it was necessary to develop a protein sample preparation protocol to separate the proteins into two fractions and to eliminate the lactose interference. For the sample preparation, the casein micelles and soluble protein fractions were obtained from milk prepared with different concentration factors, and their respective permeates were obtained by microfiltration. This was performed using the following steps: first, acetic acid (1.2 M) was added to precipitate the casein micelles up to reach the isoelectric point (pH = 4.6), and the sample was centrifuged for 5 min at 5000 rpm. Second, the supernatant that contained the whey proteins and lactose was subjected to precipitation with trichloroacetic acid (30% w/v). To reach the separation level desired, the suspension was centrifuged at 15000 rpm for 30 min. Both precipitates were then resuspended in a Na2HPO4 buffer (500 mM) solution. The sample was appraised to a known volume for protein determination. All the centrifugation steps used a microcentrifuge (Heraeus Sepatech, Biofuge 15 model, U.S.A.). The protein samples were analyzed by the bicinchoninic acid method using the Protein Research Reagents Kit (Pierce: BCA Protein Assay Reagent, U.S.A.). The measurements were performed at 562 nm using a Plate Lector (ELx 800, BIOTEK Instrument Inc., USA). The apparent retention coefficient (R) was determined for the casein micelles and soluble proteins for microfiltration selectivity. The definition is presented in eq 5.

Table 1. Pump Characteristic Curves and Cross-Flow Velocities pump characteristic curves pump

avg. flow (L/min)

avg. cross-flow velocity (m/s)

PA 0711

2.01

1.13

PA 2511

5.31

2.90

PA 411

7.85

4.29

coefficient of determination

equation Q = −0.145Pi + 2.121 Q = −0.080Pi + 5.410 Q = −0.275Pi + 8.296

R2 = 0.9959 R2 = 0.9923 R2 = 0.9956

The permeate flux was determined by direct permeate mass registration over time using an electronic scale (Shimadzu, BX 4200H, Japan). Full recirculation mode was used in all processes, that is, returning both the concentrate and the permeate streams to the feed tank, as shown in Figure 1. Actually, the permeate was continuously measured and it was returned to the feed tank at discrete intervals. Therefore, all experiments were performed in quasi-stationary state because the concentration of the feed stream was almost constant during the process time. 2.3. Equipment Start-Up. At the beginning of each process, the permeate pressure was increased and adjusted using compressed air. The skim milk began to circulate through the membrane with a transmembrane pressure equal to zero. Then, the permeate pressure was slowly decreased to reach the needed value for the desired ΔPT for each experiment. This ensured that the fouling onto the membrane, in each process, was in correspondence to the work transmembrane pressure. This way, the membrane was never exposed to higher transmembrane pressure than set point, and therefore, it was prevented an undesired higher fouling and/or hysteresis effect.36 Moreover, this type of start-up procedure avoids rapid ΔPT increase across the membrane and the process can starts with a subcritical ΔPT. 2.4. Flux versus Transmembrane Pressure Curve Determination. For each process condition, for a given temperature, velocity and concentration factor, 2 L of skim milk were processed. When starting, the lowest ΔPT in the working range was selected. The pressure working operation ranges for each pump and cross-flow velocity are shown in Table 2. During all the experiments working in these ranges, no significant flux diminishing was found. Table 2. Working Range for the Transmembrane Pressure pump

cross-flow velocity (m/s)

transmembrane pressure (bar)

PA 0711 PA 2511 PA 411

1.13 2.90 4.29

0.02−0.7 0.1−1.5 0.1−1.8

The flux versus time curves were drawn until J∞ was reached, using the criteria described in eq 4: Jt + 1 − Jt Jt

< 5%

R=1−

(4)

Each step lasted 30 min, and for all of the experiments, J∞ was achieved within 30 min. The time required for the J calculation was 2 min, and each protein determination sample was obtained by collecting permeate fractions at 5 min intervals for each transmembrane pressure. A 6 mL sample was taken, a

CP CF

(5)

where C is the concentration, and the superindexes P and F are the permeate and feed streams, respectively. The same equation can be used for determination of protein retention coefficient, for both soluble and casein micelle. 416



Article

Table 3. Variables and Levels Used for Flux versus Transmembrane Pressure Curve Construction level

pseudocomponents value

equation applied low intermediate high

cross-flow velocity (v)

vPC −1 0 1

concentration factor (CF)

v − 2.71 = (4.29 − 1.13)/2

CF − 1.0 CFPC = (1.5 − 0.5)/2

1.13 m/s 2.90 m/s 4.29 m/s

temperature (T)

TPC =

T − 50 (60 − 40)/2

40 °C 50 °C 60 °C

0.5 1.0 1.5

dJ = α(JL − J ) dΔPT

2.7. Experimental Design. The variables analyzed on the flux versus transmembrane pressure curve behavior were the cross-flow velocity, the concentration factor and temperature. The statistical analysis was performed using the transformation of the original values to pseudocomponents. The levels used for each variable and the equations for the corresponding pseudocomponents are shown in Table 3. A factorial experimental design 33 with central points was performed.39 Because three variables were used, three replicates of each central point were performed for error determination. An experimental design with center points aids in the investigation of the curvature in the region around the center. These points also stabilize the estimation of the variance in and around the center. The value of 2.90 m/s for the cross-flow velocity is not exactly a center point. In fact, the corresponding pseudocomponent value was 0.12, which means that the orthogonality design was not perfect. However, the largest variance inflation factor (VIF) equals 1.056, a low enough value to consider the orthogonal design with no confounding effects.38 Moreover, an extra concentration factor (CF = 3.0) was tested at the low and high levels of temperature and cross-flow velocity, generating four additional experiments in addition to the original experimental design. This was performed to check whether the flux versus transmembrane pressure curves had a good agreement with the exponential model at highly concentrated milk but was not considered for the experimental design. 2.8. Data Fitting. The data obtained during the skim milk microfiltration processes were adjusted to the exponential pattern proposed in this work (i.e., eq 14) using the minimum square methodology.39 From these results, two important parameters were determined during microfiltration, that is, the limiting flux and the critical transmembrane pressure under different conditions of the cross-flow velocity, concentration factor, and temperature. 2.9. Statistical Analysis. The effects of the cross-flow velocity, concentration factor and temperature on the limiting flux and the critical transmembrane pressure were calculated using ANOVA. Following this procedure, a regression model (quadratic response surface) was determined. Table 4 shows some parameters for the determination of goodness-of-fit, that is, how well the data fit to the model.

