journal of MEMBRANE

SCIENCE

E L S E V I E R Journal of Membrane Science 118 (1996) 247-257

Quantitative measurements of the concentration polarisation layer thickness in membrane filtration of oil-water emulsions using

NMR micro-imaging

J.M. Pope a,*, S. Yao b, A.G. Fane c

a School of Physics, Queensland UniversiO~ of Technology, GPO Box 2434, Brisbane, Qld 4001, Australia b School of Physics, The University of New South Wales, Sydney, NSW 2052, Australia

c UNESCO CentreJbr Membrane Science and Technology, The University of New South Wales, Sydney, NSW 2052, Australia

Received 23 October 1995; revised 27 March 1996; accepted 1 April 1996

Abstract

In this paper we report measurements of the thickness of the concentration polarisation layers formed during crossflow membrane filtration of an oil-water emulsion. The formation and development of the oil polarisation layers was visualised non-invasively using NMR chemical shift selective micro-imaging. A series of images was acquired during the transient state of the filtration, (i.e. while the polarisation layer was forming and the flux of filtrate was changing), prior to the establishment of steady state conditions. An estimate of the specific resistance of the concentration polarisation layers was then obtained by determining the average oil layer thicknesses and concentration at a given time from the resulting images and measuring the corresponding (length averaged) flux of filtrate gravimetrically. After the establishment of steady state conditions, the dependence of the steady state filtrate flux on crossflow Reynolds number was found to be consistent with Brownian diffusion being the main mechanism controlling the build-up of the oil polarisation layers, at least under our range of operating conditions.

Keywords: Concentration polarisation; Microfiltration; NMR micro-imaging; Oil-water emulsion; Fouling

1. Introduction

Synthetic membranes are increasingly used for filtration and separation of a range of fluid solutions and suspensions in industrial, food processing, waste treatment, biomedical and environmental applica- tions. In crossflow filtration the flow of feedstock is arranged to be tangential to the surface of the mere-

* Corresponding author. Fax: +61 7 3864 1521; E-mail: j.pope@qut.edu.au.

brane, thus limiting the build up of retained particles or solute at the surface of the membrane. This accu- mulation of material at the membrane surface is known as concentration or particle polarisation [1-3]. Polarisation layers can vary in thickness from a few microns to hundreds of microns, depending on such factors as the nature of the feed solution or suspen- sion, the module design, the crossflow rate and the trans-membrane pressure difference. In many in- stances the polarised layer provides the controlling resistance which determines the flux of permeate, thus limiting the efficiency of the membrane filtra-

0376-7388/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PII S0376-7388(96)001 07-X

248 J.M. Pope et al. / Journal of Membrane Science 118 (1996) 247-257

tion process. Furthermore, the extent of the polarisa- tion can have an important influence on membrane fouling and long-term loss of flux. It is therefore a key parameter in determining the performance and efficiency of membrane filtration modules in many practical applications.

Polarisation layers are formed in crossflow filtra- tion as a result of convection of solute or particles towards the membrane surface, driven by the flux of permeate through the membrane. In the steady state this is balanced by diffusion away from the surface. Previous studies have mainly been restricted to ob- serving oil gel or "filter cake" layers (in the case of filtration of suspensions of solid particles), deposited more or less permanently on the surface of the membrane. These studies have generally used inva- sive methods such as physical sampling or section- ing, coupled with conventional optical or scanning microscopy, to observe the dimensions and structure of the cake layer remaining after the flow of feed- stock has been turned off. Such methods clearly cannot be used to study concentration polarisation layers which dissipate rapidly when the flux of per- meate is removed. However Wandelt et al. [4] have recently employed MRI methods to study the deposi- tion of suspended bentonite particles on a membrane surface by making use of changes in proton spin density and NMR relaxation times (T 1 and T 2) with particle concentration to render the filter cake visible in the NMR images. In this study, we report the use of chemical shift selective NMR micro-imaging to visualise the formation of oil polarisation layers dur- ing crossflow filtration of an oil-water emulsion.

