Particle deposition and layer formation at the crossflow microfiltration

Transcription

1 ELSEVIER Journal of Membrane Science 124 ( journal of MEMBRANE SCIENCE Particle deposition and layer formation at the crossflow microfiltration Justus Altmann *, Siegfried Ripperger Technische Unit ersitiit Dresden, lnstitut~r Verfahrenstechnik und Urnwelttechnik. Lehrstuhl Mechanische VeUhhre~lstechnik, D Dresden, Germany Received 11 July 1996: accepted 6 August 1996 Abstract A microscopic model of the layer formation and the cake growth at the crossflow microfiltration will be introduced. The model considers the hydrodynamic, adhesive and friction forces acting on a single particle during the filtration process. It can be shown that mainly the balance between the lift force and the drag force of the filtrate flow determines the layer tk~rmation at the membrane. Particle attachment to the layer is mostly an irreversible process. This is due to the large influence of the adhesive forces. The irreversibility of particle attachment was proved by experiments with monodisperse particles. The introduced model allows the prediction of the instationary crossflow filtration processes. The filtration rate and structure of the formed layer can be calculated. In the case of a filtration at constant transmembrane pressure the model calculation shows a good correspondence to the experimental results. Kevwords: Microfiltration; Layer formation: Layer structure: Particle deposition; lnstationary crossflow filtration 1. Introduction In 1907 Bechhold [1] found by experiments, that at the filtration of colloidal and very fine suspensions a flow parallel to the filter medium increases the filtrate volume before the filter medium is blocked due to a compact layer formation. Bechhold used a stirred filtration cell to create the shear flow across the filter media. Today the crossflow filtration is a standard operation in many medical and technical applications. A flow parallel to the filter medium 'Corresponding author. Tel.: ; fax: {t58: vtaltm@rcs.urz.tu-dresden.de. reduces the formation of the layer and keeps it at a low level. So it is possible to get a quasi-stationary filtrate flow for a long time. The crossflow filtration is influenced by complex effects of a great number of parameters, e,g. crossflow velocity, transmembrane pressure, membrane resistance, layer resistance, size distribution of the suspended particles, particle form, agglomeration behavior and surface effects of the particles etc. In the last years a lot of models have been developed to understand and describe the processes of the crossflow microflltration (e.g. [2-7]). Until now, a closed theory to describe the mechanism of the crossflow filtration could not be developed because of these complex relationships. ( /97/$17.00 Copyright 1997 Published by Elsevier Science B.V. All rights reserved. Pll S(t (96)

2 120 J. Altmann, S. Ripperger / Journal of Membrane Science 124 (1997) The present paper makes a contribution to understand the mechanisms of the crossflow filtration of suspensions with fine particles. Starting point of the investigation is the consideration of the forces acting on a single particle. The forces are caused by hydrodynamic and adhesive effects. The estimation of the forces allows the prediction of the particle deposition behavior on the layer. The knowledge of the mechanisms of the particle deposition makes it possible to calculate stationary filtrate flow, layer structure and the instationary filtration processes. Laser I I Ah J Object 2 CCD-line 2. Experimental set-up For the experimental study an experimental set-up according to Fig. 1 was used. The experimental set-up shows the typical functions of a non-continuous crossflow system. The membrane module is 400 mm long. The width of the flow channel is 60 ram, the height 3 mm. A microporous membrane made of polyamide with a nominal pore size of 0.2 txm was used as filter media. Crossflow velocities are in the range from 0.5 to 4 m/s. The implementation of a window into the membrane module allows the in-line observation of the particle deposition and the layer growth. The Fig. 2. Principle of a laser triangulometer. layer height was measured in-situ with a commercial laser triangulometer. The principle of the laser triangulometer is shown in Fig. 2. Diatomaceous earth and monodisperse spherical silica particles were used as particle systems. The size distribution of diatomaceous earth is shown in Fig. 3. The volume concentration at all experiments was 0.3%. Fig. 4 shows typical curves of a filtration of diatomaceous earth at constant transmembrane pressure. The large flux at the beginning of the filtration i 7 Inlet (~ = 13St~ ro cp ~ ~ a I I m;ear shur e~l~ n t Fig. 1. Experimental set-up. Outlet kg

