A hydrodynamic comparison between rotating disk and vibratory dynamic filtration systems

Journal of Membrane Science 242 (2004) 155–167

A hydrodynamic comparison between rotating disk and vibratory dynamic filtration systems Michel Y. Jaffrin∗ , Lu-Hui Ding, Omar Akoum, Ambroise Brou Biological Engineering Department, Technological University of Compiegne, UMR CNRS 6600, BP 20529, 60205 Compiegne, France Received 28 February 2003; received in revised form 25 July 2003; accepted 30 July 2003 Available online 28 July 2004

Abstract The purpose of this work is to compare the effects of various hydrodynamic parameters (transmembrane pressure, shear rate, fluid viscosity and solute concentration) on the permeate flux provided by two different dynamic filtration systems using same membrane material and same fluids. Tested systems were two rotating disk modules designed in our laboratory and a VSEP pilot with a circular vibrating membrane. Tests fluids consisted of baker’s yeast microfiltration (MF) at 0.2 ␮m and of UHT skim milk ultrafiltration (UF) at 50 kDa. The characteristic shear rate was taken to be the maximum one (γ m ) at the membrane outer rim in each module. It was varied by changing the rotation speed of the disk or by changing the vibration frequency of the VSEP. The highest permeate fluxes were obtained with rotating disks equipped with vanes because they generated the largest shear rates. But in MF, when the disk speed was adjusted to produce the same maximum shear rate as in the VSEP, permeate fluxes variations with time in both modules were identical at the same TMP and yeast concentration. Flux variations with TMP were also very close in this case. In concentration tests by MF at constant speed or frequency, permeate fluxes (J) in L h−1 m−2 provided by the two rotating disks (with and without vanes) and the VSEP were well correlated by a single equation, J = 4.3 × 10−6 γ m 1.46 , where the shear rate was varied by the concentration change. Permeate fluxes were also similar in UF of milk for the VSEP and rotating disk when shear rates were matched. The variation of permeate flux with shear rate at constant concentration for the two rotating disks systems with and without vanes was correlated by a single equation J = 0.136γ m 0.594 , while the corresponding equation for the VSEP was J = 0.110γ m 0.587 . Our data suggest that, in these devices, the flux is mainly governed by the maximum shear rate and not by details of internal flow and can be increased to very high levels by increasing rotation speed or vibration amplitude or by equipping the disk with large vanes. This information can be used for scaling up industrial systems. © 2004 Elsevier B.V. All rights reserved. Keywords: Dynamic filtration; Rotating disk; Vibrating filtration system; Microfiltration of yeast suspension; Milk ultrafiltration

1. Introduction Shear-enhanced or dynamic filtration consists in creating the shear rate at the membrane by a relative motion between the membrane and a moving part such as a rotating disk or an impeller. This method has shown to be very effective in microfiltration (MF) of biological suspensions [1–3], especially for macromolecule recovery [4–6]. The reason for its good performance is that very high shear rates are produced with a low inlet flow, and therefore, a low pressure drop in the module. Consequently the transmembrane pressure (TMP) can be kept very low, and the combination of ∗ Corresponding author. Tel.: +33 3 44 23 43 98; fax: +33 3 44 20 48 13. E-mail address: [email protected] (M.Y. Jaffrin).

0376-7388/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.memsci.2003.07.029

high shear rates and low TMP facilitates macromolecules transmission through the membrane. When shear-enhanced devices are used in ultrafiltration [7,8], the very high shear rate effectively reduces concentration polarization and it is then advantageous to use high TMP since the permeate flux keeps increasing until higher pressure levels than in conventional crossflow filtration. The main drawback of rotating disk systems is their complexity and the cost of building industrial scale modules, which require several large diameter disks mounted on the same axis and rotating at high speed. Membrane replacement is also a delicate and complex operation. An original alternative concept, the VSEP (New Logic Intern, CA, USA) has been proposed in 1992 by Armando et al. [9]. A similar system (PallSep) was also commercialized by Pall Corporation, NY, USA. This vibratory shear-enhanced system consists in