According to the resistance in series model, the establishment of a concentration polarisation layer during the course of filtration can be regarded as adding an additional hydraulic resistance in series with the membrane itself. Thus the flux of permeate is given by [5,6]

AP

J = ~(Rm + Rp) ([)

where AP is the trans-membrane pressure differ- ence, R m and Rp are the hydraulic resistance of the membrane and the concentration polarisation layer respectively, and ~/ is the viscosity of the feedstock (solution, suspension or emulsion). In general the

resistance of the concentration polarisation layer, Rp may be expressed as

Rp = rp• (2)

with 6 and rp being respectively the thickness and the resistance per unit thickness of the concentration polarisation layer. In practice both Rp and 6 will in general be a function of time, axial distance along the module, (in the case of crossflow filtration), and the conditions under which the module is operated. The parameter rp is related to the specific resistance of the layer (i.e. resistance per unit "cake" loading) by

rp = ~po(1 - ~) (3)

where c~ is the specific resistance of the polarisation layer (m/kg) , Po is the particle (oil drop) density ( k g / m 3) and E is the voidage of the polarised layer (i.e. (1 - e) is therefore the volume fraction of oil in the polarised layer).

Experimental determination of the specific resis- tance of the concentration polarisation layers is usu- ally obtained from flux versus time data for "un- stirred" filtration [7]. However this is not strictly appropriate for stirred conditions or where diffusive or shear-induced back-transport of depositing species occurs. It is clear that a direct measurement of the polarisation layer thickness and the concentration of the polarised layer would allow calculation of its specific resistance from the above equations and hence facilitate experimental investigation of the fac- tors affecting the formation and composition of the concentration polarisation layer under different oper- ating conditions. However, hitherto, non-invasive techniques have not been available for this purpose. Recently, we have demonstrated that NMR chemical shift selective imaging can be used for the observa- tion of concentration polarisation layers formed dur- ing filtration of oil-water emulsions in a hollow fibre membrane module [8]. The use of chemical shift selective micro-imaging methods [9] meant that we were able to pick up the signal from the oil concentration polarisation layer separately from that due to the feedstock. In this paper we report quantita- tive measurements of the concentration polarisation layer thickness obtained in this way for a tubular membrane module during filtration of an oil-water

J.M. Pope et al./Journal of Membrane Science 118 (1996) 247-257 249

emulsion (5% v /v) . An estimate of the specific resistance of the oil layer is then obtained based on the resistance in series model. A number of images obtained under different crossflow conditions after the filtration had reached the quasi-steady state, are also presented. Gravimetric measurements of the flux of permeate in the steady state, as a function of crossflow Reynolds number, were then used to inves- tigate the mechanism by which the oil droplets are removed from the polarisation layer under equilib- rium conditions.

2. Materials and methods

The tubular membrane filtration module used in this study is shown schematically in Fig. 1. The length of the module was 40 cm, with an effective length for the active portion of the membrane of approximately 35 cm. The tubular membrane was an "Accurel" polypropylene membrane manufactured by Enka, with an average pore size 0.2-0.4 /zm, inner diameter 5.2 mm and wall thickness of approx- imately 1.65 mm. The glass tube forming the outer wall of the module had an outer diameter of 12 mm and a wall thickness of approximately 1 mm. Both ends of the tubular membrane were open and the oil-water emulsion was fed into the lumen at one end and removed from the other end, while the permeate was collected from the outer shell region between the membrane and the outer glass tube. A tubular membrane module was used for this study (in preference to the multi-hollow fibre membrane mod- ule we employed previously [8]) because of its rela-

Imaging Planes Permeate outlet

1 I I •

Fluid outlet I I I Fluid inlet Plane-view

~ Tubular membrane Section-view

Fig. 1. Diagram of the tubular membrane module used in this study, as described in the text.

Gauge-2 Membrane module Gauge-1 Rotameter

I ~ :::::::::::::::::::: =~ ( ~

V ~ 3 Valve-1 ~

I1 .......... Reservoir

Fig. 2. Schematic diagram of the pump-driven recirculation sys- tem used to control the operating conditions for membrane filtra- tion.

tively simple geometry, which facilitates determina- tion of the average thickness of the concentration polarisation layers.

