NMR imaging of local cumulative permeate flux and local cake growth in submerged microfiltration processes

Journal of Membrane Science 371 (2011) 52–64

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NMR imaging of local cumulative permeate flux and local cake growth in submerged microfiltration processes Steffen Buetehorn a,∗ , Lavinia Utiu b,1 , Markus Küppers b , Bernhard Blümich b , Thomas Wintgens a,c , Matthias Wessling a , Thomas Melin a a b c

Chemical Process Engineering - AVT.CVT, RWTH Aachen University, Turmstraße 46, 52056 Aachen, Germany Macromolecular Chemistry - ITMC, RWTH Aachen University, Worringerweg 1, 52056 Aachen, Germany Institute for Ecopreneurship - IEC, University of Applied Sciences Northwestern Switzerland, Gruendenstrasse 40, CH-4132 Muttenz, Switzerland

a r t i c l e

i n f o

Article history: Received 9 September 2010 Received in revised form 12 January 2011 Accepted 13 January 2011 Available online 22 January 2011 Keywords: Submerged microfiltration Colloidal silica Local cumulative permeate flux Cake growth Cake removal Nuclear magnetic resonance (NMR) imaging

a b s t r a c t Microfiltration processes are frequently used for rejecting dispersed solid matter from biological suspensions such as activated sludge. Previous studies in the field of these so-called membrane bioreactors (MBRs) have shown that the cake formation is self-accelerating for a submerged filtration at imposed flux. This means that the local permeation is reduced where the local cake layer is relatively thick, which is compensated by an enhanced filtration in regions with thinner cakes. Hence, a permeate flux distribution and a transient non-uniform cake growth are occurring along the membrane and were investigated by nuclear magnetic resonance (NMR) imaging in the framework of this study. The investigations have shown that the local cumulative permeate flux increases linearly with a decrease in vertical distance from the point of permeate extraction. This results in thicker cake layers in the vicinity of the permeate line. The cake growth rate was found to increase as the setpoint permeate flux increases or the solids concentration increases. The efficiency of cake removal due to air bubbling was higher in case of higher aeration pressures and longer aeration sequences. The impact of aeration pressure on the cleaning efficiency levels off for longer aeration cycles. Nevertheless, an increase in duration of aeration in the range of lower aeration pressures was consistently followed by a reduction in local cake layer thickness. This suggests that critical aeration conditions might exist. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Nuclear magnetic resonance (NMR) imaging is known as a powerful tool for a non-invasive observation of synthetic membrane processes [1–3]. Typical applications include the visualisation of shell-side nutrient supply in bioreactors [4,5], the flow distribution in hollow-fibre reactors [6,7] and hemodialyzers [8–10], dean vortices as a strategy to control concentration polarisation [11], mass transfer enhancement due to spacers [9,12,13] or baffles [12,14] as well as gas-liquid flow in porous media [15]. Moreover, flow patterns in the lumen of tubular membrane configurations were investigated with NMR by a number of research groups [16]. Pangrle et al. [17] estimated the desired axial flow velocity in the membrane lumen by measuring the feed flow rate and assuming a parabolic (i.e. laminar) velocity profile. It was observed that the lumen-side velocity decreases with increasing distance

∗ Corresponding author. Tel.: +49 241 80 95994; fax: +49 241 80 92252. E-mail addresses: [email protected] (S. Buetehorn), [email protected] (L. Utiu). 1 Tel.: +49 241 80 26449; fax: +49 241 80 22185. 0376-7388/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.memsci.2011.01.018

from the inlet (inside-out filtration), which was attributed to permeate extraction along the membrane. Using a similar approach suggested by Laukemper-Ostendorf et al. [9], Hardy et al. [10] measured the maximum flow velocity and calculated variations in local filtration rate at different axial positions (inside-out filtration). The authors attributed the linear decrease in local filtration rate with increasing distance from the inlet to a decrease in TMP due to lumen-side pressure losses. NMR imaging was also applied to visualise concentration polarisation and cake-layer formation in membrane filtration processes. As model substances, oil–water emulsions [18–21] and suspensions containing clay particles [22], bentonite particles [23,24], iron (III) oxide particles [25] and colloidal silica particles [26] were used. Schmitz et al. [23] and Wandelt et al. [24] observed an erosion of bentonite particles, thinner cake layers and a decrease in cake porosity due to an enhanced cross-flow. As a follow up of these efforts, Fane and co-workers used NMR imaging techniques to visualise the filtration of oil–water emulsions [18–21]. A series of NMR measurements during the transient filtration stage was capable of monitoring the evolution of oil-layer growth and oil concentration changes in the layer [21]. They found that the decline in average permeate flux corresponds to an increase in oil-layer thickness and

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an increase in oil concentration in the layer. The oil polarisation layer was thicker where surface shear due to the cross-flow was lower [18]. Although maximum feed velocities of up to 45 mm/s were measured, a flow of the oil layer induced by the bulk-phase flow was not detectable [18–20]. Airey et al. [26] investigated cakelayer formation in inside-out cross-flow filtration of colloidal silica at constant transmembrane pressure difference (TMP) with a single tubular membrane. It was shown that an asymmetric cake layer was formed during the filtration, which was due to buoyancy effects in the horizontal test cell. The maximum thickness of the cake layer was chosen as an indicator for the influence of operating parameters on the filtration performance. It was observed that the maximum cake thickness increases as the permeate flux decreases with time until steady-state conditions are reached. The maximum cake thickness and the time to reach steady-state were found to decrease as the cross-flow velocity increases. An increase in TMP led to an increase in maximum cake layer thickness. Variations in horizontal position of the setup indicated that the maximum cake thickness increases with increasing distance from the inlet and reaches a plateau. In contrast to the above filtration of an oil–water emulsion conducted by the same group, a significant movement of the silica layer induced by the tangential flow was observable. The NMR investigations presented in the paper at hand focus on a submerged outside-in microfiltration of colloidal silica particles using a single hollow-fibre membrane. The permeate flow in the lumen and the cake layer formed on the surface were visualised at different vertical positions along the fibre. In contrast to previous studies [26], the average instead of the maximum cake layer thickness was determined from two-dimensional images. To the best of our knowledge, our investigations are the first NMR study to evaluate the impact of setpoint permeate flux and solids concentration on the cake growth as well as the impact of aeration pressure and duration of aeration on the cake-layer removal. The spatial- and time-resolution of velocity and cake-growth measurements allow monitoring transient phenomena such as the self-accelerating nature of cake build-up in submerged microfiltration. 2. Materials and methods 2.1. Hollow-fibre membranes For both velocity and cake-growth studies, hollow-fibre membranes of the PURON® configuration were provided by Koch Membrane Systems GmbH. The single fibres were cut to 1 m long sections. They show an outer diameter of do,HF = 2.6 mm and a hydraulic internal diameter of di,HF = 1.7 mm (see Section 2.4.1). The polyether sulphone (PES) membrane shows a nominal pore diameter of 50 nm and is supported by a polyester tissue [27]. Besides these technical data provided by the supplier, additional investigations have shown that the pure water permeability of a washed membrane sample is in the range of 1400 L/(m2 h bar). The removal of dextran (dxtb2000, Polymer Standards Service) was relatively low (maximum rejection < 60%), thus indicating an open pore structure in the active separation layer as confirmed by scanning electron microscopy (SEM) images. Moreover, zeta-potential measurements have shown that the membrane samples are negatively charged for a pH in-between 3 and 10. Further details on the membrane characteristics are given by Buetehorn et al. [28]. 2.2. Model suspension Alkaline, aqueous dispersions of amorphous colloids of spherical shape were used for the cake formation studies to ensure stable and reproducible conditions. The silica (SiO2 ) stock dispersion