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a stack of circular plane membranes mounted in a cylindrical housing which is spun in torsional oscillations around a vertical axis at a resonant frequency of about 60 Hz. Each compartment contains two membranes separated by a gasket and a permeate collecting system. Since this system is compact, without internal moving parts, with a fluid channel height of about 3.5 mm [10], it can accommodate up to 140 m2 of membrane in a single module. This system probably requires less energy to operate on a large scale than rotating disks systems because membrane displacement is amplified by the resonance. Vane and Alvarez [11], using a 10 m2 VSEP module for removal of volatile organic compounds by pervaporation, reported that the power spent in vibrations was small, about 2 kW for their 15 in. diameter module. In addition, the power per m2 of membrane area has been estimated to be half in the 140 m2 module of that in a 20 m2 module. The shear rate at the VSEP membrane is created by the inertia-induced relative motion of the fluid which moves at 180◦ out of phase as in the case of a Stokes layer near an oscillating plate. As a consequence, this shear rate varies sinusoidally with time and increases with local membrane azimuthal displacement proportionally to radius. As rotating disk systems, the VSEP can also be operated with small inlet flows, permitting to retain a low TMP when operated in MF. The VSEP has also been used for removal of humic substances in river water coagulated by polyaluminum chloride [12]. These authors used a 100 kDa regenerated cellulose membrane and compared the VSEP performance with that of hollow fiber modules. When the VSEP was operated at its resonant frequency, the permeate flux decayed from 400 L h−1 m−2 to 200 after 100 h of filtration. Chemical cleaning permitted to restore the flux to 300 L h−1 m−2 . Bian et al. [13] also used the VSEP for the same application but with NF membranes, which eliminated the need of a pretreatment by coagulation and investigated the effect of frequency on its performance. They obtained at resonant frequency a 95% rate of removal of humic substances which dropped to 85% after a permeate volume of 10 m3 m−2 of membrane. As expected, both the permeate flux and the rate of removal dropped rapidly when the membrane displacement was reduced by lowering the frequency. Echizen and Unno [14] also used a VSEP for the concentration of fat globules in milk with membranes of various pore sizes, 0.2, 0.5 and 1.0 ␮m and confirmed the beneficial effect of oscillations on the permeate flux and globule transmission as they showed that capture of fat globules by the membrane decreased when oscillation amplitude was increased. In a recent paper [15], the performances of the VSEP and two CR (Raisio Flootek) modules equipped with a rotating rotor were compared in water treatment by UF for the pulp and water industry. The rotor tip velocity was 13.7 m s−1 in the lab scale pilot CR 200 and 19.1 m s−1 in the industrial scale module CR 1000 (13.5 m2 membrane area). Various membranes from 10 to 50 kDa were tested. While initial fluxes were similar in both devices around 160 L h−1 m−2 ,

after 10 h of filtration, the CR 200 yielded a higher permeate flux (196 L h−1 m−2 ) than the VSEP (114 L h−1 m−2 ) equipped with the same 30 kDa membrane at 200 kPa, possibly due to a slight heating of the solution by the rotor friction. In addition the tests in the VSEP were apparently conducted at a displacement amplitude of 1.6 cm rather than the 2.9 cm observed at resonant frequency. This paper illustrates the complexity of a comparing the performance of different types of dynamic filtration devices which have specific operating constraints such as a minimum 200 kPa TMP for the VSEP and are very sensitive to changes in rotation speed or vibrating frequency. Thus the purpose of our paper is to compare the effect of various hydrodynamic parameters (TMP, shear rate, concentration, etc.. . . ) on the permeate flux obtained from rotating disks and vibrating systems, using data from tests performed in our laboratory with the same membrane and same tests fluids. To ensure fluid reproducibility we have selected baker yeast suspensions for MF and UHT commercial skimmed milk for UF. One of our goals was to investigate whether the permeate fluxes of these devices in various configurations could be correlated by a single parameter such as a characteristic shear rate on the membrane.

2. Material and methods 2.1. Rotating disk systems Two types of modules were designed in our laboratory. The smaller one, described by Bouzerar et al. [16,17], had a 15.4 cm i.d. short circular housing machined from polyamide PA6, in which a 14.5 cm aluminum disk rotates at variable speeds up to 3000 rpm around a horizontal hollow shaft (Fig. 1). A 190 cm2 membrane, supported by a 0.3 mm thick polypropylene grid, was mounted on the front plate opposite to the shaft, while the fluid inlet was located on the back plate on the shaft side. The feed was centrifuged by the disk towards its rim and passed to the membrane side, where it recirculated between the fixed membrane and the disk in a helicoidal path, before being evacuated through the hollow

Fig. 1. Schematic of rotating disk module.

M.Y. Jaffrin et al. / Journal of Membrane Science 242 (2004) 155–167

shaft. Permeate was collected from a tap at the top of the front plate. The fluid peripheral pressure was measured at the top of the cylindrical housing by a Validyne DP15 pressure transducer. The test fluid was fed from a thermostated reservoir by a Masterflex peristaltic pump at a flow rate of 30 L h−1 in MF, in order to be in excess of the highest permeate flow rate encountered. In UF, a volumetric piston pump was used at a flow rate of 60 L h−1 . A larger module was built in stainless steel with a 26 cm i.d. housing receiving a 460 cm2 annular membrane (inner radius, R1 = 4.7 cm, outer radius R2 = 13.0 cm, disk radius Rd = 12.0 cm) and was used in milk ultrafiltration. Due to technical constraints, only inlet and outlet fluid pressure were measured in this unit. The maximum rotation speed was 1500 rpm and the feed flow 180 L h−1 . Several types of disks were used in these units. Initial disks (denoted as smooth) were flat on both sides. Subsequent disks were equipped with radial vanes of various heights, 2 mm for the large module and 2, 4, and 6 mm for the small one. 2.2. Calculations of membrane shear rate The flow field between the membrane and a rotating flat disk has been analyzed previously by Bouzerar et al. [17]. Boundary layers developed along the disk and the membrane since the axial gap between them was larger than 5 mm. The flow was generally turbulent except at low speeds and in the central part since the Reynolds number 4R22 ων−1 , where ω is the disk angular velocity, reached 2 × 105 at 1500 rpm when r > 4.5 cm for water. It is well known [18] that the inviscid core between the boundary layers rotates at the angular velocity kω, where k, less than 1, is a velocity coefficient which depends on disk geometry. Coefficients k for various disks were determined by regression from peripheral pressure measurements taken on the housing rim at various angular velocities, using Bernoulli’s equation [17] p(r) = 21 ρk2 ω2 r 2 + p0