Recirculation of the emulsion was achieved by using the flow system shown schematically in Fig. 2, in which the feedstock was driven by a small pump. The crossflow rate and trans-membrane pressure dif- ference were controlled by means of valves 1 and 2. The by-pass, controlled by valve 3, allowed for an additional adjustment of the crossflow rate while maintaining a constant trans-membrane pressure dif- ference. The flow rate of the emulsion at the inlet of the module was measured directly by a rotameter incorporated in the circuit. The volumetric flow rates of the permeate and of the feedstock were measured at the outlet of the module by collecting the appro- priate outflows in a beaker and recording the mass flow per unit time using an electronic balance.

The oil-water emulsion was made from a com- mercial cutting oil (Caltex Trusol DD), dispersed (5% v / v ) in water doped with CuSO 4. Its method of preparation has been described earlier [8]. For this study, in order to minimise the effects of changes in membrane fouling on the observed transient decay of permeate flux arising from formation of the polarisa- tion layer (rather than changes in fouling of the membrane itself), the tubular membrane module was operated under "well fouled" conditions. In general, membrane fouling gives rise to a long term decline in filtrate flux, but we have found that for a "well fouled" membrane (i.e. one that had been exten-

250 J.M. Pope et al . / Journal of Membrane Science 118 (1996) 247-257

sively used previously to filter the same emulsion under similar operating conditions of trans-mem- brane pressure difference and feedstock flow rate), this long term decline was negligible over the time scale of our measurements, when compared with the initial transient reduction in flux associated with formation of the polarisation layer. The latter was found to occur typically over a time scale of an hour or so (see below) at the relatively low trans-mem- brane pressure differences employed in our study.

The NMR imaging equipment employed and the pulse sequence used for the chemical shift selective imaging have been described in detail in our previ- ous publication [8]. In particular, in order to follow the establishment of the concentration polarisation layers, the acquisition time of an individual 2D oil

[ ]

[ ]

selective image was kept to approximately 10 min (i.e. short compared with the time constant for estab- lishment of the oil polarisation layers). A data matrix 128 by 128 was acquired giving a pixel size of 94

/xm for a 12 mm square field of view. A slice thickness of 1 mm was used, with a sequence repeti- tion time T R = 1.0 s and number of scans NS = 4 for signal averaging. This gave both reasonable signal intensity and adequate spatial resolution for measur- ing the thickness of the concentrated oil layer on the inner surface of the tubular membrane.

The 2D cross sectional images obtained by chemi- cal shift selective NMR imaging in this way were then analysed on a pixel by pixel basis to obtain both an average oil layer thickness, ~ and a normalised

intensity, I (averaged over the selected image cross

[ ]

[ ] Fig. 3. A group of 2D oil selective NMR images (only 6 from 12 acquired images are shown here), obtained for a cross section of the tubular membrane module, 25 cm from the inlet of the feed emulsion, demonstrating the transient development of the concentration polarisation oil layer on the membrane surface. The first image was obtained immediately before the feed emulsion was turned on showing the "well fouled" status of the membrane module while the remaining images were obtained after the feed emulsion had been turned on, respectively, for (b) 10 min, (c) 40 min, (d) 70 min, (e) 115 min and (f) 205 min (see text for the operating conditions).

J.M. Pope et al. / Journal of Membrane Science 118 (1996) 247-257 251

section), using the following formulae for this pro- pose:

npZIA ~-d (4)

and

I - (5) np

where n i is the number of pixels in the oil polarisa- tion layer with intensity li, n p = ~ n i is the total number of pixels forming the apparent oil layer, ZIA is the area of each pixel and d is the internal diameter of the tubular membrane, with the assump- tion of that 6 is much smaller than d. Variations in normalised image intensity I should reflect changes in volume fraction of oil in the polarisation layer (1 - e ) .