(6)

According to eq 6, when the transmembrane pressure is null, there is no permeate flux (ΔPT = 0 → J = 0). Therefore, eq 7 can be obtained as follows:

∫0

J

dJ = (JL − J )

∫0

ΔPT

α ·dΔPT

(7)

Integrating this expression results in the following equation.

⎛ J ln⎜⎜ L ⎝ JL −

⎞ ⎟⎟ = α ·ΔPT J⎠

(8)

Then, when clearing the flux value, eq 9 is obtained: J = JL (1 − exp(−α ·ΔPT))

(9)

If eq 9 is derivate and the resulting expression is evaluated at the origin (0,0), then the slope of a tangent straight line from the origin is obtained (JLα). Therefore, the tangent straight line to the curve in the origin is represented by the following equation: J = JL α ·ΔPT

(10)

This can be interpreted as the behavior that a microfiltration process should have if the phenomenon of fouling did not exist. Rather, no particle accumulation takes place on the membrane, and fouling does not build up, according to the theory of critical flux.16 When ΔPT → ∞, the limit for eq 9 can be calculated as follows: LIM J = LIM JL (1 − exp(−α ·ΔPT))

ΔPT →∞

ΔPT →∞

(11)

Then, the asymptote equation can be written as follows: J = JL

(12)

Equation 12 is the curve obtained when the limiting flux, that is, the maximum flux that is possible to obtain for a previously established set of conditions, has already been reached. The same interpretation of the asymptote has been shown by Yeh.41 To find the value for the critical transmembrane pressure, eqs 10 and 12 were intersected. The intersection is shown in Figure 2 and the interception point (ΔPT*, J*) can be observed. Then, if the (ΔPT)* is evaluated on eq 9, a new intersection point can be found ((ΔPT)C, JC) which represents this critical value where a transition exists among zones, that is, between the zone when “low fouling” exists on the membrane (J < JC, and J is near to J = JC/(ΔPT)CΔPT) and another zone (J > JC). Therefore, the value at the intersection point (J*) is derived from eqs 10 and 12.

3. THEORETICAL CALCULATION In this section, an equation was proposed for modeling the flux versus transmembrane pressure curves and using it to determine operational parameters during microfiltration. To model this phenomenon, it is proposed that the variation in permeate flux, as a factor of the transmembrane pressure exerted, is proportional to the difference between the maximum permeate flux obtained experimentally (JL), and the flux observed at a certain transmembrane pressure, that is,

JL = JL α ·(ΔPT)* 417

(13)


It represents how well the data variability is explained by the model. All the model variables are there included. An improved regression value could be obtained by increasing the number of coefficients, but this action may lead to an overfitting risk.39 In consequence, the coefficient of determination adjusted by degrees of fredom is better to describe the goodness-of-fit in this kind of models.

coefficient of determination (R2)39

It is similar to the coefficient of determination but it excludes some effects, typically, the nonsignificant ones. Finally, 0 < Radj2 < R2 < 100 is always true.

It determines how well the model fits the experimental data. The smallest possible value is 0 with no upper limit (SEE > 0). The lower is the SEE value, the more adequate is the model.

standard error of estimate (SEE)39

coefficient of determination adjusted by the degrees of fredom (Radj2)39

It is a numerical measure of the model ability to predict the outcome. A zero value indicates a perfect fit and this last one becomes progressively worse as long as the value increases (MAE > 0).

mean absolute error (MAE)40

meaning

It represents the numerical difference between the observed value and the predicted one. It can be interpreted as a distance between the each experimental points to the corresponding estimated point in the model.

residual (RES)39

param.

Table 4. Parameters for Goodness-of-Fitting Determination

1 n

n i=1

∑ |f (xi) − yi |

1 n−k−1

n i=1

∑ (f (xi) − yi )2

418 n 1 (∑i = 1 (f (xi) − yi )2 ) ⎞ n−k−1 ⎟100 n 1 ∑i = 1 (y ̅ − yi )2 ⎟⎠ n−k−h

where y ̅ is the average number of observations, n is the number of data points, k is the number of independent variables in the regression model, and h is the number of nonsignificant variables or those ones that have been eliminated from the model.

⎛ 2 R adj = ⎜⎜1 − ⎝

where y ̅ is the average number of observations, n is the number of data points, and k is the number of independent variables included in the regression model.

n ⎛ ∑ (f (xi) − yi )2 ⎞ ⎟100 R2 = ⎜⎜1 − i =n1 ∑i = 1 (yi − yi )2 ⎟⎠ ⎝

where n is the number of data points, and k is the number of independent variables in the regression model.

SEE =

where n is the number of data points.

MAE =

where f(xi) is the estimated value, and yi the observed one.

RES = f (xi) − yi

equation

Industrial & Engineering Chemistry Research Article



Article

higher at 40 °C than 50 or 60 °C; moreover, for low transmembrane pressure, lower rejection coefficients can be achieved. For transmembrane pressure higher than 0.5 bar the average retention coefficient, at 60 °C, was in the range from 30 to 40%. When the transmembrane pressure was lower than 0.5 bar, at 60 °C, the average retention coefficient was in the range from 20 to 40%. Therefore, operation under low transmembrane pressure and high temperature leads to lower soluble protein retention, which is appropriate and expected for this kind of microfiltration.10,44−46 4.2. Flux versus Transmembrane Pressure Curves Determination. During all the trials, the Reynolds number inside the module was higher than 2100, and hence, a turbulent regime was obtained. Figure 3 presents the flux versus

Figure 2. Intersection of eqs 10 and 12.

where (ΔPT)* is the transmembrane pressure at the intersection point among curves, and rearranging, (ΔPT)* = 1/α. Therefore, it was assumed that the latter value represents a critical transmembrane pressure value (ΔPT)C. For transmembrane pressure values under (ΔPT)C, the flux is proportional to the transmembrane pressure applied. This condition is known as the subcritical region.16 Then, the exponential model for all transmembrane pressure range is expressed by eq 14. Exponential models such as eq 14 have been previously used in membrane technology for describing the flux decline along time, such as J = J0·exp(−at), considered among a family of exponential−decay curves.42 ⎛ ⎛ ΔPT ⎞⎞ J = JL ⎜⎜1 − exp⎜ − ⎟⎟⎟ ⎝ (ΔPT)C ⎠⎠ ⎝