53

Bypass

Deaeration valve

PI

Inlet

TI

Peristaltic pump

Balance

Permeate line

Buffer tank y Hollow-fibre membrane

Measurement range

Data logging

L=1m

Test cell

Outlet Fig. 1. Schematic of the NMR test rig.

BINDZIL® 9950 was provided by eka Akzo Nobel with a solids concentration of 31.8 vol.%, a specific surface area of 80 m2 /g, a pH of 9 and a density of 1.4 kg/L [29]. Furthermore, the stock dispersion contains 0.1 wt.% of Na2 O and small amounts of sodium chlorite as a biocide. The desired solids concentrations for the filtration tests (i.e. 0.2, 0.4 and 0.6 vol.%) were adjusted by adding deionised water to the stock dispersion. This causes the pH to further increase to about 10 due to a reaction of Na2 O and water. The particle size distribution was relatively narrow, with an average particle size in the range of 85.7 nm and slight deviations for different solids concentrations only. Settling of particles from the bulk phase was not observed in filtration experiments lasting for up to 8.5 h. Moreover, zetapotential measurements indicated a negative surface charge of the particles. This suggests that neither particle aggregation nor particle adsorption on the negatively charged membrane significantly affect the filtration performance. Rheological investigations proved that the model suspension shows shear-thinning characteristics, i.e. the apparent viscosity decreased with increasing shear rate. An increase in solids concentration caused an increase in apparent viscosity. Previous studies conducted by Rosenberger et al. [30] have shown similar trends for membrane bioreactor (MBR) sludge. More details on the characteristics of the model suspensions are given by Buetehorn et al. [31]. 2.3. Experimental setup and test protocol The test rig schematically shown in Fig. 1 was built for both permeate-flow and cake-formation visualisation studies. The setup consists of a flexible tube of 8 mm internal diameter and 2 m in length, which serves as the shell of the test cell filled with stagnant feed (water or silica suspension). A continuous feed supply is permitted by gravity flow from a buffer tank into the test cell. The cell is equipped with a single quasi-tight hollow-fibre, which is sealed at the bottom and is connected to the permeate extraction line at the top end using heat shrink tubing. A pressure transducer (STS, series ATM) and a thermocouple (DIN IEC 584, type K) in the permeate line are connected to a data logging system (DASYLab 10.0.0) to measure the filtration parameters online. The setup was operated with constant setpoint permeate flux in

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submerged outside-in mode. A balance (ACCULAB, ALC-3100.2) allows online permeate flux monitoring and a remote control of the rotation speed of the peristaltic pump (ISMATEC MCP Standard, ISM 734B pump head, MASTERFLEX 06409-13 TYGON pump tubing). For comparative experiments, the vertical position of the entire setup can be manually adjusted between y = 0 cm and a maximum distance of y = 40 cm from the point of permeate extraction (see Fig. 1). The permeate-flow visualisation was conducted with 1 g/L of copper sulphate (CuSO4 ) dissolved in deionised water. The addition of this substance reduces the longitudinal relaxation time T1 of the water protons and shortens the duration of an NMR measurement. However, adding CuSO4 to the silica suspension causes particle settling, so that combined studies of cake formation and permeate flow were not performed at this stage of investigations. Prior to the silica filtration tests, the membranes were washed with deionised water for approximately 1 h. The pure water permeability (PWP) was measured as an integrity check. The reference (feed) pressure was measured before the filtration was initiated using the transducer in the permeate line. The measured TMP evolution was corrected for T = 20 ◦ C. A final TMP of 800 mbar was chosen as an abort criterion. A virgin membrane and fresh silica suspension were used for every single test run. Permeate backwashing was not involved in the filtration sequence. The impact of air bubbling on the removal of the cake layer was investigated. For this purpose, the outlet valve was connected to a central pressurised air line. A continuous or intermittent aeration during the NMR measurement is not feasible since intensive fluid motion negatively affects the cake-to-bulk contrast. Therefore, three aeration cycles with continuous filtration were performed in-between the NMR measurements. The aeration sequence was initiated after a filtration period of 35 min without aeration. Subsequent to this, the NMR measurements were interrupted and a single aeration cycle with an air pressure of 0.3 or 0.5 bar (air flow rates were not measurable at this stage) and a duration of 30 or 60 s was conducted. A dead time of 30 s before and after an aeration cycle was provided to control the aeration device manually. Each aeration cycle was followed by a single NMR measurement before the next aeration cycle started. 2.4. NMR imaging NMR imaging allows monitoring the composition of a sample by measuring the distribution of mobile protons in any slice of the specimen [2]. For this purpose, the entire shell of the test rig is exposed to a static magnetic field, so that the protons (i.e. the 1 H hydrogen nuclei) align with the field. Afterwards, a radio frequency pulse is applied, which creates an oscillating magnetic field from the proton magnetisation perpendicular to the main field. The protons reach an excited state when absorbing energy from the oscillating field. A signal is detected by the receiver coil when the protons return from excitation back to equilibrium. This signal is a function of the individual relaxation properties of the components of the specimen and is transformed to images weighted by the longitudinal (T1 ) or transverse relaxation time (T2 ). All NMR measurements were performed on a Bruker DSX 200 spectrometer with a field strength of 4.7 T. The spectrometer has a vertical bore of 89 mm in diameter and is equipped with an (x,y,z)-imaging system with a maximum gradient strength of about 1 T/m. For excitation and signal detection, a 20 mm standard birdcage coil was used and operated at a 1 H resonance frequency of 200.047 MHz. The measurements were performed at room temperature (T = 20 ◦ C). They are sub-divided into two categories, (i) dynamic imaging of permeate flow in the membrane lumen and (ii) static imaging of cake layer formation on the membrane surface. The parameter settings for the two different pulse sequences