3. Results and discussion

A representative set of oil selective images ob- tained with the tubular membrane filtration module described above, at an axial position z -= 25 cm from the inlet of the feed emulsion, is shown in Fig. 3. These images clearly illustrate the establishment of the oil concentration polarisation layer on the inner surface (lumen side) of the tubular membrane as a function of time. (Only 6 from a total of 12 acquired images are shown here.) The corresponding operat- ing conditions were: trans-membrane pressure drop ZIP = 65 kPa, crossflow Reynolds number Re = 110 (corresponding to a flow rate for the feed emulsion Q = 0.45 ml / s ) and an initial permeate flux J6 -- 4.0 1 m - 2 h - 1. The latter compares with a flux of 650 1 m -2 h 1 obtained for a clean (unfouled) membrane filtering pure water under similar operating condi- tions. The lower initial flux, compared with that which might be anticipated for a fresh (unused) membrane was simply the result of the module being operated in the "well fouled" condition. In this case, the main fouling mechanism appears to be the deposition of oil within the body of the membrane itself (see below). This process, unlike the formation of the polarisation layers (which dissipate rapidly on removal of the trans-membrane pressure difference),

can only be reversed by the use of appropriate detergents to clean the membrane.

From the images shown in Fig. 3 we can see that, for a given axial position, the oil concentration polar- isation layer was not completely uniform in thick- ness either at the beginning of the filtration (i.e. in the early stages of the transient state) or at the end of the filtration (after the quasi-steady state had been reached, corresponding to an approximately constant permeate flux). However it was observed to pass through a more uniform phase during the transient state. In addition, it is evident that the thickness of the oil layer increased substantially during the time course of the filtration. The reason for the observa- tion of a non-uniform oil layer in the early stages of filtration probably reflects the effects of non-uniform permeability over the surface of the membrane aris- ing either from heterogeneity in the membrane itself or in the prior fouling of the membrane, which is a function of its history and previous treatment. The non-uniformity in the oil layer which was observed to develop towards the end of filtration is believed to be due to buoyancy effects in the concentrated oil- in-water emulsion which forms the polarisation layer, since the thickest region consistently appeared at the top of the module as the quasi-steady state was approached, independent of rotation of the whole module by 180 ° about its axis between successive experiments. These effects could not therefore have resulted from non-uniformities in the membrane it- self.

It is also worth noting that a small amount of oil signal was often observed on the shell side, as a result of coalescence at the outer surface of the membrane of small oil droplets which were able to pass through the membrane wall. The average droplet size of the oil-water emulsion used as feedstock in this study was approximately 0.15 /zm, obtained from light scattering measurement at 25°C. By com- parison, the average pore size of the microfiltration membranes used was 0.2-0.4 /xm. In Fig. 3, oil signals (manifest by high signal intensity in the oil selective images) from within the body of the mem- brane itself reflect the extent of membrane fouling. It is clear that the signals contributed by membrane fouling were relatively unchanged during the course of the current study. Although a small amount of oil was sometimes observed in the permeate, the overall

252 J.M. Pope et al. / Journal of Membrane Science 118 (1996) 247-257

oil retention by the membrane was high and net oil transport through the membrane was considered to be negligible.

Fig. 4 shows plots of the conventional (length averaged) permeate flux ( J > versus time for three different operating conditions. Here ( J > was mea- sured by weighing the permeate flow over a given time (typically 5 min) during the acquisition of each image. Typically the permeate flux exhibited an approximately exponential decay reflecting the estab- lishment of the concentration polarisation layer. Slight variations of the initial flux between these three measurements are due to the effects of mem- brane fouling. The images were then analysed on a pixel by pixel basis using Eqs. (4) and (5) to obtain the average thickness and intensity of the oil layer. The results are shown in Fig, 5 where both of the thickness and intensity are plotted as a function of time. From Fig. 5 we can see that, whereas under our operating conditions the average thickness of the oil polarisation layer, 6, continued to increase over a time scale of hours before reaching a quasi-steady state, the corresponding signal intensity, I, appeared to reach a plateau more rapidly. The apparent step of the signal intensity (Fig. 5b) observed during the transient region is probably a consequence of the finite digital resolution of our images. This also results in an under-estimation for the intensity of the thinner oil polarisation layers (which are comparable to the pixel size) during the early stages of formation

500

400

300 :::a.

t,~

200

1 0 0 '

0

1.0

0 .8 '

0.6"

c 0.4"

0.2"