(1a)

where p0, is the pressure when the disk is at rest and ρ denotes fluid density. Since the permeate is collected at atmospheric pressure, the mean transmembrane pressure is obtained by integration of Eq. (1a) over membrane area from r = 0 to R2 as ptm = pc − 41 ρk2 ω2 R22

(1b)

where pc is the peripheral pressure at r = R2 . The shear rate on the stationary membrane has been calculated by Bouzerar et al. [16] in the turbulent regime to be γwt (r) = 0.0296ν−0.8 (kω)1.8 r 1.6

(2a)

where ν is the fluid kinematic viscosity. Since the aim of this paper is to compare the performance of several dynamic filtration devices with different geometries, we have selected as representative shear rate that on the membrane under the

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Table 1 Maximum shear rate on the membrane outer rim for the small module Small module

Maximum shear rate γ m (s−1 )

N (rpm) γ m (s−1 ) (×10−4 ) Smooth disk k = 0.45 γ m (s−1 ) (×10−4 ) 6 mm vanes k = 0.84

500 1000 1500 2000 2500 0.825 2.87 5.96 10.0 14.9 2.54

8.83

18.3

30.8

46.0

disk edge (at r = Rd ) where it is maximum. The justification is that we have shown that it is the membrane outer ring which contributes the most to the permeate flow while the central part contributes little. Thus, averaging the shear rate over the membrane area would introduce a bias when comparing fully circular membranes as in the small module with annular ones as in the large module and the VSEP. This maximum shear rate is then given by γm = 0.0296ν−0.8 (kω)1.8 R1.6 d

(2b)

Although Eqs. (2a) and (2b) have been derived for a flat disk, they will be used also with disks equipped with vanes, but taking the value of k corresponding to these disks. Values of maximum shear rates on the membrane for water at 20 ◦ C at various speeds and with various disks are listed in Table 1 for the small module and Table 2 for the large one using values of coefficients k found by Brou et al. [3] to be equal to 0.45, 0.65, and 0.84 respectively for a disk without vanes (denoted as smooth disk) and disks equipped with 2 and 6 mm high vanes. Kinematic viscosities used in calculations are listed in Table 4. 2.3. The VSEP module The filtration module depicted in Fig. 2 was a VSEP Series L (New Logic international, Emeryville, CA, USA). This unit has been described before [10,11]. It was equipped with a single circular membrane, of 13.5 cm outer radius R2 , 4.7 cm inner radius R1 with an effective area of 500 cm2 . The shaft supporting the membrane housing acts as a torsion spring which transmitting the oscillations of a lower plate in the base, which is vibrated by an eccentric drive motor. The housing motion consists in azimuthal oscillations in its own plane with displacement amplitude “d” depending upon frequency and which was measured using an accelerometer [10] to be 30 mm on the membrane outer edge at the max-

Table 2 Maximum shear rate on the membrane outer rim for the large module Large module

Maximum shear rate γ m (s−1 )

N (rpm) γ m (s−1 ) (×10−4 ) Smooth disk k = 0.45 γ m (s−1 ) (×10−4 ) 2 mm vanes k = 0.65

500 750 1000 1250 1500 2.10 4.36 7.31 1.09 15.2 4.07

8.45

14.2

21.2

29.4

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Fig. 2. Schematic of VSEP system.

imum allowed frequency (F) of 60.75 Hz. This frequency can be adjusted by an electronic controller. The module was fed from a thermostated and stirred 10 l tank by a peristaltic pump at 30 L h−1 in MF and by a volumetric piston pump at a flow rate of 180 L h−1 in UF tests. We have verified earlier [10] that, at frequencies above 58 Hz, the permeate flux was insensitive to feed flow variation above 30 L h−1 , since at high enough frequencies, the shear rate at the membrane is mainly controlled by the membrane displacement. As shown in [10], the membrane shear rate varies sinusoidally with time and is proportional to radius. It is therefore maximal at the membrane periphery. The maximum shear rate with time at periphery was calculated in [19] to be γm = 21/2 d(πF)3/2 ν−1/2

(3)

and was taken as the characteristic shear rate for the VSEP. It must be noted that the displacement d decreases rapidly as frequency is reduced from 60.75 Hz and the effect of frequency on shear rate is much larger than suggested by Eq. (3). Inlet, outlet and permeate pressures were measured by VALIDYNE DP 15 (Validyne Corp., Northridge, CA, USA) pressure transducers in order to determine the TMP as mean of inlet and outlet pressures since the permeate was atmospheric. The TMP was adjusted by a valve on the outlet tubing. It must be noted that, when the fluid kinematic viscosity increases, the shear at the membrane decays faster in the rotating disk system than in the VSEP as ν−0.8 versus ν−0.5 .