Fig. 2. Axial permeate velocity distribution inside the lumen of a single hollow-fibre (J = 30 L/(m2 h), c (CuSO4 ) = 1 g/L).

are summarised in Table 1. A brief introduction to the velocityencoding pulse sequence and the cake-visualisation pulse sequence is presented in Appendix A. A more detailed description of the NMR background can be found elsewhere [32]. In the following sections, the methodology for processing the velocity and cake formation images is outlined. 2.4.1. Data processing for permeate-flow visualisation The raw velocity data were zero-filled from 32 × 32 × 1 to 64 × 64 × 1 pixels in a field of view (FOV) of 11 mm × 11 mm × 2 mm. This increased the nominal spatial resolution in radial direction from 343.8 to 171.9 ␮m. A subsequent Fourier transformation leads to velocity images taken during pure water filtration under steady-state conditions. Each velocity image represents a slice at a certain distance y from the point of permeate extraction. The velocity data characterises the flow averaged over a data acquisition time of 04:30 mm:ss. The axial flow in the feed channel and the pore structure is almost zero. Most important is the observation of the permeate flow in the membrane lumen as shown in Fig. 2, which allows an estimation of the permeate flux distribution along the membrane. Since all velocity measurements were restricted to a steady-state pure water filtration without particles, single NMR measurements at different vertical positions y were sufficient to fully capture permeation conditions along the membrane.

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Table 1 NMR settings for permeate-flow and cake-growth visualisation. NMR settings

Velocity pulse sequence

Cake-growth pulse sequence

Sequence type Data acquisition time [mm:ss]

3D phase-encoding Low resolution: 2 × 02:15 High-resolution: 2 × 17:19 1000 7 – 4 11 × 11 × 2 Low-resolution: 32 × 32 × 1 High-resolution: 128 × 128 × 1 Low-resolution: 64 × 64 × 1 High-resolution: 256 × 256 × 1

3D gradient echo 03:25 100 3 45 8 9×9×2 256 × 256 × 1

Spatial resolution before zero-filling (radial) [␮m]

Low-resolution: 343.8 High-resolution: 85.9

35.2

Spatial resolution after zero-filling (radial) [␮m]

Low-resolution: 171.9 High-resolution: 43

17.6

Repetition time (TR) [ms] Echo time (TE) [ms] Flip angle [◦ ] Number of images averaged Field of view (FOV) [mm × mm × mm] Matrix size before zero-filling [pix × pix × pix] Matrix size after zero-filling [pix × pix × pix]

In addition to the above-mentioned standard settings of the velocity-encoding pulse sequence, a small number of more accurate velocity measurements were performed. For these highresolution studies, an image matrix of 128 × 128 × 1 pixels was zero-filled to 256 × 256 × 1 pixels for a field of view (FOV) of 11 mm × 11 mm × 2 mm. This corresponds to a nominal spatial resolution in radial direction of 85.9 respectively 43.0 ␮m. The aim of this additional test series was to examine the accuracy of the previous velocity measurements. These settings significantly increased the duration of an NMR measurement to 34:38 mm:ss. Therefore, the high-resolution pulse sequence is not applicable for monitoring transient flow patterns such as alterations in permeate flux distribution due to cake layer formation. In Fig. 3, high- and low-resolution images and the corresponding velocity profiles are compared. The high-resolution measurement provides a better approximation of the laminar velocity profile. This is indicated by 40 instead of 10 adjacent pixels in the membrane lumen. Therefore, reducing the spatial resolution leads to averaging over wide velocity ranges, which causes a decrease in the maximum value of measured velocities. Moreover, a relatively sharp decline in vertical velocity was observed for the high-resolution images, as compared to a rather smooth decline for the lower resolution. The width of the high-resolution velocity profile consistently equals 1.7 mm for J = 10, 20 and 30 L/(m2 h) at y = 0 cm. This parameter is later-on referred to as the characteristic internal diameter of the hollow-fibre di,HF . It is worth mentioning that di,HF is larger than the internal diameter of the support tissue of about 1.2 mm as claimed by the membrane manufacturer. This discrepancy might be due to a penetration of the axial permeate flow into the porous structure of the support tissue. To validate the measured permeate velocity distribution along the fibre, the inflowing and outflowing streams are balanced over a volume element Am dy according to V˙ y = V˙ y+dy + Javg Am = V˙ y+dy + Javg do,HF dy

 4

and 2 V˙ y+dy = v¯ y+dy di,HF

 , 4

(3)

with the cross-sectional area of the lumen Ai , the average permeate velocity v¯ at the vertical positions y as well as y + dy and the internal diameter of the hollow-fibre di,HF . The average velocity is zero at y = L and equals the product of average permeate flux and the ratio of lateral to cross-sectional area of the membrane at the position y = 0 cm. Hence, the boundary conditions used to solve this differential equation are

v¯ (y = L) = 0

(4)

and

v¯ (y = 0) = Javg

do,HF  L Am = Javg 2  . Ai d

(5)

i,HF 4

Eqs. (1)–(5) lead to a distribution of vertical permeate velocity along the membrane of

v¯ (y) = 4Javg

do,HF 2 di,HF

(L − y),

(6)

for which lumen-side pressure losses were neglected. This simple approximation is aimed at being used for validating the NMR methodology under well-defined conditions of pure water filtration. The velocity data can be further processed by estimating the average flow velocity v¯ from the measured maximum velocity vmax by assuming laminar conditions and parabolic velocity profiles [9,10,17],

v¯ (y) =

1 vmax (y). 2

(7)

Subsequently, the local cumulative permeate flux (1)

In Eq. (1), V˙ y corresponds to the outflowing lumen-side stream (flow in negative y-direction), V˙ y+dy to the inflowing lumen-side stream and Javg Am to the permeating stream. The permeating stream is expressed as the product of average permeate flux Javg and membrane area Am , with the outer diameter of the hollow-fibre do,HF and the infinitesimal distance dy. Using the continuity equation, the lumen-side streams can be described as 2 V˙ y = v¯ y Ai = v¯ y di,HF

512 × 512 × 1

(2)

Jcum (y) = v¯ (y)

 2 di,HF Ai 4 = v¯ (y) Am (y) do,HF (L − y)

(8)

is calculated as the product of average permeate velocity and crosssectional area of the membrane lumen  2 Ai = di,HF (9) 4 divided by the lateral area of the hollow-fibre from the very end (y = L) to the position y, Am (y) = do,HF (L − y).