0.0

(a)

o

A 6 o &

i 1

o o 3

o o

o o A

&

I

2 3

Time (hour)

A 6 &

(b)

0

e

o o S 2 ~ ° ' , @

8 o 0 3 •

& A 6 A A

Time (hour)

Fig. 5. Plots of (a) oil layer thickness fi, and (b) the intensity of the oil layer, 1 versus time calculated from NMR images for three different operating conditions, (O) Ap = 75 kPa, Re = 110, (~ ) Ap = 6 5 kPa, Re= 110 and (A) Ap = 65 kPa, Re= 365. (The signal intensities presented here were normalised for each group individually.)

5 -

4

3 0J

2 D.

e

°1

e &

A & & &

• o o o o o

o • o

1 i D i

0 1 2 3

Time (hour)

Fig. 4. Length averaged permeate flux, ( J > versus time for three different operating conditions, as measured by weighing the fil- trate accumulated in a given time period (approximately 5 min) during the acquisition of the image, (©) Ap = 75 kPa, Re = 110, (~ ) Ap =65 kPa, Re = 110 and (A) Ap =65 kPa, Re= 365.

of the oil polarisation layer. We have however as- sumed that the expression for the concentration po- larisation induced resistance, Rp = rp 6 [Eq. (2)], is still valid at this stage.

It should be noted from Figs. 4 and 5 that the time constant for the build-up of the layers is significantly longer than would be expected for most practical applications. This is due to the dilute nature of the feed and the relatively low permeate fluxes attained in this study. The signal intensity data in Fig. 5 are consistent with the volume fraction of oil in the polarised layer being approximately in the range 0.4-0.6 under steady state conditions. This is similar to our observations for the same oil-water emulsion using hollow fibre membranes [8] and can be com- pared with values of around 0.4 inferred from flux versus concentration data for other soluble oil emul-

J.M. Pope et al. / Journal of Membrane Science 118 (1996) 247-257 253

sions [3,7]. One possible interpretation of the achievement of a quasi-steady state thickness for the oil polarisation layer in Fig. 5a is that convection of oil droplets to the boundary layer is balanced by axial flow of the layer to the feedstock outlet. How- ever attempts to detect flow of the boundary layer using NMR flow imaging techniques [10,11] proved unsuccessful, indicating that the polarisation layer was stationary in the axial direction within an experi- mental error of _+ 7.5 /xm/s [12]. Based on an upper limit for the axial flow of + 7.5 /xm/s and an effec- tive length for the membrane module of 25 cm we estimate that this mechanism could only account for removal of 15% of the oil deposited on the mem- brane by convection. A more plausible mechanism for removal of oil from the polarisation layer is therefore diffusive and /or shear induced radial back transport (see below).

In order to obtain an estimate of the resistance per unit thickness of the oil polarisation layer rp and hence the specific resistance c~, the directly mea- sured length averaged permeate flux, ( J ) is substi- tuted for the (localised) flux of permeate, J in Eq. (1). Thus we have

1 + rp (t)) (6)

<J(t)> Where R m is defined as the resistance of the "well fouled" membrane defined by R'~ = R m + Rf, and Rf is the contribution to the hydraulic resistance

1.0

>

y = 0 .21630 + 8 .5890e-4x RA2 = 0 .957

0.8

0,6 '

0 . 4 -

Y 0.2'

0.0 , ] , l

I O0 200 300 400 500

a (p m)

Fig. 6. Plot of the reciprocal of the (length averaged) permeate flux, ( J ) versus the thickness of the oil polarisation layer, during the transient state of the filtration, as used for estimation of the resistance per unit thickness, rp of the oil layer. The correspond- ing operating conditions are AP = 65 kPa and Re = 110.