Values of maximum shear rates on the membrane in the VSEP, for water at 20 ◦ C at various frequencies, are listed in Table 3. The permeate flux was measured by collecting the permeate in a beaker continuously weighted on an electronic scale (Sartorius, Germany) connected to a microcomputer calculating the derivative of the collected volume with respect to time and dividing it by membrane area. The fluid temperature was monitored in the tank by a Digitron platinum resistance thermometer (SIFAM Ltd., Torquay, Devon, UK). 2.4. Test fluids 2.4.1. Yeast suspensions These suspensions were prepared by mixing baker’s yeast (Saf Instant, Le Saffre, France) in ultrapure osmosed water at various concentrations ranging from 3 to 120 g L−1 . The yeast cell mean diameter measured by laser granulometry was 5.2 ± 2.1 ␮m. A symmetric Nylon membrane (Ultipor, Pall Corp., New York, USA) of 0.2 ␮m pore size was used in MF of yeast suspensions in the rotating disk and VSEP devices. Table 3 Maximum shear rate on the membrane outer rim for the VSEP VSEP

Maximum shear rate γ m (s−1 )

Frequency F (Hz) γ m (s−1 ) (×10−4 )

58 1.15

59 2.02

59.5 3.32

60 6.67

60.4 9.40

60.6 10.5

60.75 11.2

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Table 4 Concentration, temperature, kinematic and dynamic viscosities of fluids used in the study Fluid

Concentration or VRR

Temperature (◦ C)

ν (m2 s−1 ) (×106 )

µ (Pa s−1 ) (×103 )

Yeast suspensions

3 g L−1

20 25 20 25

1.138 1.013 1.634 1.454

1.136 1.010 1.631 1.450

45

1.06 1.31

0.98 1.36

20 g L−1 UHT milk

VRR = 1 VRR = 1.8

2.4.2. Skim milk The test fluid in all tests was a commercial UHT (sterilized at ultra high temperature) skim milk (Printiligne, Patˆurages de France). This milk has been sterilized at 140 ◦ C for 3 s and possesses the following composition: casein: 25.6 g L−1 , whey proteins: 6.4 g L−1 , lactose: 46 g L−1 and calcium: 1.2 g L−1 . According to Miralles et al. [20], protein composition of UHT milk is similar to that of pasteurized milk, except that whey proteins may be partially denatured, to the rate of 20% for ␣-lactalbumin and 65% for ␤-lactoglobulin [21]. Tests were generally carried out at initial concentration with a volume reduction ratio, (VRR) equal to 1 or at VRR = 1.8 which is the standard operating concentration for this process in industry, except in concentration tests where high VRR were sought. The milk pH was measured by a pH-meter Mettler Toledo MP 125 (Switzerland). The average initial pH in the tests was 6.5 and never dropped by more than 0.3, indicating the absence of bacterial development. Table 4 lists dynamic and kinematic viscosities for the fluids at the various concentrations and temperatures used in the tests which will be used to calculate shear rates shown in the figures.

The same membrane polyethersulfone (PES) 50 kDa was used in the two rotating devices and the VSEP for UF of milk. 2.4.3. Cleaning procedure Before and after each test, the circuit was first rinsed with demineralized water, then washed with 5 l of Ultrasil (Henkel, Germany) P3-25F solution (0.5% in demineralized water) at 50 ◦ C for 15 min and rinsed again with 5 l of demineralized water. A new membrane was used in each test.

3. Results 3.1. A microfiltration of yeast suspensions 3.1.1. Variation of permeate flux with time at VRR = 1 The variation of permeate flux with time for a 3 g L−1 yeast suspension using the small rotating disk module equipped with a 0.2 ␮m nylon membrane at a speed of 2000 rpm is displayed in Fig. 3. Tests were carried out in the small module with a smooth disk and a disk equipped

Fig. 3. Variation of permeate fluxes with time in MF of 3 g L−1 yeast suspensions for the small rotating disk module with two types of disks and the VSEP.

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Fig. 4. Variation of permeate fluxes with time in MF for a yeast concentration of 20 g L−1 (small module).

with 6 mm vanes at a temperature of 25 ◦ C. The results from a similar test conducted with the VSEP using the same suspension and the same membrane, at its maximum frequency of 60.75 Hz, but under slightly different conditions (a TMP of 30 kPa and a temperature of 20 ◦ C) are also shown for comparison. The corresponding maximum shear rates on the membrane calculated using Eqs. (2b) and (3) are also indicated in the figure. It is interesting to note that the permeate fluxes yielded by the smooth disk and the VSEP are virtually identical, while their maximum shear rates are close, respectively, 0.99 × 105 and 1.12 × 105 s−1 . As expected, the disk equipped with vanes, which produces a mean shear rate three times larger than the smooth disk, gives a much higher permeate flux than the other two systems, but which decays with time over a longer period. The same comparison is shown in Fig. 4 at a yeast concentration of 20 g L−1 . The comments made at 3 g L−1 apply also here. The VSEP and the rotating disk device without vanes yield virtually identical permeate fluxes, except for the first 3 min of filtration, with respective mean shear rates of 8.80 × 104 s−1 at 20 ◦ C for the VSEP and 7.44 × 104 s−1 at 25 ◦ C for the rotating disk. At both concentrations, the VSEP needs a slightly higher shear rate to yield the same permeate flux than the rotating disk, but this can be explained by the temperature and TMP differences. In these devices, the effect of temperature is two-fold. An increase in temperature will decrease both permeate viscosity and retentate kinematic viscosity. Both effects should contribute to increase permeate flux. Thus it is not surprising that, under less favorable TMP and temperature conditions, the VSEP needs a higher shear rate to achieve the same permeate flux as the rotating disk module.