(10)

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Fig. 3. Velocity images (left) and vertical permeate velocity profiles (right) for high- and low-resolution measurements (J = 30 L/(m2 h), c (CuSO4 ) = 1 g/L, y = 0 cm).

According to Eq. (8), the local cumulative permeate flux equals zero for y = L and equals the average (i.e. setpoint) permeate flux for y = 0 cm. 2.4.2. Data processing for cake-growth visualisation The raw cake-formation data were zero-filled from 256 × 256 × 1 to 512 × 512 × 1 pixels in a field of view (FOV) of 9 mm × 9 mm × 2 mm. This corresponds to an increase in nominal spatial resolution in radial direction from 35.2 to 17.6 ␮m. The images shown in Fig. 4 correspond to an instantaneous cake morphology averaged over a data acquisition time of 03:25 mm:ss. Every single NMR measurement was initiated with a dead time of 7 s and ended with a delay of 10 s before the next measurement started. The signal of the bulk phase and the membrane material is much lower than the signal of the permeate flow, which is an artefact due to rapid fluid motion. A sufficient cake-to-bulk contrast is permitted by significant differences in local particle concentration, which affects the relaxation properties of the water protons [26]. Therefore, the cake layer appears as an annulus of high signal intensity as shown in Fig. 4. These images correspond to the proton density weighted with the longitudinal relaxation time T1 . The data were further processed using a MATLAB® routine to count the pixels representing the cake layer in each image. The cross-sectional area of the cake is calculated as Acake (y) = Npix (y)a2pix ,

(11)

leading to an average cake layer thickness at the vertical position y of ı(y) =

Npix (y)a2pix Acake (y) = , do,HF  do,HF 

(12)

with the number of pixels in the cake layer Npix , the pixel size apix and the outer diameter of the hollow-fibre do,HF . For the derivation of Eq. (12), it was assumed that ı(y)  do,HF ,

(13)

which is valid for all experimental conditions investigated. This data processing was conducted for the second of three adjacent measured slices (2 mm slice thickness, 3 mm inter-slice distance). If severe image artefacts were observed in the second slice, one of the two other slices was chosen instead.

Fig. 4. Evolution of cake layer formation on the outer membrane surface (J = 20 L/(m2 h), c (SiO2 ) = 0.4 vol.%, y = 0 cm).

S. Buetehorn et al. / Journal of Membrane Science 371 (2011) 52–64

57

100

v (max) [mm/s]

80

60

40

30 20

20

10 0

0

10

20

30

40

60

70

80

90

100

Position y [cm] Fig. 5. Comparison of experimental results (data points) and the simplified model (curves): maximum permeate velocity as a function of vertical position and average permeate flux (J = 10–30 L/(m2 h), di,HF = 1.7 mm, vmax = 2.15 vavg , c (CuSO4 ) = 1 g/L).

3.1. Determination of permeate flux distribution 3.1.1. Velocity profile along the membrane In Fig. 5, the measured maximum permeate velocity is plotted as a function of vertical position and average permeate flux for all parameter combinations investigated. It was found that an increase in average permeate flux causes the maximum velocity to increase linearly. An increase in distance from the point of permeate extraction leads to a linear decrease in maximum permeate velocity. The latter trend is caused by an acceleration of lumen-side permeate flow due to an accumulation of permeate collected from the fibre end (y = L) towards to the point of permeate extraction (y = 0 cm). Moreover, the linear velocity profile indicates that the lumen-side pressure loss is lower than the pressure loss experienced by the liquid permeating through the pore structure. This observation is in agreement with previous findings reported by Pangrle et al. [17]. Each experiment was repeated three times with a measurement error of 1.5% on average and 7.1% maximum. It is known that the permeate velocity drops to zero at y = L = 1 m, which is confirmed by an extrapolation of the experimental results with an average deviation of 7.6% and a maximum deviation of 9.0% (results not shown). These discrepancies are presumably due to slight variations in effective membrane lengths and an insufficient positioning of the experimental setup for y = / 0 cm. The investigations indicated that the ratio of maximum and average permeate velocity equals 2.15 for the low-resolution measurements,

 vmax   v¯

low-resolution

= 2.15.

(14)

A factor of 2 characterises a laminar flow in circular tubes, see Eq. (7). This slight deviation from the parabolic velocity profile is presumably due to a flow channel partially blocked by the porous support tissue. Nevertheless, Re numbers of less than 55 clearly indicate a laminar permeate flow. It is worth mentioning that the ratio according to Eq. (14) equals 2.79 for the high-resolution measurements, which provides evidence for the loss of information when analysing low- instead of high-resolution images. The predicted maximum velocity profiles along the fibre according to Eq. (6) are compared to the measured maximum velocity data points in Fig. 5. It was found that the model slightly underestimates the measured velocities. This discrepancy might be due to the fact that the lumen-side pressure loss was neglected for the derivation of the simplified model. This pressure loss leads to a

decrease in permeate pressure from the fibre end towards the point of permeate extraction and causes an increase in local TMP. For this reason, higher driving forces close to the point of permeate extraction are occurring, which are not represented by the simplified model. Nevertheless, relative deviations of 4.4% on average and a maximum deviation of 9.8% indicate an acceptable agreement with experimental data. 3.1.2. Estimation of local cumulative permeate flux The local cumulative permeate flux Jcum can be estimated from the distribution of average permeate velocity along the membrane according to Eq. (8). This parameter equals the average (i.e. setpoint) permeate flux Javg at the position y = 0 cm, / f (y). Jcum (y = 0) = Javg =

(15)

Jcum is plotted as a function of vertical position and average permeate flux in Fig. 6. It is shown that an increase in average permeate flux or a decrease in distance from the point of permeate extraction is followed by an increase in Jcum . The negative slope of the curves increases as the average permeate flux increases, with the steepest slope of −0.05 L/(m2 h cm) occurring for Javg = 30 L/(m2 h). This corresponds to a maximum flux decline of 2 L/(m2 h) along a membrane of 40 cm in length. These 50

40

J (cum) (y) [LMH]

3. Results and discussion

30

30 25

20

20 15 10

10

0

0

10

20

30

40

Position y [cm] Fig. 6. Local cumulative permeate flux as a function of vertical position and average permeate flux with linear trend lines (Javg = 10–30 L/(m2 h), di,HF = 1.7 mm, vmax = 2.15 vavg , c (CuSO4 ) = 1 g/L).