from membrane fouling, which was assumed to be approximately constant during the time course of the filtration in the current study. According to Eq. (6), by plotting the reciprocal of the length averaged permeate flux ( J > v e r s u s the average oil layer thick- ness 6, both rp, and the resistance of the "well fouled" membrane R' m, can be obtained from the slope and the l / ( J ) intercept, respectively. One of these plots obtained for constant trans-membrane pressure difference AP = 65 kPa and Re = 110 is shown in Fig. 6. From Fig. 6 we obtain R m = 5.05 × 10 ~3 m -1, which is 145 times higher than that of the clean membrane filtering pure water, Rrn = 3.5 X 10 ~ m -~. In addition, for the resistance per unit thickness of the oil layer we obtain rp = 2.0 × 1017

m -2. Applying Eq. (3) with the oil density, Po, of 800 kg m -3 and E of 0.5, we obtain an estimate for the specific resistance c~ of 5 × 1014 m kg 1. This estimate can be compared with a value of 2 X 1015 m kg- i obtained from unstirred filtration of a differ- ent cutting oil [7] for which the mean drop sizes were approximately 100 nm. The discrepancy is partly accounted for by differences in mean drop size (150 nm in this study), since c~ is inversely related to the square of the drop size. However, Eq. (6) is strictly valid only for a uniform membrane and oil polarisation layer such that the local flux of permeate is everywhere equal to its average value. If the oil polarisation layer exhibits significant non-uniformi- ties, the use of an average thickness for the oil layer from Eq. (4) can be shown to result in an under- estimate for rp and hence the specific resistance ~. Further discrepancies probably result from uncertain- ties in the relationship between image intensity and oil concentration in the oil-selective images, together with differences in droplet size distribution, surface charge and applied pressure.

Under current operating conditions, with 3 hav- ing a maximum value of a few hundreds of microns, these results imply an oil polarisation layer resis- tance which may be comparable to that of the fouled membrane itself, or two orders of magnitude larger than that of the clean membrane. We were able to confirm that this additional membrane resistance did not arise from a change in fouling, by turning off the flow of feedstock for a short time. The oil polarisa- tion layer dissipated on the timescale of a typical chemical shift selective imaging sequence (about 10

254 J.M. Pope et al. / Journal of Membrane Science 118 (1996) 247-257

rain). On turning the flow on again, the initial flux of filtrate was restored to approximately its original value. It was possible to cycle the membrane through a series of experiments similar to those shown in Fig. 4, with fairly reproducible results.

After the filtration process has reached quasi- steady state conditions, the oil concentration polari- sation layer is in dynamic equilibrium. Consequently the flux of filtrate may be affected by changes in operating conditions, in particular the concentration of the emulsion &, the trans-membrane pressure difference Ap and the crossflow Reynolds number Re, which affect the thickness of the oil polarisation layer 3. In general, according to the concentration polarisation model, for laminar flow of a colloidal solution or suspension in a tube or conduit of circu- lar cross section with porous walls we expect [13]

where ~b and ~w are respectively the concentrations of colloidal particles (or in this case oil emulsion

[ ]

droplets) in the bulk filtrate and at the membrane wall and k is the mass transfer coefficient given by

k = ( s )

Here D is the diffusion coefficient for the oil droplets and ~/ the shear rate at the concentration polarisation boundary layer. This in turn is determined by the crossflow Reynolds number which may be written

pd2~ Re = (9)

2~7

where p and ~ are, respectively, the density and viscosity of the solution/suspension and d is the internal diameter of the conduit (in this case the tubular membrane). Thus if the diffusion coefficient for the oil droplets is determined by Brownian diffu- sion, with D independent of shear rate and given by the Stokes-Einstein relation D = kbT/6~r, where k b is Boltzmann's constant, T the absolute tempera-

O

Jill Fig. 7. A set of oil selective NMR images showing the concentration polarisation oil layer on the membrane surface after the filtration had reached the steady state under different crossflow rates: (a) Re = 1665, (b) Re = 1100, (c) Re = 735, (d) Re = 477, (e) Re = 376 and (f) Re = 110 while the trans-membrane pressure difference was kept at 65 kPa.

J.M. Pope et al . / Journal of Membrane Science 118 (1996) 247-257 255

10

~v

=~ .o

I . . . . . . . . i 100 1000

Reynolds number

10000

Fig. 8. The logarithim of (length averaged) stationary permeate flux (J> versus the logarithm of crossflow Reynolds number Re.

ture and r the (average) radius of the oil droplets, from Eqs. (7)-(9) it follows that the (length aver- aged) permeate flux should vary as the 1 /3 power of the crossflow Reynolds number Re. In contrast for shear enhanced diffusion we expect a diffusion coef- ficient proportional to the shear rate, giving a length averaged flux which varies linearly with Reynolds number [13].