The percentage gain produced by vanes on the quasi-steady permeate flux (after 70–90 min) seems to be less than at 3 g L−1 . 3.1.2. Variation of permeate flux with TMP at VRR = 1 This variation is displayed in Fig. 5 for the same conditions of yeast concentration, temperature, rotation speed and vibration frequency as in Fig. 3 for a smooth disk, a disk with 6 mm vanes and the VSEP. The permeate flux of the VSEP this time is slightly higher than that of the smooth disk, even though its mean shear rate on membrane is slightly smaller. As expected the 6 mm vanes disk produces the highest permeate flux which keeps increasing until a TMP of at least 130 kPa. 3.1.3. Variation of permeate flux with mean membrane shear rate at VRR = 1 For the rotating disk systems, the shear rate was varied by increasing the rotation speed, while for the VSEP it was varied by reducing the oscillation frequency. Decreasing the vibration frequency from resonance reduces the displacement amplitude d, and consequently the shear rate at membrane according to Eq. (3). As a consequence, the permeate flux follows a pattern close to that of the membrane displacement amplitude and drops rapidly until a frequency of 59 Hz and more slowly thereafter. The results of such tests obtained in our laboratory for a yeast concentration of 20 g L−1 [3] are plotted in log–log coordinates in Fig. 6. It can be seen that, in both systems, the variation of stabilized permeate flux with maximum shear rate is more important at high shear rates as if there was a switch from laminar to turbulent regime when fluid velocity is increased at larger shear rates. Data for the

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161

Fig. 5. Variation of permeate fluxes with TMP in MF of 3 g L−1 yeast suspensions for the small rotating disk module with two types of disks and the VSEP.

For the VSEP, corresponding correlations are, for γ m < 33,000 s−1

smooth disk are above those for the VSEP taken from an earlier publication from our laboratory [10], but the correlation lines are almost parallel, both at low and high shear rates. For the disk, the flux in L h−1 m−2 is given by, for γ m < 20,000 s−1

0.189 J = 5.44γm

0.186 J = 6.17γm

(4a)

0.502 J = 0.207γm

(4b)

It must be stressed that numerical coefficients such as 6.17 in Eq. (4a), etc., are only valid for the flux and shear rate units considered here, respectively, L h−1 m−2 and s−1 .

and for γ m > 20,000 s−1 by 0.567 J = 0.140γm

(5a)

and for γ m > 33,000 s−1 (5b)

Fig. 6. Variation of permeate fluxes in MF of yeast suspensions at 20 g L−1 with maximum membrane shear rate for the rotating disk module at variable speed and the VSEP system at variable frequency.

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Fig. 7. Variation of permeate fluxes with yeast concentration in concentration tests for the rotating disk system at 2000 rpm and the VSEP at 60.75 Hz.

3.1.4. Concentration tests We compare in Fig. 7 the permeate fluxes measured at various concentrations after 90 min of filtration at initial concentration in order to reach a quasi-steady regime in the rotating disk module. Each point represents a different experiment run at constant concentration but with suspensions of increasing concentration. When concentration exceeded 80 g L−1 , the permeate was no longer recycled in order to further increase the concentration. The VSEP data were obtained in a similar manner with 90 min constant concentration tests run at 3, 20 and 150 g L−1 . Above 200 g L−1 , data were obtained by not recycling the permeate. In this case again, it can be seen that data obtained with the smooth disk at 2000 rpm are virtually identical to those of the VSEP. In addition both set of data obey the semi-logarithmic law of the thin film theory [22], represented by a straight line in Fig. 7. With a 6 mm vanes disk, permeate fluxes are much larger, especially at low concentration in accordance with Fig. 3. It is worth noticing that, in dynamic filtration systems, increasing the yeast concentration decreases the permeate flux by two different mechanisms. In addition to the higher mass flux of particles towards the membrane which result in more rapid and thicker cake build-up, there is, according to Eqs. (2b) and (3), a reduction in membrane shear rate caused by an increase in retentate kinematic viscosity. The reduction should be higher for the rotating disk device than for the VSEP since the exponent of ␯ in the denominator of Eq. (2b) is larger than in Eq. (3). When the permeate flux data of Fig. 7 are plotted in terms of the maximum membrane shear rate using the kinematic viscosity of yeast suspensions given in Table 4, we observed in Fig. 8 that the permeate fluxes in L h−1 m−2 obtained both

with the rotating disk module and the VSEP are expressed as 1.459 J = 4.3 × 10−6 γm