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1.0

TMP (T = 20 °C) [bar]

0.8

0.6

0.4

0.2

0.0 0

10

20

30

40

Time t [min] Fig. 7. Reproducibility of results: evolution of TMP for three different test runs (J = 20 L/(m2 h), c (SiO2 ) = 0.4 vol.%, y = 0 cm).

trends indicate that lumen-side pressure losses affect the permeate flux distribution for a steady-state filtration of pure water. Similar trends were previously observed by Hardy et al. [10]. In addition to that, the local cumulative permeate flux estimated for the position y = 0 cm is on average 6.9% higher than the pump-controlled permeate flux. This might be due to a smaller effective membrane area resulting in higher actual flux values. 3.2. Cake-growth determination Before evaluating the impact of operating parameters on the microfiltration performance, the methodology of NMR data processing was established by conducting a reproducibility study. The corresponding TMP rise for three test runs under the same conditions is plotted in Fig. 7. The filtration performance is characterised by an increase in TMP rise in the first part of the experiment, whereas the TMP slope levels off during a second filtration stage. This decrease in fouling rate dTMP/dt is presumably attributed to gravity and back-diffusion, which counteract drag forces caused by the permeating liquid. For a filtration with hollow-fibre membranes at imposed permeate flux, the feed flow passes through concentric lateral areas. These areas are getting smaller as the flow approaches the membrane, so that the curvature of the fibre results in an acceleration of feed flow. Gravitational forces and diffusion gain more relevance as the cake layer thickness increases and drag forces weaken due to a decline in radial flow velocity. This reduction in deposition-enhancing forces is followed by a more pronounced particle removal. Therefore, the inflexion point of the function TMP = f(t) indicates if particle deposition dominates (first filtration stage) or if the removal of particles or particle aggregates from the cake layer is governing (second filtration stage). In addition to that, a constant particle deposition on curved surfaces is characterised by a decreasing cake growth rate with time. This is due to a smaller cake growth increment for a continuously increasing effective membrane area (membrane + growing deposition layer) and is therefore an effect complementary to the enhanced particle back-transport for thicker cakes. NMR cake formation images were processed following the strategy described in the materials and methods section. The resulting cake thickness versus time for three different test runs under the same conditions is plotted at the top-left of Fig. 8. The cake thickness is measurable after about 5.5 min of filtration. This delay might be due to both limitations in spatial resolution and/or a transition

from concentration polarisation (not detectable) to particle deposition (detectable) at a critical concentration in the boundary layer. The cake thickness continuously increases and the cake growth rate decreases during the experiment, which is in good agreement with the TMP evolutions. A logarithmic trend line fits the measured cake height evolution best. Larger fluctuations in cake layer thickness were observed for TMP > 600 mbar, which might be due to thicker cakes and less pronounced drag forces at the end of the experiment. The interrelationship between TMP (integral measurement) and cake-layer thickness (local measurement at position y) is shown at the top-right of Fig. 8. The TMP increases exponentially as the cake thickness increases. In addition to cake formation due to particle deposition only, also cake compaction might occur. In the following sections, the term “cake compaction” represents cake compression, particle migration and an infiltration of smaller particles into the existing cake structure, which reduce the cake porosity. These phenomena would explain the increasing slope with increasing cake thickness. Alternatively, an initial cake build-up close to the point of permeate extraction and a delayed cake build-up closer to the fibre end or a continuously reducing growth rate of cakes forming on curved surfaces might cause the exponential rise. At the bottom of Fig. 8, the ratio of TMP (integral measurement) divided by the corresponding cake thickness (local measurement at position y) is plotted versus time. This parameter is later on referred to as TMP/cake-height ratio and describes the TMP required to overcome 1 ␮m of cake thickness at the vertical position y. Therefore, the evolution of this ratio characterises the dynamics of cake formation. The trend line shows a linear increase in TMP/cake-height ratio with time. This indicates that the cake was either compacted, was predominantly formed in other parts of the membrane at the end of the experiment or that the cake growth rate was reduced as the deposition layer continuously grows on the curved membrane surface. However, an isolation of these three phenomena is unfeasible since changes in local cake porosity or local permeate flux are not detectable with the current NMR approach. These outcomes indicate an acceptable reproducibility of results for both TMP rise and cake-layer formation. The cake growth was represented best by (i) a logarithmic trend line for the evolution of cake thickness, (ii) an exponential trend line for the TMP as a function of cake thickness and (iii) a linear trend line for the evolution of the TMP/cake-height ratio. Therefore, the same regression lines will be applied for all subsequent data processing to allow for a better comparability of results. 3.2.1. Distribution of cake properties along the membrane A number of researchers have found that cake-layer formation in microfiltration processes occurs non-uniformly along the membrane [33–36]. This is due to alterations in local particle deposition rate, which leads to a higher filtration resistance where the cake layer is thicker. The evolution of cake thickness at three different vertical positions is presented in Fig. 9. It is observed that the data points scatter more for positions y = / 0 cm. One explanation could be the fact that the membrane orientation in the test cell is not straight, so that the membrane touches the inner wall in an uncontrolled manner. This membrane-wall contact is inhibited at y = 0 cm where the membrane is fixed with glue, which serves as a spacer and leads to a better reproducibility of results. The experimental setup will be further improved to allow for a precise positioning of the fibre inside the test cell and an automatic positioning of the test rig relative to the measurement slice. Nevertheless, qualitative conclusions can be drawn despite this scatter of data points for y = / 0 cm. The cake layer at y = 0 cm appears to be thicker than at the other positions during the entire experiment and for the whole range of TMP. Only marginal differences in cake growth were found when comparing the vertical positions y = 20 and 40 cm. The characteristic time span to reach a