Fig. 7 shows a number of oil selective images obtained under steady state conditions (i.e. after both the thickness and concentration of the oil layer had reached equilibrium), for different values of the crossflow Reynolds number, while the trans-mem- brane pressure difference was kept at 65 kPa. These results clearly show that (1) as expected for a given trans-membrane pressure difference, an increase of crossflow Reynolds number tends to inhibit the es- tablishment of the oil layer and (2) a limiting value of the crossflow Reynolds number was observed for the appearance of oil concentration polarisation lay- ers. In the current study, a value for this critical Reynolds number (Re) c = 1350 was obtained for a trans-membrane pressure difference TMPD = 65 kPa. When the crossflow rate exceeded this value, no oil layer was observed.

Finally, a log-log plot of the length averaged steady state filtrate flux, < J> versus the crossflow Reynolds number, Re, is shown in Fig. 8. From Fig. 8, a value of 0.34 _+ 0.02 for the exponent of the Reynolds number was obtained. This value agrees very well with the 1 /3 power predicted theoretically for laminar flow on the assumption that back diffu- sion of the oil droplets from the polarisation layer is

dominated by Brownian diffusion rather than shear enhanced diffusion. This is consistent with our ex- perimental conditions of relatively small averaged oil droplet size and low shear rates. Davis [13] quotes the ratio of shear induced to Brownian diffusion coefficients as

D s r/~/r 3

Db kbT (10)

For our case, with Re = 1000, this ratio has a value of approximately 0.07. In contrast, for the higher shear rates and particle sizes used by Wandelt et al. [4], we obtain Ds/D b = 2.3, consistent with their observed Reynolds number exponent of between 0.6 and 0.8.

4. Conclusions

In this paper we have demonstrated the potential of the NMR micro-imaging technique for quantita- tive investigation of the oil concentration polarisa- tion layers formed during membrane filtration of an oil-water emulsion. The 2D cross sectional images, obtained by chemical shift selective imaging clearly exhibit details of the establishment of the concentra- tion polarisation layers on the surface of the mem- brane. The thickness of the oil concentration polari- sation layer can thus be measured non-invasively. The specific resistance of the oil layer may then be estimated based on measurements of the thicknesses and intensity of these layers. It should be emphasised that the thickness of the oil layers obtained by NMR, as illustrated here, represents a mean value, averaged over the image slice, at a given axial position along the module. In the analysis of the results to obtain the specific resistance of the polarisation layer, we have assumed this value to be representative of the module as a whole, in order to relate it to the length averaged f u x of permeate ( J > via Eq. (6). Similar results obtained for different axial positions indicate this to be a reasonable approximation in practice. In principle it may be possible, using NMR flow imag- ing techniques [10,11] to obtain a direct measure- ment of the localised flux of permeate at a particular axial position [14] thus making it possible to obtain a more precise, spatially localised value for the spe- cific resistance of the polarisation layers.

256 J.M. Pope et al./ Journal of Membrane Science 118 (1996) 247-257

In our experiments the oil layer was observed to dissipate within seconds or minutes of turning off the flow of feedstock. This was confirmed both by direct observation, using very short imaging times (of ap- proximately 2 min, albeit with rather poor signal to noise S / N ) and by observing the restoration of the initial permeate flux following a short interruption to the flow of feedstock. For these (relatively thick) tubular membranes, we have also been able to ob- serve the build up of an oil signal from within the body of the membrane, as a result of permanent fouling by oil droplets entering the membrane pores. Such fouling leads to a further (long term) increase in membrane resistance and hence loss of flux. In some applications it can (at least partially) be re- moved by back-flushing or the use of solvents or detergents. Thus the MRI technique also has the potential to be employed in investigating both the mechanisms of membrane fouling and subsequent membrane cleaning.