(6)

Eq. (6) shows a larger flux dependence with shear rate than Eqs. (4) and (5). This implies that concentration will cause a larger decrease in permeate flux than the same shear reduction caused by lowering the rotation speed or frequency at initial concentration represented by Eqs. (4) and (5). Thus, the difference between these two fluxes decreases can be attributed to the sole effect of concentration increase. 3.2. Ultrafiltration of skim milk 3.2.1. Variation of permeate flux with TMP This variation is illustrated in Fig. 9 for the small module at rotation speeds of 1000 and 2000 rpm for a smooth disk, a disk with 6 mm vanes and for the VSEP at 60.75 Hz. With the smooth disk, the permeate flux reaches a plateau of 111 L h−1 m−2 at 2000 rpm corresponding to a membrane shear rate of 9.12 × 104 s−1 . The VSEP produces a smaller maximum permeate flux (104 L h−1 m−2 ) for a slightly larger membrane shear rate (1.15 × 105 s−1 ). With a 6 mm vanes disk, the permeate flux reaches a maximum of 200 L h−1 m−2 at 2000 rpm and a pressure of 550 kPa. Corresponding data for the large module are displayed in Fig. 10 for a smooth disk and a disk equipped with 2 mm vanes at a rotation speed of 1250 rpm. This speed was selected to obtain with the smooth disk a maximum membrane shear rate close to that of the VSEP. Since this unit was built in stainless steel, the maximum TMP were higher than with the smaller unit. Figs. 9 and 10 confirm that, at high shear rates, the permeate flux reaches its

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163

Fig. 8. Variation of permeate fluxes with maximum membrane shear rate during concentration tests of Fig. 7.

maximum at higher pressure since concentration polarization is reduced. For comparison we have included in Fig. 10 VSEP data shown in Fig. 9. Here the VSEP membrane shear rate is slightly higher than that for the smooth disk (9.96 × 104 s−1 ) and its permeate flux is larger below 900 kPa and lower at higher pressures.

modules and by the VSEP, when this shear rate is varied by reducing the rotation speed or the oscillation frequency in the VSEP. It is interesting to observe in Fig. 11 that permeate fluxes measured in the two modules, using disks with and without vanes, obey, to a good approximation, the same correlation in terms of membrane shear rate which is given by

3.2.2. Variation of permeate flux with membrane shear rate As in the case of yeast suspensions, we compare the variations with maximum membrane shear rate of maximum permeate fluxes at VRR = 1 provided by the rotating disk

0.595 J = 0.143γm

(7a)

where γ m is given by Eq. (2b) for the rotating disk module. The existence of a single correlation means that permeate

Fig. 9. Variation of permeate fluxes with TMP in UF of skim milk for the small rotating disk module with two types of disks and the VSEP.

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Fig. 10. Variation of permeate fluxes with TMP in UF of skim milk for the large rotating disk module with two types of disks and the VSEP.

flux is governed mainly by the membrane shear rate and not by details of the internal flow and of the housing or disk geometry. The corresponding correlation of the VSEP at VRR = 1 is 0.572 J = 0.134γm

(7b)

where γ m is given by Eq. (3). It can be seen that the variations of permeate flux with shear rate, represented by the exponents of γ m are almost

identical for the VSEP and the rotating disk modules, while the permeate flux given by the VSEP are 40% smaller at the same shear rate. The same observation can also be made on results obtained with milk concentrated at VRR = 1.8. The permeate fluxes are, as expected, lower than at VRR = 1 and, given, for the rotating disk by 0.587 J = 0.110γm (8a) and for the VSEP by 0.576 J = 0.090γm

(8b)

Fig. 11. Variation of permeate fluxes in UF of milk with maximum membrane shear rate for the rotating disk module at variable speed and the VSEP system at variable frequency, for VRR =1 and 1.8.

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At this concentration, VSEP permeate fluxes are 29% smaller at the same shear rate than those from the rotating disk with 6 mm vanes. 3.2.3. Concentration tests Such tests are normally carried out by recycling only the retentate in the tank and not the permeate. But in order to eliminate the effect of initial fouling, the first 110 min of tests were carried out at initial concentration by recycling both permeate and retentate in the tank. In addition, during the first 5 min of filtration, the retentate valve was kept open, and then it was shut progressively to reach the desired TMP to minimize initial fouling. After 110 min, the permeate recirculation was stopped and the concentration phase was started until the retentate volume became equal to the dead volume, in order to reach the maximum value of volume reduction ratio (VRR). The variation of permeate flux with ln(VRR) is displayed in Fig. 12 for the small module with a smooth disk an a disk with 6 mm vanes, a TMP of 300 kPa and a rotation speed of 2000 rpm. It is seen for the smooth disk that the permeate flux drops slowly below a VRR of 1.3 while, at higher concentrations, it obeys the classical concentration polarization law of the form J = J0 − K ln(VRR)