S. Buetehorn et al. / Journal of Membrane Science 371 (2011) 52–64

140

59

1.0

0.8 100

TMP [bar]

Cake thickness δ [µm]

120

80 60

0.6

0.4

40 0.2

20 0 0

10

20

30

0.0

40

0

20

40

60

80

100

120

140

Cake thickness δ [µm]

Time t [min]

Ratio TMP/ δ [mbar/µm]

12 10 8 6 4 2 0 0

10

20

30

40

Time t [min] Fig. 8. Evolution of cake-layer thickness with a logarithmic trend line (top-left), TMP versus cake layer thickness with an exponential trend line (top-right) and evolution of TMP/cake-height ratio with a linear trend line (bottom) (data points of three different test runs, J = 20 L/(m2 h), c (SiO2 ) = 0.4 vol.%, y = 0 cm).

certain cake thickness suggests that the cake is formed next to the point of permeate extraction first, with a delayed cake growth towards the end of the fibre. However, detailed knowledge about local cake-porosity changes and transients in local permeate flux are still lacking, so that a comprehensive prediction of the nonuniformity of cake growth along the membrane is difficult at this stage.

140

Cake thickness δ [µm]

120

0 20

100

40

80 60 40 20 0 0

10

20

30

40

Time t [min] Fig. 9. Evolution of cake-layer thickness for three different vertical positions (J = 20 L/(m2 h), c (SiO2 ) = 0.4 vol.%, y = 0–40 cm).

3.2.2. Impact of average permeate flux and solids concentration The TMP as a function of deposited particle volume is presented in Fig. 10 for different permeate flux values and solids concentrations. The results indicate that two filtration stages are observable. The first stage is characterised by an increase of the slope dTMP/dV(SiO2 ), whereas the slope levels off in the second stage of filtration. Moreover, an increase in average permeate flux leads to a significant increase in dTMP/dV(SiO2 ). This trend is due to more pronounced compressive pressure in the cake, which may enhance cake compaction. In contrast to this, similar slopes for all three solids concentrations do not provide evidence for enhanced cake compaction as the solids concentration increases. Nevertheless, the TMP was found to rise faster with time in the range of higher solids concentrations (results not shown). The corresponding cake growth rates were estimated as the time required to reach an arbitrary threshold of 50 ␮m cake thickness and are summarised in Table 2. The characteristic time span decreases as the permeate flux or the solids concentration increases. This relationship is consistent with the integral monitoring of TMP evolution and is due to higher particle deposition rates and rapid cake build-up. It is worth mentioning that the cake thickness values scattered severely at the end of the experiment. This scatter is more pronounced for low permeate flux values and low solids concentrations, i.e. in the range of lower compressive pressure in the cake. 3.2.3. Efficiency of air bubbling In submerged microfiltration processes, flow is induced by air bubbles to generate shear at the membrane surface to partly

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1.0

1.0 30

25

20

15

10

0.8

TMP (T = 20 °C) [bar]

TMP (T = 20 °C) [bar]

0.8

0.6

0.4

0.2

0.0 0.0

0.3

0.6

0.9

1.2

1.5

0.6 0.2 0.4

0.4 0.6

0.2

0.0 0.0

0.1

0.2

0.3

0.4

0.5

V (SiO2) [cm^3]

V (SiO2) [cm^3]

Fig. 10. TMP as a function of deposited particle volume and average permeate flux (J = 10–30 L/(m2 h), c (SiO2 ) = 0.4 vol.%) (left) or solids concentration (c (SiO2 ) = 0.2–0.6 vol.%, J = 20 L/(m2 h)) (right). Table 2 Time to reach 50 ␮m cake thickness as a function of average permeate flux and solids concentration (y = 0 cm). Javg [LMH]

10 15 20 25 30

c (SiO2 ) [vol.%] 0.2

0.4

Time to reach ı = 50 ␮m [min] 325.0 56.1 49.5 31.2 17.8

44.3 35.3 14.1 15.6 9.5

0.6

32.2 16.9 13.7 12.8 5.4

remove the cake layer. In this study, the efficiency of cake-layer removal is expressed as the cake thickness divided by its initial thickness after 35 min of filtration. The removal efficiency after 1, 2 and 3 consecutive aeration cycles with continuous filtration is presented in Table 3, see Section 2.3 for more details concerning the aeration sequence. In general, it was found that cake removal is enhanced as the aeration pressure or the duration of aeration increases, see below for more details. • Aerating for 30 s at 0.3 bar relative air pressure causes a gradual decrease in cake thickness after 1, 2 or 3 consecutive aeration cycles. While the cake thickness observed after the first cycle does not provide evidence for cake-layer removal, the second and third cycle cause a significant decrease in cake height.

Table 3 Cake thickness after each aeration cycle relative to the initial thickness after 35 min of filtration as a function of aeration pressure and duration of aeration (J = 20 L/(m2 h), c (SiO2 ) = 0.4 vol.%, y = 0 cm). Duration of aeration [s ON]

Time of measurement

Aeration pressure [bar] 0.3

0.5

30

After filtration After cycle 1 After cycle 2 After cycle 3

Cake thickness/initial cake thickness [%] 100.0 100.0 100.7 66.7 81.0 70.6 73.7 71.3

60

After filtration After cycle 1 After cycle 2 After cycle 3

100.0 63.9 55.3 68.9

100.0 64.3 59.1 48.2

• Increasing the duration of aeration from 30 to 60 s leads to a rapid decrease in cake thickness after the first cycle, whereas less benefit is due to the subsequent aeration steps. • Increasing the aeration pressure from 0.3 to 0.5 bar with a cycle duration of 30 s indicates a more efficient cake removal due to the first aeration cycle, as compared to no removal for the lower aeration pressure. Once more, the second and third aeration steps did not contribute significantly to any further cake removal. • Regarding the first aeration cycle, longer aeration periods of 60 s with an air pressure of 0.5 bar did not lead to any significant difference in cake removal compared to shorter aeration cycles of 30 s. Nevertheless, a slight gradual decline in cake thickness was due to cycles 2 and 3 for the longer aeration period at 0.5 bar.