5. List

A A

d

I

J

J6

(J) ni np NS a p

O Re

(Re) c

Re

R m

Rm Rp

rp

of symbols

area of a pixel (picture element) inner diameter of the tubular membrane normalised intensity of the oil layer signal (averaged over the apparent oil layer) intensity of an individual pixel permeate flux initial flux of permeate for a °'well fouled" membrane length averaged permeate flux number of the pixels with intensity 1 i total number of pixels forming the oil layer number of scans for NMR signal averaging trans-membrane pressure drop volumetric crossflow rate crossflow Reynolds number critical crossflow Reynolds number for the observation of the oil layer contribution to membrane resistance from membrane fouling resistance of (unfouled) membrane resistance of the "wel l fouled" membrane resistance of concentration polarisation (oil) layer resistance per unit thickness of concentration polarisation (oil) layer

G z

repetition time for NMR signal acquisition axial position along the filtration module

5.1. Greek symbols

"q

qVb

q~w

P Po

specific resistance of the oil polarisation layer oil polarisation layer thickness voidage of the oil polarisation layer feedstock shear rate at the concentration po- larisation layer viscosity of feed emulsion concentration of oil droplets in the bulk feed- stock concentration of oil droplets at the membrane wall density of feed emulsion density of soluble oil

Acknowledgements

The authors would like to acknowledge the Aus- tralian Research Council for financial support of this project. We also thank V. Chen, M. Costello and J. Wu for helpful discussions.

References

[1] W.S.W. Ho and K.K. Sirkar (Eds.), Membrane Handbook, Van Nostrand Reinhold, New York, 1992.

[2] G. Belfort, Synthetic Membrane Processes, Academic Press, Orlando, FL, 1984.

[3] S. Lee, Y. Aurelle and H. Roques, Concentration polarisa- tion, membrane fouling and cleaning in ultrafiltration of soluble oil, J. Membrane Sci., 19 (1984) 23-38

[4] B. Wandelt, P. Schmitz and D. Houi, Investigation of tran- sient phenomena in crossflow-microfiltration of colloidal sus- pension using NMR micro-imaging, Proc. Sixth World Filtra- tion Congr., Nagoya, 1993, pp. 601-606.

[5] J.G. Wijmans, S. Nakao and C.A. Smolders, Hydrodynamic resistance of concentration polarisation boundary layers in ultrafiltration, J. Membrane Sci., 22 (1985) 117-135

[6] C.A. Romero and R.H. Davis, Transient model of crossflow microfiltration, Chem. Eng. Sci., 45 (1990) 13-25

[7] P. Lipp, C.H. Lee, A.G. Fane and C.J.D. Fell, A fundamental study of the ultrafiltration of oil-water emulsions, J. Mem- brane Sci., 36 (1988) 161-177

[8] S. Yao, M. Costello, A.G. Fane and J.M. Pope, Non-invasive observation of flow profiles and polarisation layers in hollow

J.M. Pope et al. / Journal of Membrane Science 118 (1996) 247-257 257

fibre membrane filtration modules using NMR micro-imag- ing, J. Membrane Sci., 99 (1995) 207-216

[9] H. Rumpel and J.M. Pope, Chemical shift contrasting in magnetic resonance imaging: a comparison of different meth- ods, Concepts Magn. Reson., 5 (1993) 43-55

[10] P.T. Callaghan and Y. Xia, Velocity and diffusion imaging in dynamic NMR microscopy, J. Magn. Reson., 91 (1991) 326-352

[11] J.M. Pope and S. Yao, Quantitative NMR imaging of flow, Concepts Magn. Reson., 5 (1993) 281-302

[12] S. Yao, A.G. Fane and J.M. Pope, An investigation of the fluidity of concentration polarisation layers in crossflow membrane filtration of an oil-water emulsion using chemical shift selective flow imaging, submitted.

[13] R.H. Davis, Theory for crossflow microfiltration, in W.S.W. Ho and K.K. Sirkar (Eds.), Membrane Handbook, Van Nos- trand Reinhold, New York, 1992.

[14] S. Yao, NMR Flow Micro-imaging: With Applications to Studies of Membrane Filtration Modules, Ph.D Thesis, UNSW, 1995.