Figure 3. Effect of temperature on the flux versus transmembrane pressure curves obtained during skim milk microfiltration using ceramic membranes of 0.14 μm and 3.6 mm of hydraulic diameter. (v = 2.9 m/s and CF = 1.0)

transmembrane pressure curves at different temperatures. It shows that when the temperature was increased, the maximum value for the flux increased as well. Moreover, a good fit of the experimental curves to the exponential model in all the trials (R2 ≥ 98.56%). The limiting flux was achieved at pressures higher than 0.64 bar. To clarify how to compute the limiting transmembrane pressure, the following example is shown. Using the data obtained for the curve shown in Figure 3 at 40 °C and fitting it to eq 14, eq 17 is obtained:

(14)

Additionally, by evaluating eq 14 at ΔPT = (ΔPT)C, eq 15 is obtained, and it directly relates the critical flux value with the limiting flux. J[(ΔPT)C ] = JC = 0.632JL

(15)

This analytical result for the critical flux value is close to that obtained by Bacchin.43 The author related the critical flux with a thickness of the critical boundary layer and also established that the critical flux is equal to 2/3 of the limiting flux value. For the calculation of the limiting transmembrane pressure (ΔPT)L, it was considered that this value was reached when the flux value was at least 95% of the limiting flux value. This value agrees with the experimental data. For this determination, eq 15 was used, obtaining eq 16. (ΔPT)L = −(ΔPT)C ·ln(1 − 0.95) ≈ 3(ΔPT)C

⎛ ⎛ ΔP ⎞⎞ J = 45.80⎜1 − exp⎜ − T ⎟⎟ ⎝ 0.21 ⎠⎠ ⎝ R2 = 99.30%

(17) 2

In this case, JL is 45.80 L/m /h, and (ΔPT)C is 0.21 bar. Then, using eq 15, the critical flux can be computed as JC = 28.94 L/ m2/h, and using eq 16, the limiting transmembrane pressure can be calculated as (ΔPT)L = 0.64 bar. Therefore, the critical and the limiting point were [28.94 L/m2/h; 0.21 bar] and [45.80 L/m2/h; 0.64 bar], respectively. Figure 4 shows the effect of the cross-flow velocity on the flux versus transmembrane pressure curves. These curves also had a good fit with the exponential model (R2 ≥ 99.42%). As expected, when the cross-flow velocity was increased, an increase in the limiting flux was observed.14,47 Another effect of this parameter on the curves can be observed: when the crossflow velocity is increased, the limiting transmembrane pressure increased significantly from 0.08 bar for 1.13 m/s to 1.05 bar

(16)

4. RESULTS AND DISCUSSION 4.1. Membrane Selectivity. When using membrane of 0.14 um cutoff, a high casein micelle retention and low retention for soluble proteins are expected during skim milk microfiltration.10,44−46 In all experiments, the casein micelle retention coefficient was higher than 99.99% regardless of cross-flow velocity, concentration factor, temperature, and transmembrane pressure. Even for low transmembrane pressure, no significant casein amounts were detected in the permeate stream. Additionally, the soluble protein rejection was 419



Article

Figure 6 shows the experimental limiting flux (JL) and the flux calculated (JL̂ ) using eq 14 for each experiment. A simple

Figure 4. Effect of the cross-flow velocity on the flux versus transmembrane pressure curves obtained during skim milk microfiltration using ceramic membranes of 0.14 μm and 3.6 mm of hydraulic diameter. (T = 50 °C and CF = 1.0)

Figure 6. Correlation between the experimental and predicted limiting flux results obtained during skim milk microfiltration using ceramic membranes of 0.14 μm and 3.6 mm of hydraulic diameter. Data for all concentrations, temperatures, and cross-flow velocities used in this research (n = 34).

for 4.29 m/s. That means that when a low cross-flow velocity is used for skim milk microfiltration, a low transmembrane pressure is needed to achieve a balance between the convection and erosion within the membrane−solution interface.48 Figure 5 shows the effect of the concentration factor on the flux versus transmembrane pressure curves for skim milk

linear regression model was used for testing the relationship between the results. The corresponding correlation is presented in eq 18: JL̂ = 1.0064JL

(18) 2

For this case, the correlation coefficient (R ) was higher than 99.88%. That means that the variables are highly correlated. An ANOVA test was performed using the data for JL and JL̂ . Before that, normality, independence and homoscedasticity were corroborated.38 The results showed that there were no significant differences between the populations of the JL and JL̂ data at a 95% confidence level. Both data populations showed the same mean value (p-value > 0.05) and the same standard deviation (p-value > 0.05). Additionally, the equality for both distributions was checked using the Kolmogorov−Smirnov test (p-value > 0.05). It was concluded that the experimental value is equal to the value obtained by fitting the data using eq 14, that is, JL=JL̂ . Further, a residual analysis was performed for a goodness of fit evaluation. The hypothesis, which indicates that residues come from a normal distribution, was accepted at the 95% confidence level (p-value > 0.05) using the Kolmogorov− Smirnov test. Therefore, eq 14 is valid for limiting flux determination. 4.4. Effect of the Cross-Flow Velocity, Concentration Factor, and Temperature on Limiting Flux. For the determination of the effects of those variables on limit flux, a multiple regression model39 for three factors was fitted. The general model is showed in eq 19. In this case x1 is the crossflow velocity, x2 is the concentration factor, and x3 is the temperature.