These outcomes suggest that a critical aeration pressure might exist, above which a single and relatively short aeration cycle leads to a removal of more than 30% of the initial cake layer thickness. Aeration sequences with pressures below this value require more than just one aeration cycle to achieve similar removal efficiencies. Moreover, as long as the aeration pressure is above this critical value, the filtration performance is less sensitive to variations in duration of aeration. These observations are in qualitative agreement with previous findings that a critical aeration rate for enhancing the filtration performance exists [37]. The TMP evolutions corresponding to the four different aeration strategies are presented in Fig. 11. The first part of the curves is equivalent to the two-stage cake formation introduced in the previous sections. The second part is characterised by fluctuations in TMP in response to surface shear due to air bubbling. The amplitude of these fluctuations becomes larger as the aeration pressure or the duration of aeration increases. This observation is consistent with the above cake removal determination. Interestingly, the gradual decrease in local cake thickness observed for an aeration with 0.3 bar for 30 s is less pronounced in the integral TMP evolution. Moreover, a pronounced gradual TMP recovery for an aeration with 0.3 bar for 60 s respectively with 0.5 bar for 30 s was measured, which was in both cases not accompanied with a corresponding gradual cake removal at y = 0 cm. The most significant gradual decrease in TMP was observed for an aeration with 0.5 bar for 60 s, for which a significant removal due to the first aeration cycle and only a slight gradual removal due to aeration cycles 2 and 3 was measured. These discrepancies further demonstrate limitations in evaluating local cake growth and removal without knowledge about the distribution of these properties along the membrane.

S. Buetehorn et al. / Journal of Membrane Science 371 (2011) 52–64

1.0

principle. The upcoming studies based on the novel pulse sequence, however, are expected to provide detailed insights into highly transient and heterogeneous cake-growth patterns, which are not detectable with conventional monitoring techniques. For this reason, NMR imaging will be applied as a powerful tool for a noninvasive observation of self-acceleration phenomena in submerged microfiltration processes at imposed permeate flux.

With aeration

Without aeration

TMP (T = 20 °C) [bar]

0.8

0.6

0.4

0.3 bar, 30 s

Acknowledgements

0.3 bar, 60 s

The authors thank eka Akzo Nobel for providing the silica suspension, Koch Membrane Systems GmbH for providing the hollow-fibre membranes and all student research assistants for their fruitful contributions to this project. Financial support of the German Research Foundation (DFG) is acknowledged. These investigations were part of the PATHFINDER project “Visualisation of Cake Layer Formation and Pore Blocking in Microfiltration Processes using Magnetic Resonance Tomography (MRT)” in the framework of the “Exploratory Research Space @ RWTH Aachen (ERS)”.

0.5 bar, 30 s

0.2

0.5 bar, 60 s 0.0

0

61

20

40

60

Time t [min] Fig. 11. TMP evolutions for four different aeration sequences (J = 20 L/(m2 h), c (SiO2 ) = 0.4 vol.%).

Appendix A. 4. Conclusions and outlook NMR imaging was applied to non-invasively visualise the distribution of local permeate flux and local cake growth for a microfiltration of silica suspensions. A single fibre test rig was operated in submerged outside-in mode at constant permeate flux. It was found that the distribution of local cumulative permeate flux varies as a function of setpoint permeate flux and vertical position y. This was observed for a filtration of pure water without particles and indicates the significance of lumen-side pressure loss on the filtration performance. For a submerged filtration of model suspensions containing colloidal silica, the formation of heterogeneous cakes of greater thickness close to the permeate extraction were observed. The cake-growth rate was found to increase as the permeate flux or the solids concentration increases. The cake-removal efficiency due to air bubbling was enhanced with an increase in aeration pressure or duration of aeration. These very first aeration studies suggest that a critical aeration pressure concerning the efficiency of a single and relatively short aeration cycle might exist. The microscopic visualisation of the filtration process was in good agreement with an integral monitoring of TMP evolution. The results indicate that gravity-driven and/or diffusive backtransport of deposited particles gain more relevance as the cake thickness increases. Efforts are currently under way in collaboration with the University of Twente (Enschede, The Netherlands) to evaluate the impact of diffusive back-transport of deposited particles on the cake-layer formation [38]. Cake compaction resulting from an increase in solid compressive pressure might occur as the cake layer grows, but was not detectable with the current NMR approach. Therefore, a novel pulse sequence will be used in future studies to capture permeation and cake formation simultaneously combined with online-monitoring of cake porosity alterations. For the latter aspect, an improved cake-to-bulk image contrast by avoiding fluctuations in background noise is desirable to observe cake compaction phenomena. In addition to that, the positioning of the membrane inside the test cell and of the entire test rig relative to the stationary NMR device will be optimised. Moreover, the aeration device will be extended to allow for an operation under more defined conditions (bubble size, air flow rate, duration of aeration and aeration frequency). The NMR results presented in this paper are consistent with an integral monitoring of the filtration performance or simple modelling approaches and are therefore interpreted as a proof of

A.1. Velocity-encoding pulse sequence It is known that the convective or diffusive displacements of nuclear spins in the presence of a magnetic field gradient alter the phase or amplitude of the NMR signal. This interrelationship can be combined with conventional NMR imaging (NMRI) to obtain velocity images [39]. Different flow imaging methods were suggested by a number of research groups [39–41] and can be classified as follows [41]. • Inflow/outflow methods make use of the fact that the signal intensity changes if a spin moves into or out of a selected measurement slice. • Time of flight (TOF) methods can monitor different velocity components based on a frequency-encoding technique. • Phase-encoding methods as applied in this study make use of phase shifts induced by the motion of spins to measure flow velocities directly. Both the image and the velocity information from an NMR measurement rely on the same principle of spatially dependent magnetic fields provided by pulsed field gradients (PFGs). In order to obtain a spin density profile such as the image or the velocity information, the space of the measurement volume has to be encoded. For this purpose, a magnetic field with a constant gra is superposed to the static magnetic field of induction dientG   0 = Bx , By , Bz , which can be expressed as B

  = G

∂ Bz ∂ B z ∂ B z , , ∂x ∂y ∂z

 = (Gx , Gy , Gz )

(16)

The velocity-encoding pulse sequence consists of a sliceselective 90◦ radio frequency (RF) pulse in combination with a 180◦ refocusing pulse as shown in the first line of Fig. 12. Gslice , Gphase and Gread are the slice-selective, phase-encoding and frequencyencoding gradients. The echo represents the signal received from the slice of interest in the specimen. In general, the velocity phaseencoding sequence uses a pair of gradient pulses (Gvel ) of opposite sign but identical area (bipolar gradient pair with pulse duration ı and time separation ) to encode velocity information in the phase shift of the signal. The velocity-encoding gradients are applied along the axis of the hollow-fibre membrane and are of the same

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Fig. 12. Schematic representation of the pulse sequence used for permeate-flow visualisation.

sign, since a phase inversion is caused in-between the two gradient pulses by a 180◦ RF pulse. The magnetic moments or “spins” of the proton exposed to the  precess at the Larmor frequency ω associated with the gradient G  0 at the position r, local magnetic field B ω(r) = 

   B 0  + G · r .