(9)

where J0 is equal to 110.1 L h−1 m−2 at 300 kPa. The actual fluxes at initial concentration are lower than these values since Eq. (9) holds only above VRR = 1.3. The mass transfer coefficient K is 58.9 L h−1 m−2 . The corresponding maximum VRR obtained by extrapolation to J = 0 is 6.7. The variation of permeate flux with concentration was markedly different when a 6 mm vanes disk was fitted in the module. Not only permeate fluxes were higher than with the smooth disk, but they remained practically constant until a VRR of

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3. So Eq. (9) only applies at VRR larger than 3 with a mass transfer coefficient of 104.4 L h−1 m−2 at a TMP of 300 kPa. The maximum VRR obtained by extrapolation to zero flux was 9.2. This figure is much higher than the value of 6.4 observed in crossflow ultrafiltration with tubular membranes [23]. The variation of permeate flux in UF of UHT milk with VRR using the VSEP at its maximum frequency is also represented in Fig. 12. It follows very well the thin film theory of Blatt et al. [22] with a theoretical limiting VRR of 8.66 corresponding to a gel concentration, which is close to that obtained with the rotating disk. But at the same VRR, the permeate fluxes yielded by the VSEP are close to those of the smooth disk device even though the TMP was higher for the VSEP, 400 kPa versus 300. It is interesting to note that the permeate flux from the VSEP does not drop as fast with increasing VRR as those from the rotating disk in accordance with Eqs. (2b) and (3) which show that the increase in kinematic viscosity has less effect on the VSEP shear rate. As in the case of yeast suspensions, the VSEP permeate flux measured during concentration tests of Fig. 12 are represented as a function of the maximum membrane shear rate in log-log coordinates in Fig. 13 together with the corresponding correlation when the shear rate was varied at VRR = 1 and the same TMP of 400 kPa by changing the frequency. The VSEP flux-shear rate-correlation during the concentration test is found to be, for a flux in L h−1 m−2 1.257 J = 3.4 × 10−5 γm

(10)

While at VRR = 1, it is 0.533 J = 0.168γm

(11)

Fig. 12. Variation of permeate fluxes with VRR in milk concentration tests for the rotating disk system at 2000 rpm and the VSEP at 60.75 Hz.

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Fig. 13. Variation of VSEP permeate fluxes with maximum membrane shear rate during the concentration test of Fig. 12.

The difference between the two fluxes at the same shear rate is due to the contribution of increasing milk protein concentration which produces a larger resistance to filtration. The slight difference between the coefficients of Eqs. (8) and (11) is due to the TMP difference. Data of Eq. (8) correspond to the maximum fluxes with TMP while those of Eq. (11) were taken at TMP = 400 kPa.

4. Discussion and conclusion Although our experiments using rotating disk and VSEP systems were carried out independently and under different conditions in some tests, our data suggest that permeate flux maxima with TMP in these systems for a specific fluid are mainly governed by a single parameter, the maximum membrane shear rate. Although internal flows inside these two devices present different characteristics, their respective permeate fluxes are very close if corresponding maximum shear rates are the same. Moreover, all data can be correlated with the same generic equation n J = Aγm

(12)

in which the constant A depends upon the system of units considered. In this paper, the flux was expressed in L h−1 m−2 and shear rate in s−1 . This result can be particularly useful for scale up of industrial systems. If highest permeate fluxes were obtained with the rotating disk device, it was because this system could generate higher shear rates than our L101 VSEP pilot, especially when the disk was equipped with large vanes.

In the rotating disk device, the membrane shear rate is steady and increases with radius (r) as r1.6 . In the VSEP, it varies sinusoidally with time and proportionally to radius. It is interesting to note the similarity of exponents of γ m between Eqs. (7a) and (8a) at VRR = 1, and between Eqs. (7b) and (8b) at VRR = 1.8. However, Figs. 6 and 11 show that, for the same maximum shear rate and same fluid, the VSEP flux is lower than that of the rotating disk. This difference would have been less if we had taken the time-mean shear rate of the VSEP rather than the maximum with time. A difference between the two systems lies in the dependence of shear rate with retentate kinematic viscosity. The shear rate will decay faster with increasing kinematic viscosity ν in the rotating disk than in the VSEP since it is proportional to ν−0.8 versus ν−0.5 in the VSEP. Therefore, if the retentate is concentrated with time in a batch system, the flux should be expected to decay more rapidly as VRR increases in the rotating disk module than in the VSEP. This conclusion is confirmed in Fig. 12, except for data using the disk with vanes at VRR < 3.

Nomenclature C d dp F J k K

yeast concentration (g L−1 ) membrane displacement amplitude at rim (mm) pore size (␮m) frequency (Hz) permeate flux (L h−1 m−2 ) velocity coefficient (rotating disk) mass transfer coefficient (L h−1 m−2 )

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N p(pc ) ptm Qi R1 , R2 Rd VRR

rotation speed (rpm) pressure (at membrane periphery) (Pa) transmembrane pressure (Pa) inlet flow rate (L h−1 ) inner (outer) radius (m) disk radius (m) volume reduction ratio

Greek letters γm maximum shear rate at membrane (s−1 ) µ dynamic viscosity (Pa s) ν kinematic viscosity (m2 s−1 ) ω disk angular velocity (rad s−1 )