Figure 5. Effect of the concentration factor on the flux versus transmembrane pressure curves obtained during skim milk microfiltration using ceramic membranes of 0.14 μm and 3.6 mm of hydraulic diameter. (T = 50 °C and v = 2.9 m/s)

microfiltration. In this case, a good fit between the experimental data and the exponential model was observed (R2 ≥ 99.42%). As expected, the concentration factor had an impact on JL as previously reported.49,50 When the diluted skim milk was processed, a higher limiting flux was achieved. A similar observation was noted by Carić et al.,51 who found that the limiting flux decreases when the protein concentration increases. Related to the limiting transmembrane pressure, the lowest value of 0.43 bar was observed for the concentrated milk (CF = 1.5), and the highest value of 0.67 bar was observed for the diluted milk (CF = 0.5). 4.3. Comparison between the Limiting Flux Experimental Value and the Value Determined through the Exponential Model. For each trial, the limiting flux was determined in two ways: first, as the maximum flux value that can be reached for one experimental condition set and, second, by fitting eq 14 to all the experimental data collected for the same experimental condition and deriving JL.

f (x1, , x 2, , x3) = β0 + β1x1 + β2x 2 + β3x3 + β4 x12 + β5x 2 2 + β6x32 + β7x1x 2 + β8x1x3 + β9x 2x3 + ε (19)

where β0 is the constant coefficient; β1, β2, and β3 are the coefficients of the linear effects; β4, β5, and β6 are the coefficients of the quadratic effects; β7, β8, and β9 are the coefficients of the interaction effects, and ε is the model error. During the experimental design analysis, all the studied variables, their quadratic effects, and their interactions were 420



Article

considered. The analysis presented a good fit, obtaining a coefficient of determination corrected by the degrees of freedom (Radj2) of 98.18%. Moreover, the analysis revealed that all the studied variables and their interactions were significant (p-value < 0.05), except the temperature and crossflow velocity quadratic effects (p-value > 0.05). The temperature and cross-flow velocity quadratic effects were excluded to obtain a more precise model. The eq 20 represents the quadratic model fitted for the permeate limiting flux in L/m2·h as a function of the concentration factor, cross-flow velocity and temperature. This is for variables as pseudocomponents inside the working range (0.5 ≤ CF ≤ 1.5; 1.13 m/s ≤ v ≤ 4.29 m/s, and 40 °C ≤ T ≤ 60 °C) and excluding the quadratic effects previously mentioned.

Pressure. Performing a similar analysis to the one performed with the limiting flux, eq 21 shows the results for the effect of the cross-flow velocity, concentration factor and temperature on the critical transmembrane pressure. Again, during the analysis of all the studied variables in the experimental design, their quadratic effects and interactions were considered. The analysis presented a good fit, obtaining a coefficient of determination corrected by the degrees of freedom of 97.83%. Moreover, the analysis revealed that all the studied variables had significant effects (p-value < 0.05), but in this case, only the cross-flow velocity quadratic effect and its interaction with the concentration factor and temperature were significant (p-value > 0.05). For that reason, the temperature and concentration factor quadratic effects, and their interactions, were excluded to obtain a more precise model. Equation 21 represents the quadratic model fitted for the critical transmembrane pressure in bar as a function of the concentration factor, cross-flow velocity, and temperature. This was for variables as pseudocomponents inside the working range (0.5 ≤ CF ≤ 1.5; 1.13 m/s ≤ v ≤ 4.29 m/s; and 40 °C ≤ T ≤ 60 °C), excluding the effects previously mentioned.

JL = 50.97 − 22.76CFpc + 41.37vpc + 9.86Tpc + 11.44CFpc 2 − 17.27CFpcvpc − 3.98CFpcTpc + 7.84vpcTpc

(20)

From eq 20, CFpc, vpc, and Tpc are the variables as pseudocomponents (−1 ≤ CFpc ≤ 1; −1 ≤ vpc ≤ 1; and −1 ≤ Tpc ≤ 1). During the adjustment, it was verified that Radj2 = 98.12%. The standard error of estimate was 5.61, and the mean absolute error was 3.98. Both values were considered adequate. The analysis confirmed that the temperature, the concentration factor and the cross-flow velocity effects were significant (p-value < 0.05). Moreover, all the interactions and the concentration factor quadratic effects were significant (p-value < 0.05). In this case, a residual analysis was performed for a goodness of fit evaluation. Using the Kolmogorov−Smirnov test, the hypothesis, which indicates that residues come from a normal distribution, was accepted at the 95% confidence level (p-value > 0.05). Consequently, this model can be used for limiting flux determination during skim milk microfiltration under different conditions for cross-flow velocity, concentration factor, and temperature; and as such, it is useful for limiting flux predicting on various conditions.52 By observing eq 20 and considering the working range for each variable, the effect of the velocity seems to be the most significant. This is in agreement with the fact that an increase in the cross-flow velocity is the simplest way of creating turbulence, changing hydrodynamics conditions,53,54 and, therefore, reducing membrane fouling.55 Its immediate effect is the limiting flux improving, even at low cross-flow velocities. 56 In general, this flux can be modified by manipulating the hydrodynamic conditions and the system physical−chemical properties.25 For example, Samuelsson et al.20 determined that it was a linear Reynolds’ number function. Similar observations have been made for the critical flux, which increases with increasing cross-flow velocity.21,30 Additionally, it is considered a function of system hydrodynamic23,30 and a Reynold’s number function.23,50 This agrees with the fact that eq 15 relates JC and JL. Other investigations showed that JC increases with an increase of surface repulsion and membrane-colloid interactions.21,30,57 The higher the potential energy required for the particles interaction is,57 the lower the possibility that the particles coagulate or are deposited onto the membrane surface. Therefore, the critical flux is related to the particle stability. 4.5. Effect of the Cross-Flow Velocity, Concentration Factor and Temperature on the Critical Transmembrane

(ΔPT)C = 0.1597 − 0.0316CFpc + 0.1650vpc − 0.0183Tpc − 0.0438CFpcvpc + 0.0319vpc 2 − 0.0152vpcTpc (21)

In eq 21, CF pc , v pc , and T pc are the variables as pseudocomponents (−1 ≤ CFpc ≤ 1; −1 ≤ vpc ≤ 1; and −1 ≤ Tpc ≤ 1). During the adjustment, the Radj2 was improved to 98.08%. The standard error of estimate was 0.02, and the mean absolute error was 0.01. Both values were considered satisfactory. The analysis confirmed that the temperature, the concentration factor and the cross-flow velocity had significant effects (p-value < 0.05). Moreover, all the interactions and the quadratic effect of the cross-flow velocity were significant (pvalue < 0.05). For the critical transmembrane pressure, it is clear that the most significant effect is the cross-flow velocity, as can be observed in eq 21. Thus, if the velocity inside the module changes, the operational conditions will also change. In general, the limiting flux has been described by several authors18−20,58 who related this concept (or its value) to the system hydrodynamic and fluid properties.20,25 For its prediction, several back-transport models have been used59−66and several authors have studied the critical flux since the concept was introduced for the first time by Field et al.16 The critical flux is dependent on the system hydrodynamics,21,23,30 as was previously mentioned, and is a function of other variables, such as solids concentration50 and particle size.30,50 During the skim milk microfiltration using the membrane of 0.14 μm cutoff and 6 mm hydraulic diameter, a positive effect of the temperature and velocity increase were observed on the permeate limiting flux. Likewise, the velocity has a positive effect on the limiting and critical transmembrane pressure, but the temperature has a negative effect on those parameters. The concentration effect is also important. When the milk solids concentration increased, a limiting flux decrease was observed, as well as the transmembrane pressure that is necessary to obtain it. The critical flux and transmembrane critical pressure diminished in the same way. 421