(17)

In a stationary fluid, the nuclear spins accumulate a positive phase shift during the first part and an equal negative phase shift during the second part of a bipolar velocity-encoding gradient. Therefore, stationary spins experience a net phase shift of zero. When the fluid flows, spins moving through the specimen are at different locations when applying the bipolar gradients. Moving spins precess at different frequencies and accumulate a non-zero net phase shift. For this reason, the phase shift of the spins corresponds to a time integral of the frequency of precession,



 G(t) · r dt.

(t) = 

(18)

t

 are funcThe position r of the moving spins and the gradient G tions of time, whereas the gyromagnetic ratio  is constant. Using a Taylor series expansion of r with respect to time, Eq. (18) leads to



(t) = 





 G(t) · r0 +

t

1 + n!



dn r dt n



dr dt



t+



t=0

t n dt.

1 2



d2 r dt 2



t2 + . . . t=0

(19)

t=0

Neglecting the second term and all higher-order terms, Eq. (19) simplifies to



(t) =  r0 · t

 dt +  v0 · G(t)



  0 + v0 · m  1 ), (20) G(t)t dt = (r0 · m

t

 1 as the zeroth and first order moments of the  0 and m with m gradient modulation function and v0 = (dr/dt)t=0 as the velocity perpendicular to the measurement slice. Therefore, the signal con 0 ) and tains two phase modulations, one from position-encoding (m  1 ). In order to separate the velocanother from velocity-encoding (m ity information from the spatial information, two pulsed gradient spin echo (PGSE) measurements with different velocity gradient strengths are required. This means that a series of two data sets is measured and separately Fourier-transformed. Subsequently, the phase shift in each pixel is calculated by subtracting the first data set from the second in order to extract the spatial information. This provides a phase shift map which is directly related to the flow velocity perpendicular to the measurement slice. In the resulting velocity

Fig. 13. Schematic representation of the pulse sequence used for cake-growth visualisation.

images, the intensities correspond to the velocity values in each pixel as an average over the data acquisition time. Further details concerning the NMR settings for permeate-flow visualisation are given in Table 1 and by Utiu et al. [32]. A.2. Cake-visualisation pulse sequence In Fig. 13, the gradient echo sequence for cake-growth visualisation is illustrated. The top line shows the RF pulse sent into the sample and the corresponding echo signal. The other three lines show the slice-selection (slice), the phase-encoding (phase) and the frequency-encoding (read) gradients. The slice-selection gradient was applied in order to select an imaging slice perpendicular to the vertical fibre. The frequency-encoding gradient is applied first in one direction (negative polarity) in order to dephase transverse magnetisation, and second in the opposite direction (positive polarity) to rephrase transverse magnetisation. The maximum signal echo forms when the area under the positive part of the frequencyencoding gradient equals the area under the negative part that precedes the echo. Data acquisition is conducted in the presence of the positive Gread gradient. The spatial information of the specimen can be reconstructed by Fourier transformation of the recorded signal. For the observation of cake layer formation, conventional T1 weighted NMR images were taken with a standard gradient echo sequence using a short repetition time. This is done to partially saturate the signal from spins with a long longitudinal relaxation time T1 . These spins correspond to relatively low concentrations of colloidal silica, i.e. to the bulk phase signal. Gradient echo imaging was introduced by Frahm and Haase [42–46] as a method to speed-up data acquisition. The corresponding pulse sequence is simpler than a spin echo sequence and can be performed more rapidly. This permits a variety of tasks including real-time magnetic resonance imaging (MRI), flow imaging [43,46] and 3D or volume imaging [44]. In contrast to a spin echo sequence, no 180◦ pulse is used for refocusing. The spins are realigned by reversing the direction of their precession rather than changing their phase. Another significant difference to a spin echo sequence is the flip angle of the RF excitation pulse, which can be varied in addition to the repetition time (TR) and the echo time (TE). The flip angle is usually equal or close to 90◦ for a spin echo sequence, but commonly varies over a range of about 10–80◦ for gradient echo sequences. A larger flip angle provides more pronounced T1 weights of the image and improves the image contrast. In this study, the cake formation was captured simultaneously in three adjacent slices with a thickness of 2 mm each. The centre-lines of the first, second and third slices are located at distances of 5, 10 and 15 mm from the glue

S. Buetehorn et al. / Journal of Membrane Science 371 (2011) 52–64

connection, which corresponds to an inter-slice distance of 3 mm. Further details concerning the NMR settings for cake-growth visualisation are given in Table 1 and by Utiu et al. [32].

RF SEM TOF

63

radio frequency scanning electron microscopy time of flight

Nomenclature Symbols a A B c d FOV G J L m N pH P r t T T TE TMP TR

v V y ˛ ␥ ı ı   ω

edge length [m] area [m2 ] magnitude of magnetic field [T] concentration [vol.%] diameter [mm] field of view [mm × mm × mm] magnitude of applied gradient [T/m] permeate flux [L/(m2 h), LMH] length [m] moment of the gradient [T s/m] or [T s2 /m] number pH value pressure [bar] spatial position [m] time [min] temperature [◦ C] relaxation time [s] echo time [ms] transmembrane pressure [bar] repetition time [ms] velocity [mm/s] volume [L] vertical distance [cm] angle of radio frequency pulse [rad] gyromagnetic ratio [Hz/T] cake thickness [␮m] pulse duration [s] pulse time separation [s] phase of spins precessing in magnetic field [rad] Larmor frequency [rad/s]

Subscripts 0 static, zeroth 1 longitudinal, first 2 transverse after filtr. after filtration avg average cake cake layer cum cumulative HF hollow-fibre i internal, index m membrane max maximum o outer phase phase-encoding pix pixel read frequency-encoding slice slice-selection vel velocity-encoding x, y, z coordinates Abbreviations PES polyether sulphone MBR membrane bioreactor NMR(I) nuclear magnetic resonance (imaging) PFG pulsed field gradient PGSE pulsed gradient spin echo

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[25]

[26]

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[29] [30] [31]

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