References [1] U. Frenander, A.S. Jönsson, Cell harvesting by cross-flow microfiltration using a shear-enhanced module, Biotech. Bioeng. 52 (1996) 397–403. [2] A. Pessoa, M. Vitolo, Evaluation of cross-flow microfiltration membrane using a rotary disc-filter, Process Biochem. 33 (1998) 39–45. [3] A. Brou, L.H. Ding, M.Y. Jaffrin, Dynamic microfiltration of yeast suspensions using rotating disks equipped with vanes, J. Membr. Sci. 197 (2002) 269–282. [4] C. Harscoat, M.Y. Jaffrin, R. Bouzerar, J. Courtois, Influence of fermentation conditions and microfiltration process on membrane fouling during recovery of glucuronane polysaccharides from fermentation broths, Biotech. Bioeng. 65 (1999) 500–511. [5] A. Brou, M.Y. Jaffrin, L.H. Ding, J. Courtois, Microfiltration and ultrafiltration of polysaccharides produced by fermentation using a rotating disk dynamic filtration system, Biotech. Bioeng. 82 (2003) 429–437. [6] S.A. Lee, A. Burt, G. Russoti, B. Buckland, Microfiltration of recombinant yeast cells using a rotating disk dynamic filtration system, Biotech. Bioeng. 48 (1995) 386–400. [7] M.M. Dal-Cin, C.N. Lick, A. Kumar, S. Lealess, Dispersed phase back transport during ultrafiltration of cutting oil emulsions with a spinning disc geometry, J. Membr. Sci. 141 (1998) 165–181. [8] L.H. Ding, O. Akoum, A. Abraham, M.Y. Jaffrin, High shear skim milk ultrafiltration using rotating disk filtration system of various configurations, AIChE 49 (2003) 2433–2441.

167

[9] A.D. Armando, B. Culkin, D.B. Purchas, New separation system extends the use of membranes, in: Proceedings of the Euromembrane 92, Paris, vol. 6, Lavoisier, Paris, 1992, p. 459. [10] O. Al-Akoum, M.Y. Jaffrin, L.H. Ding, P. Paullier, C. Vanhoutte, An hydrodynamic investigation of microfiltration and ultrafiltration in a vibrating membrane module, J. Membr. Sci. 197 (2002) 37– 52. [11] L.M. Vane, F.R. Alvarez, Full-scale vibrating pervaporation membrane unit: VOC removal from water and surfactant solutions, J. Membr. Sci. 202 (2002) 177–193. [12] K. Takata, K. Yamamoto, R. Bian, Y. Watanabe, Removal of humic substances with vibratory shear enhanced processing membrane filtration, Desalin 117 (1998) 273–282. [13] R. Bian, Y. Watanabe, N. Tambo, G. Ozawa, Removal of humic substances by UF and NF membrane systems, Water Sci. Tech. 40 (1999) 121–129. [14] E. Echizen, H. Unno, Concentration of fat gobules in milk by an oscillating membrane unit, Trans. IChemE. 79 (2001) 3–12. [15] T. Huuhilo, P. Vaisänen, J. Nuortila-Jokinen, M. Nyström, Influence of shear on flux in membrane filtration of integrated pulp and paper mill circulation water, Desalin 141 (2001) 245–258. [16] R. Bouzerar, L. Ding, M.Y. Jaffrin, Local permeate flux-shearpressure relationships in a rotating disk microfiltration module: implications for global performance, J. Membr. Sci. 170 (2000) 127– 141. [17] R. Bouzerar, M.Y. Jaffrin, L. Ding, P. Paullier, Influence of geometry and angular velocity on performance of a rotating disk filter, AIChE J. 46 (2000) 257–265. [18] H. Schlichting, Boundary Layer Theory, 7th ed., McGraw-Hill, New York, NY, 1968, pp. 213–218. [19] O. Al-Akoum, L.H. Ding, M.Y. Jaffrin, Microfiltration and ultrafiltration of UHT skim milk with a vibrating membrane module, Sep. Purif. Techol. 28 (2002) 219–234. [20] B. Miralles, B. Bartolone, M. Ramos, L. Amigo, Determination of whey protein to total protein ratio in UHT milk using 4th derivative spectroscopy, Intern. Dairy J. 10 (2000) 191–197. [21] E. Enright, A.P. Bland, E.C. Needs, A.L. Kelly, Proteolysis and physicochemical changes in milk on storage as affected by UHT treatment, plasmin activity and KIO3 addition, Intern. Dairy J. 9 (1999) 581–591. [22] W.F. Blatt, A. Dravid, A.S. Michaels, L. Nelson, Solute polarization and cake formation in membrane ultrafiltration: causes, consequences and control techniques, in: J.E. Flinn (Ed.), Membrane Science and Technology, Plenum Press, New York, NY, 1970, p. 47. [23] A.K. Bouzaza, M.Y. Jaffrin, B.B. Gupta, Effect of flow and pressure pulsations on milk ultrafiltration by mineral membranes, in: Proceedings of the ICIM 89, 1st International Conference on Inorganic Membranes, Montpellier, 3–6 July 1989, p. 439.