Article

Some authors have observed these effects on the critical or limiting fluxes working with skim milk. During microfiltration using ceramic membranes (0.14 μm cutoff, 6 mm hydraulic diameter at 55 °C), an increase in the limiting flux was observed when the cross-flow velocity was increased.20,46 A positive effect of the cross-flow velocity over the critical flux was observed by other authors as well.23,30 Yourvarong et al.36 and Baruah et al.67 noted the same effect of the concentration factor that has been verified in this work; that is, the critical flux increases when the protein concentration decreases. Yourvarong et al.36 also proposed a relationship stating that critical flux is proportional to the shear stress and inversely proportional to the concentration. Few studies have been published relating the values of the critical and limiting transmembrane pressures, and fewer are available concerning the effect of the cross-flow velocity, temperature, and concentration factor on the limiting and critical transmembrane pressures during skim milk microfiltration. Some data can be obtained by the inspection of figures already published in the literature,22,25,68−70 from which further discussion can be made. In a study conducted by GésanGuiziou et al.,68 when using a multitubular membrane of 0.1 μm at 50 °C, it was observed that the critical transmembrane pressure was lower than 0.5 bar. In another work with the same cutoff and temperature,69 the critical and limiting transmembrane pressures were lower than 0.2 bar; however, the cross-flow velocity at which the experiments were performed was not reported. Piry et al.70 performed experiments for module length evaluation at 6 m/s and 55 °C using a 0.1 μm zirconia membrane. Their results, as determined by inspecting their curves, showed that the limiting transmembrane pressure was lower than 0.4 bar. Similar results can be observed in the work of Grandison et al.22 The critical transmembrane pressure was 0.5 bar or lower, and the limiting pressure was under 1 bar at 3.4 m/s and 50 °C using a tubular membrane (200 kDa, PVDF). In the work of Yourvarong et al.,25 the critical transmembrane pressure was lower than 1 bar (200 kDa, PVDF, 50 °C, and 3.4 m/s). Moreover, Yourvarong et al.36 showed that using a PVDF membrane of 200 kDa at 50 °C and 3.4 m/s, the critical transmembrane pressure was 0.24 bar. However, none of the above-mentioned works discussed the effect of the cross-flow velocity, temperature, or concentration factor on the critical or limiting transmembrane pressure. In summary, under a set of experimental conditions, by data adjustment to eq 14, the limiting flux (JL) and critical transmembrane pressure ((ΔPT)C) were estimated. Then, using eqs 15 and 16, respectively, the critical flux (JC) and limiting transmembrane pressure ((ΔPT)L) can be calculated. In this way, two important points in the flux vs transmembrane pressure curves are established: [JC, (ΔPT)C] and [JL, (ΔPT)L]. If eq 14 and these previously mentioned points are graphed, Figure 7 is obtained. Figure 7 depicts the three operational zones for the transmembrane pressure using the analysis of eq 14. Despite the fact that the real value of the limiting transmembrane pressure is higher than that estimated by using eq 16, operating the process under the latter might prevent, or at least diminish, long-term reversible fouling. This type of fouling causes a slow flux decrease over time, typically during hours of operation before the process has to be stopped for cleaning.3

Figure 7. Relationship between J and ΔPT during microfiltration. The three fouling zones are shown, in addition to the critical flux (JC) and limiting flux (JL).

In relation to the methodology used for the determination of the critical transmembrane pressure, the literature shows another graphical method for the determination of the critical flux that was proposed by Bacchin et al.71 In that method, they drew the curve J vs JW for the same transmembrane pressure, determined as JC, the value where J = JW/2. The term JW is the flux obtained using pure water at the same temperature and cross-flow velocity. They could have used the same concept by graphing the J vs ΔPT curves and JW/2 vs ΔPT. The graphic method by Bacchin et al.71 will always give higher values for (ΔPT)C than those reported in this research. That is because during all the trials conducted in this work, the critical flux was found to be of the weak type. 17 Even at very low transmembrane pressures, the permeate flux was always smaller than the water flux for the same operating conditions. Consequently, in this research, the critical flux values were smaller because the curves of J vs ΔPT are strictly increasing. Moreover, using the Bacchin et al.71 methodology, the values for the critical flux could be equal or larger than the limiting flux, leading to possible misunderstanding. Finally, some advantages and disadvantages for the use of eq 14 can be pointed out. The model’s main advantage is that it allows the efficient determination of four of the most important parameters in membrane module operation. These parameters are the limiting flux, critical flux, limiting transmembrane pressure and critical transmembrane pressure. Additionally, the model offers an excellent adjustment for experimental data, and the JL determination is estimated using all of the data (all the transmembrane pressures for a condition set and not just the maximum value). This results in a lower error in the determination of JL. The only model disadvantage is that it does not allow predicting when cake compaction takes place nor does it explain how the flux behaves in that condition. Fortunately, cake compaction is not interesting in productive terms because it is the worst operational condition, that is, the flux decreases and modifies the selectivity, retaining more whey proteins during skim milk microfiltration. Operating a microfiltration module within this transmembrane pressure range would lead to more severe membrane fouling, and hence, the use of higher concentrations of cleaning agents, and more frequent restoration cycles, leading to reduced system productivity. In summary, eq 14 is useful as a model for estimating JL and (ΔPT)C, and eq 20 and 21, allow JL and ΔPT predicting on various conditions of temperature, concentration factor and cross-flow velocity, in the studied ranges, during skim milk microfiltration using ceramic membranes of 0.14 μm and 3.6 422



Article

mm of hydraulic diameter. Looking further, this equation may allow automatic control system to adjust skim milk microfiltration parameters to operate at critical or limiting point in a concentration process.