3 J. Altmann, S. Ripperger / Journal of Membrane Science 124 (1997) ~ ~ 80 w(y) x E E 30 6o Particle ~20, 40 ~----~ o" 10 i Panicle Size x pm v~ Fig. 5. Acting forces on a single particle. Membrane lll!i!/i II1i1!! Fig. 3. Panicle size distribution of diatomaceous earth. is only influenced by the membrane resistance. With growing layer the flux decreases. The layer height reaches the steady state very quickly, while the filtrate flow has a longer start-up time. This typical behavior could be observed at all experiments. 3. Theory of the layer formation Starting point of the theory is the consideration of the forces acting on the single particle. Fig. 5 shows a simplified scheme of a deposited particle on the membrane. The consideration of the forces requires a distinction between two cases: forces on a streaming particle and forces on a deposited particle. On a streaming particle only hydrodynamic forces are acting, while on a deposited particle the adhesive and friction forces between the particle and the contact surface are acting additionally Forces on a streaming particle At technically relevant conditions the flow in the channel is mostly turbulent, but the size of the filtrated particles is usually smaller than the thickness of the laminar boundary layer. In the vicinity of the membrane the crossflow velocity w(y) increases linear with the distance to the membrane y. Under these conditions the following forces appear: Drag force of the filtrate flow: F, Drag force of the crossflow: F D Lift force: F L Because of the low Reynold-number, the drag forces can be estimated with the stokes-equation. The drag force of the filtrate flow F, is: kg/m 3 1,0bar 1,5m/s.1.6 F, = Fstoke~ = 3-7r. ~.x. v F (1)..1= 6000 (D ~ 2000" LI- : "~-~..,,.~ "1.2 E 0.6 "~ - [ "0.4 -J The drag force of the crossflow is influenced by the wall-bounded shear flow. This results in a higher value for the drag force. According to theoretical and experimental investigations of Rubin [11] the drag force in a linear wall-bounded shear flow is 2.11 times higher than the calculated value by the Stokes equation: F D = 2.11 Fstoke~ = 6.33" ~" 71"x" w(x/2), / I, / I,,, I, I, o Time min Fig. 4. Filtration curve of diatomaceous earth. =3.16" ~" %'x 2 (2) Eqs. (1) and (2) valid only for very low particle concentration without particle interaction. Higher

4 122 J. AItmann, S. Ripperger / Journal of Membrane Science 124 (1997) concentrations require a correction factor A in the Stokes equation: Fstokes = 3" 77"" 17 "X" pp- A( x, q0s) (3) The correction factor depends on the particle size x, the particle size distribution q3(x) and on the volume concentration ~,. Tam [8] suggested the following way to calculate this factor: 1E-7-,E8! 1E-9- i z 1E-10. 0_) o O 1E-11 It 1E-12 i') A(x, q~,) = 1 + o~ c~ ~ (4) with. _ 3. q~) 67r.m e+~367r 2.m~+24~" m~ (1 6"q~s. [q3(x) dx mn = 2 n 7r J x 3-n 2-3. ~ In the case of monodisperse particles the correction function depends only on the volume concentration, [9]: 4 + 3q~, + 3~/8 q~,- 3q~ A(,,) = (2-3 ") 2 (5) Fig. 6 shows an example of calculated values of the function A(x~, ~p,) for the diatomaceous earth suspensions. As one can see, the drag force increases with the volume concentration as well as the particle size (Fig. 6). o ( ,,, ;, loo :; I Particle size pm Fig. 6. Stokes correction versus particle size and volume concentration. 1E-13 1E-14 : : : :::::', : : : :'.:::', : '. : :::::, Particle Size pm Fig. 7. Estimation of the forces on a streaming particle. The lift force F L is caused by the shear flow. This effect was investigated e.g. by Saffmann [10], Rubin [11], McLaughlin [12] and Nirschl [13]. The results of these investigations are similar. According to the experimental and theoretical studies from Rubin the lift force can be calculated as follows: I+5.X 3 p0.5 F L = (6) The deposition of the particles depends decisively on the hydrodynamic forces in the immediate vicinity of the membrane. Fig. 7 shows an estimation of the acting hydrodynamic forces. The calculation is based on following parameters: 17 = Pa s, p = 1000 kg/m3, ~'w = 50 Pa, ~p~ = The figure shows that especially the balance from lift force and drag force of the filtrate flow is responsible for the transport of particles to the layer. At high filtration rates the drag force is higher than the lift force in a wide particle range. That means, that the particles will be transported to the layer and will be deposited there. Large particles have a higher lift force so they will not touch the layer. With decreasing filtration rate the balance between lift force and drag force of the filtrate flow shifts to smaller particle sizes. Therefore only small particles can be deposited on the layer at low filtration rates Forces on a deposited particle Adhesive and friction forces are acting on a deposited particle additionally to the hydrodynamic