5. CONCLUSIONS The use of the equation J = JL·(1 − exp(−PT/(ΔPT)C) works efficiently for a direct determination of the limiting flux and critical transmembrane pressure from the experimental data using the complete J versus ΔPT curve during skim milk microfiltration. Moreover, using simple mathematical relations, the critical flux and limiting transmembrane pressure can also be determined, and therefore, the operational zones can be described. Additionally, in this work, the critical and limiting transmembrane pressure values were reported, as well as their correlation with variables such as the concentration factor, cross-flow velocity and temperature for the case of skim milk microfiltration. Using this information, an appropriate range for the working transmembrane pressure can be estimated to prevent any undesirable membrane fouling. There are strong grounds to believe that this methodology could decrease membrane fouling and optimize membrane performance.

■

■

RT = total membrane resistance (m−1) RRF = reversible fouling resistance (m−1) R2 = coefficient of determination (dimensionless) Radj2 = coefficient of determination corrected by degrees of freedom (dimensionless) SEE = Standard error of estimate (dimensionless) μ = permeate viscosity (Pa·s) t = time (min)

REFERENCES

(1) Daufin, G.; Merin, U. Cleaning of Inorganic Membranes after Whey and Milk Ultrafiltration. Biotechnol. Bioeng. 1991, 38, 82. (2) Ishigami, T.; Fuse, H.; Asao, S.; Saeki, D.; Ohmukai, Y.; Kamio, E.; Matsuyama, H. Permeation of Dispersed Particles through a Pore and Transmembrane Pressure Behavior in Dead-End Constant-Flux Microfiltration by Two-Dimensional Direct Numerical Simulation. Ind. Eng. Chem. Res. 2013, 52, 4650. (3) Brans, G.; Schroën, C. G. P. H.; van der Sman, R. G. M.; Boom, R. M. Membrane Fractionation of Milk: State of the Art and Challenges. J. Membr. Sci. 2004, 243, 263. (4) Goudédranche, H.; Fauquant, J.; Maubois, J. Fractionation of Globular Milk Fat by Membrane Microfiltration. Lait 2000, 80, 93. (5) Henning, D. R.; Baer, R. J.; Hassan, A. N.; Dave, R. Major Advances in Concentrated and Dry Milk Products, Cheese, and Milk Fat-Based Spreads. J. Dairy Sci. 2006, 89, 1179. (6) Skrzypek, M.; Burger, M. Isoflux Ceramic Membranes-Practical Experiences in Dairy Industry. Desalination 2010, 250, 1095. (7) Beolchini, F.; Vegho, F.; Barba, D. Microfiltration of Bovine and Ovine Milk for the Reduction of Microbial Content in a Tubular Membrane: A Preliminary Investigation. Desalination 2004, 161, 251. (8) Guerra, A.; Jonsson, G.; Rasmussen, A.; Nielsena, E. W.; Edelsten, D. Low Cross-Flow Velocity Microfiltration of Skim Milk for Removal of Bacterial Spores. Int. Dairy J. 1997, 7, 849. (9) Hoffmann, W.; Kiesner, C.; Clawin-Rädecker, I.; Martin, D.; Eihoff, K.; Lorenzen, P.; Meisel, H.; Hammer, P.; Suhren, G.; P, T. Processing of Extended Shelf Life Milk Using Microfiltration. Int. J. Dairy Technol. 2006, 59, 229. (10) Lawrence, N. D.; Kentish, S. E.; O’Connor, a. J.; Barber, a. R.; Stevens, G. W. Microfiltration of Skim Milk Using Polymeric Membranes for Casein Concentrate Manufacture. Sep. Purif. Technol. 2008, 60, 237. (11) Pafylias, I.; Cheryan, M.; Mehaia, M.; Saglam, N. Microfiltration of Milk with Ceramic Membranes. Food Res. Int. 1996, 29, 141. (12) Tan, T. J.; Wang, D.; Moraru, C. I. A Physicochemical Investigation of Membrane Fouling in Cold Microfiltration of Skim Milk. J. Dairy Sci. 2014, 97, 4759. (13) Barukčić, I.; Božanić, R.; Kulozik, U. Effect of Pore Size and Process Temperature on Flux, Microbial Reduction and Fouling Mechanisms during Sweet Whey Cross-Flow Microfiltration by Ceramic Membranes. Int. Dairy J. 2014, 39, 8. (14) Cheryan, M. Ultrafiltration and Microfiltration Handbook; CRC Press: Boca Raton, FL, 1998; pp 1−615. (15) Brans, G.; van der Sman, R. G. M.; Schroën, C. G. P. H.; van der Padt, A.; Boom, R. M. Optimization of the Membrane and Pore Design for Micro-Machined Membranes. J. Membr. Sci. 2006, 278, 239. (16) Field, R. W.; Wu, D.; Howell, J. a.; Gupta, B. B. Critical Flux Concept for Microfiltration Fouling. J. Membr. Sci. 1995, 100, 259. (17) Bacchin, P.; Aimar, P.; Field, R. Critical and Sustainable Fluxes: Theory, Experiments, and Applications. J. Membr. Sci. 2006, 281, 42. (18) Baruah, G. L.; Belfort, G. A Predictive Aggregate Transport Model for Microfiltration of Combined Macromolecular Solutions and Poly-Disperse Suspensions: Model Development. Biotechnol. Prog. 2003, 19, 1524. (19) Belfort, G.; Davis, R.; Zydney, A. The Behavior of Suspensions and Macromolecular Solutions in Crossflow Microfiltration. J. Membr. Sci. 1994, 96, 1.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +56-322274218. Fax: +56-322274205. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The author would like to acknowledge CONICYT, FONDECYT/Iniciación 11110402 Project, for the financial support provided. The author also wishes to thank to Professor Jacqueline Reveco, Professor Jorge Saavedra and Professor Ariel Ochoa for the valuable help in the writing of the manuscript.

■

ABBREVIATIONS a = constant (min−1) CP = concentration in permeate stream (g/L) CF = concentration in feed stream (g/L) D[3,2] = particle mean diameter (μm) J = flux (L/m2/h) JL = limiting flux (L/m2/h) JC = critical flux (L/m2/h) Jt = flux at time t Jt+1 = flux at time t+1 (next time) JW = flux of water (L/m2/h) J0 = initial flux (L/m2/h) MAE = mean absolute error (dimensionless) MPR = membrane performance recovery (dimensionless) Q = flow (L/min) Pi = inlet pressure (bar) ΔPT = transmembrane pressure (bar) (ΔPT)C = critical transmembrane pressure (bar) (ΔPT)L = limiting transmembrane pressure (bar) R = apparent retention coefficient (dimensionless) RES = Residual (dimensionless) RF = fouled membrane resistance (m−1) RM = hydraulic membrane resistance (m−1) RIF = irreversible fouling resistance (m−1) 423



Article

(20) Samuelsson, G.; Huisman, I.; Trägårdh, G.; Paulsson, M. Predicting Limiting Flux of Skim Milk in Crossflow Microfiltration. J. Membr. Sci. 1997, 129, 277. (21) Bacchin, P.; Aimar, P. Critical Fouling Conditions Induced by Colloidal Surface Interaction: From Causes to Consequences. Desalination 2005, 175, 21. (22) Grandison, A.; Youravong, W.; Lewis, M. Hydrodynamic Factors Affecting Flux and Fouling during Ultrafiltration of Skimmed Milk. Lait 2000, 80, 165. (23) Espinasse, B.; Bacchin, P.; Aimar, P. On an Experimental Method to Measure Critical Flux in Ultrafiltration. Desalination 2002, 146, 91. (24) Pollice, A.; Brookes, A.; Jefferson, B.; Judd, S. Subcritical Flux Fouling in Membrane BioreactorsA Review of Recent Literature. Desalination 2005, 174, 221. (25) Youravong, W.; Grandison, A. S.; Lewis, M. J. The Effects of Physicochemical Changes on Critical Flux of Skimmed Milk Ultrafiltration. Membr. Sci. Technol. 2002, 24, 929. (26) Guo, W.; Vigneswaran, S.; Ngo, H. H.; Ben Aim, R. Evaluating the Efficiency of Pretreatment to Microfiltration: Using Critical Flux as a Performance Indicator. In 5th International Membrane Science and Technology Conference, Sydney, Australia; 2003. (27) Bessiere, Y.; Abidine, N.; Bacchin, P. Low Fouling Conditions in Dead-End Filtration: Evidence for a Critical Filtered Volume and Interpretation Using Critical Osmotic Pressure. J. Membr. Sci. 2005, 264, 37. (28) Stoller, M.; Chianese, A. Influence of the Adopted Pretreatment Process on the Critical Flux Value of Batch Membrane Processes. Ind. Eng. Chem. Res. 2007, 46, 2249. (29) Espinasse, B.; Bacchin, P.; Aimar, P. Filtration Method Characterizing the Reversibility of Colloidal Fouling Layers at a Membrane Surface: Analysis through Critical Flux and Osmotic Pressure. J. Colloid Interface Sci. 2008, 320, 483. (30) Howell, J. Subcritical Flux Operation of Microfiltration. J. Membr. Sci. 1995, 107, 165. (31) Guglielmi, G.; Saroj, D. P.; Chiarani, D.; Andreottola, G. Subcritical Fouling in Membrane Bioreactor for Municipal Waterwaste Treatment: Experimental Investigation and Mathematical Modeling. Water Res. 2007, 41, 3093. (32) Schutyser, M.; Belfort, G. Dean Vortex Membrane Microfiltration Non-Newtonian Viscosity Effects. Ind. Eng. Chem. Res. 2002, 25, 494. (33) Ho, C.; Zydney, A. L. Protein Fouling of Asymmetric and Composite Microfiltration Membranes. Ind. Eng. Chem. Res. 2001, 40, 1412. (34) Bouzid, H.; Rabiller-Baudry, M.; Paugam, L.; Rousseau, F.; Derriche, Z.; Bettahar, N. E. Impact of Zeta Potential and Size of Caseins as Precursors of Fouling Deposit on Limiting and Critical Fluxes in Spiral Ultrafiltration of Modified Skim Milks. J. Membr. Sci. 2008, 314, 67. (35) Gésan, G.; Daufin, G.; Merin, U.; Labbé, J.; Quemerais, A. Fouling during Constant Flux Crossflow Microfiltration of Pretreated Whey. Influence of Transmembrane Pressure Gradient. J. Membr. Sci. 1993, 80, 131. (36) Youravong, W.; Lewis, M.; Grandison, A. Critical Flux in Ultrafiltration of Skimmed Milk. Food Bioprod. Process. 2003, 81, 3. (37) Astudillo, C.; Parra, J.; González, S.; Cancino, B. A New Parameter for Membrane Cleaning Evaluation. Sep. Purif. Technol. 2010, 73, 286. (38) Ryan, T. P. Modern Experimental Design; John Wiley & Sons, I., Ed.; Wiley: NJ, 2007; p 601 pp. (39) Montgomery, D. Analysis and Experimental Design, 5th ed.; John Wiley & Sons: Hoboken, NJ, 2001; p 699. (40) Willmott, C. J.; Matsuura, K. Advantages of the Mean Absolute Error (MAE) over the Root Mean Square Error (RMSE) in Assessing Average Model Performance. Clim. Res. 2005, 30, 79. (41) Yeh, H. M. Exponential Model Analysis of Permeate Flux for Ultrafiltration in Hollow-Fiber Modules by Momentum Balance. Chem. Eng. J. 2009, 147, 202.

(42) Mallubhotla, H.; Belfort, G. Semiempirical Modeling of CrossFlow Microfiltration with Periodic Reverse Filtration. Ind. Eng. Chem. Res. 1996, 35, 2920. (43) Bacchin, P. A Possible Link between Critical and Limiting Flux for Colloidal Systems: Consideration of Critical Deposit Formation along a Membrane. J. Membr. Sci. 2004, 228, 237. (44) Hurt, E.; Zulewska, J.; Newbold, M.; Barbano, D. M. Micellar Casein Concentrate Production with a 3×, 3-Stage, Uniform Transmembrane Pressure Ceramic Membrane Process at 50 °C. J. Dairy Sci. 2010, 93, 5588. (45) Lawrence, N.; Kentish, S.; O’Connor, A.; Stevens, G.; Barber, A. Microfiltration of Skim Milk for Casein Concentrate Manufacture. Desalination 2006, 200, 305. (46) Samuelsson, G.; Dejmek, P.; Trägårdh, G.; Paulsson, M. Minimizing Whey Protein Retention in Cross-Flow Microfiltration of Skim Milk. Int. Dairy J. 1997, 7, 237. (47) Nordin, A.-K.; Jönsson, A.-S. Flux Decline along the Flow Channel in Tubular Ultrafiltration Modules. Chem. Eng. Res. Des. 2009, 87, 1551. (48) Le Berre, O.; Daufin, G. Skimmilk Crossflow Microfiltration Performance versus Permeation Flux to Wall Shear Stress Ratio. J. Membr. Sci. 1996, 117, 261. (49) Jö nsson, A.-S.; Jö nsson, B. Ultrafiltration of Colloidal DispersionsA Theoretical Model of the Concentration Polarization Phenomena. J. Colloid Interface Sci. 1996, 180, 504. (50) Wu, D.; Howell, J.; Field, R. Critical Flux Measurement for Model Colloids. J. Membr. Sci. 1999, 152, 89. (51) Carić, M.; Milanović, S.; Krstić, D.; Tekić, M. Fouling of Inorganic Membranes by Adsorption of Whey Proteins. J. Membr. Sci. 2000, 165, 83. (52) Vincent-Vela, M.-C.; Cuartas-Uribe, B.; Á lvarez-Blanco, S.; Lora-García, J. Analysis of an Ultrafiltration Model: Influence of Operational Conditions. Desalination 2012, 284, 14. (53) Zhang, W.; Zhu, Z.; Jaffrin, M.; Ding, L. Hydraulic Conditions on Effluent Quality, Flux Behavior, and Energy Consumption in a Shear-Enhanced Membrane Filtration Using Box−Behnken Response Surface. Ind. Eng. Chem. Res. 2014, 53, 7176. (54) Alexiadis, A.; Bao, J.; Fletcher, D. F.; Wiley, D. E.; Clements, D. J. Analysis of the Dynamic Response of a Reverse Osmosis Membrane to Time-Dependent Transmembrane Pressure Variation. Ind. Eng. Chem. Res. 2005, 44, 7823. (55) Krstić, D. M.; Koris, A. K.; Tekić, M. N. Do Static Turbulence Promoters Have Potential in Cross-Flow Membrane Filtration Applications? Desalination 2006, 191, 371. (56) Gebreyohannes, A. Y.; Mazzei, R.; Curcio, E.; Poerio, T.; Drioli, E.; Giorno, L. Study on the In Situ Enzymatic Self-Cleansing of Microfiltration Membrane for Valorization of Olive Mill Wastewater. Ind. Eng. Chem. Res. 2013, 52, 10396. (57) Bacchin, P.; Aimar, P.; Sanchez, V. Model for Colloidal Fouling of Membranes. AIChE J. 1995, 41, 368. (58) Lipnizki, J.; Casani, S.; Jonsson, G. Optimization of Ultrafiltration of a Highly Viscous Protein Solution Using Spiral-Wound Modules. Desalination 2005, 180, 15. (59) Chang, D.-J.; Hsu, F.-C.; Hwang, S.-J. Steady-State Permeate Flux of Cross-Flow Microfiltration. J. Membr. Sci. 1995, 98, 97. (60) Huisman, I.; Trägårdh, G.; Trägårdh, C. Particle Transport in Crossflow Microfiltration II. Effects of Particle−Particle Interactions. Chem. Eng. Sci. 1999, 54, 281. (61) Huisman, I.; Trägårdh, C. Particle Transport in Crossflow Microfiltration I. Effects of Hydrodynamics and Diffusion. Chem. Eng. Sci. 1999, 54, 271. (62) Hwang, K.-J.; Chou, F.-Y.; Tung, K.-L. Effects of Operating Conditions on the Performance of Cross-Flow Microfiltration of Fine Particle/Protein Binary Suspension. J. Membr. Sci. 2006, 274, 183. (63) Sethi, S.; Wiesner, M. Modeling of Transient Permeate Flux in Cross-Flow Membrane Filtration Incorporating Multiple Particle Transport Mechanisms. J. Membr. Sci. 1997, 136, 191. 424



Article

(64) Vera, L.; Delgado, S.; Elmaleh, S. Dimensionless Numbers for the Steady-State Flux of Cross-Flow Microfifiltration and Ultrafiltration with Gas Sparging. Chem. Eng. Sci. 2000, 55, 3419. (65) Field, R. W.; Pearce, G. K. Critical, Sustainable and Threshold Fluxes for Membrane Filtration with Water Industry Applications. Adv. Colloid Interface Sci. 2011, 164, 38. (66) Wemsy Diagne, N.; Rabiller-Baudry, M.; Paugam, L. On the Actual Cleanability of Polyethersulfone Membrane Fouled by Proteins at Critical or Limiting Flux. J. Membr. Sci. 2013, 425−426, 40. (67) Baruah, G. L.; Couto, D.; Belfort, G. A Predictive Aggregate Transport Model for Microfiltration of Combined Macromolecular Solutions and Poly-Disperse Suspensions: Testing Model with Transgenic Goat Milk. Biotechnol. Prog. 2003, 19, 1533. (68) Gésan-Guiziou, G.; Boyaval, E.; Daufin, G. Critical Stability Conditions in Crossflow Microfiltration of Skimmed Milk: Transition to Irreversible Deposition. J. Membr. Sci. 1999, 158, 211. (69) Gésan-Guiziou, G.; Daufin, G.; Boyaval, E. Critical Stability Conditions in Skimmed Milk Crossflow Microfiltration: Impact on Operating Modes. Lait 2000, 80, 129. (70) Piry, A.; Kuhnl, W.; Grein, T.; Tolkach, A.; Ripperger, S.; Kulozik, U. Length Dependency of Flux and Protein Permeation in Crossflow Microfiltration of Skimmed Milk. J. Membr. Sci. 2008, 325, 887. (71) Bacchin, P.; Espinasse, B.; Aimar, P. Distributions of Critical Flux: Modelling, Experimental Analysis, and Consequences for CrossFlow Membrane Filtration. J. Membr. Sci. 2005, 250, 223.

425


Limiting Flux and Critical Transmembrane Pressure Determination

Recommend Documents