5 ,1. Altmann, S. Ripperger / Journal Of Membrane Science 124 (1997) forces. The adhesive forces are caused by van der Waals lorces and by electrostatic interactions. The estimation of these forces is complicated, since a lot of parameters e.g. particle shape, particle roughness, adhesion distance, number of contact points and electrostatic repulsion may influence the adhesive force strongly. The van der Waals force between two ideal spheres can be calculated according to: /i ~. x F'dw -- 32" "rr. a 2 (7) 1E+7 1E-8 Z 1E-9 o ~ 1E-10 1E-11 1E 1; / JDrag Force of ) [the Cross Flow ] (a) L.I i i The action of a normal force (adhesive force and drag force of the filtrate flow) causes a friction force opposite to the drag force of the crossfiow. The friction force F v is coupled to the normal force F N by the friction coefficient /x. F,: = tz " FN = ~" ( F H + K,.) (8) The fiiction coefficient /~ consists of a rolling and a gliding part. Experimental investigations of Halow [14] showed that /~ is in the range of It is necessary to note, that these investigations were done with relatively large particles ( I~m) in gas flows. However, the range of /.~ is physically useful and is close to the Coulomb-friction coefficients and to theoretical rolling friction coefficients. The exact value of ~ has to be understood as a specific parameter of the particle system. Fig. 8 shows calculated values of the acting forces for the following case: The hydrodynamic parameters are the same as in Fig. 7. The friction coefficient was assumed as /,= I, the Lifschitz-van der Waals-constant as ~= 10 2o j and the adhesive distance as a = 0.4 nm. Graph (a) shows the forces into the direction of the crossflow and graph (b) shows the forces into the direction of the filtrate flow. Both graphs show that in the lower particle range the adhesive and the friction force are larger than the corresponding hydrodynamic force. That means, that a small single particle is irreversibly attached to the layer and cannot return into the crossflow. Only large particles or particle agglomerates can be removed from the layer. This behavior could be observed in experiments with monodisperse silica particles. The particles were filtrated at variable transmembrane pressures. First the transmembrane pressure was slowly increased up Z 1 E-7-1E-9. 1E-10. O 1E-1t IJ_ 1E+12 1E-1 0, Particle Size ~m Fig. 8. Estimation of the forces on a deposited particle. to 3 bar and after that decreased back to zero. The changing of the transmembrane pressure was so slow, that at any time a quasi stationary layer height and filtrate flow was ensured. Fig. 9 shows the dependencies of the layer height and filtrate flow on the transmembrane pressure. The crossflow velocity was 2 m/s (z.. = 15 Pa), water was used as suspension medium (p = 1000 kg/m 3, ~/= Pa s). The filtrate flow increased at low transmembrane pressures according to the membrane resistance. At higher transmembrane pressures only a very small increase of the filtrate flow could be observed, while the layer height increased linear with the transmembrahe pressure. During the decrease of the pressure the layer height changed not significantly, the filtration rate declined linear to the transmembrane pressure. This indicates, that the layer structure and resistance was not influenced by the decreasing pressure. Because of the irreversible attached particles a particle transport away from the layer did not take

6 124 J. Altmann, S. Ripperger/Journal of Membrane Science 124 (1997) ~ ~1000, Ii E E Jresistance I: ~ ~ ~'~ 1,e-Y Transmembrane pressure bar T ", :=, I, i, i, I 0, Transmembrane pressure bar Fig. 9. Filtration of 1.5/xrn monodisperse particles. place Other tests with monodisperse or narrow distributed particle systems with a size of 1.0, 0.5 and 0.24 Ixm also showed this behavior 3.3. Conclusions of the force estimation The estimation has shown that particle attachment to the layer is mostly an irreversible process. Adhesive and friction forces are dominating on a deposited particle. This effect can be concluded from the experiments: The build-up of the layer is a continual process, while the removal of the layer only takes place by removing large agglomerates or large layer fragments. A removal of the layer in form of a reverse transport from single particles could not be observed. The experiments with the monodisperse particles demonstrate the irreversible behavior of particle attachment very well. The decreasing transmembrane pressure did not cause a decreasing layer '2 height and also the layer height and the layer resistance were not changed by the varied hydrodynamic conditions (Fig. 6). The proportion of the lift force and the drag force of the filtrate flow determines the particle transport to the membrane. If the filtration velocity is zero, the lift force causes the migration velocity (lift velocity) v L. This velocity is given by the relation between lift and drag force: ~_;!.5 po.5 2 Xcrit b'l(x) = " 712 "~( Xcri,' ~s,w) (9) If the migration velocity is smaller than the filtration velocity, the particles can attach to the layer. In other cases, a higher migration velocity prevents the particle attachment. Therefore the migration velocity of a particle size Xcrit can be understood as the maximum filtration rate without particle deposition of this particle size Xcrit q~s.w is the concentration in the immediate vicinity of the membrane. Because of concentration polarization this concentration is different from the concentration in the feed. For the calculation a value of 20 vol% was used Calculation of layer growth at constant transmembrane pressure Fig. l0 shows a scheme of the calculation of the layergrowth. At the beginning of the process the FMem~brane resist~ance am, I Transmembrane pressure Ap [ IF trat on rate VF] r L incr~eases, - ~ I ~g~iclgs transp rt ~Particle transport to!the membrane i Cake layer grows i Depositedparticles [become finer ~ i ~ Cake r--esistance i _ increases I I Filtration rate decreases Fig. 10. Principle of layer growth.

7 J. Altmann, S. Ripperger / Journal of Membrane Science ) filtration rate u F is determined by the transmembrane pressure A p and the membrane resistance R M. The filtrate flow causes a convective particle transport to the membrane. Because of the particle transport and the particle deposition the layer grows. Also the layer resistance increases and the filtration rate declines. The smaller filtrate flow has two effects: First, the particle transport to the layer decreases and second, the specific cake resistance r L increases because of the deposition of finer particles. This cycle continues until the filtration rate is so small, that the particle transport to the layer becomes zero. The mathematical description is shown in the Eqs. (10)-(15). The calculation considers a complete retention of particles. The filtration rate t, F depends on the resistance of the membrane and the layer: Ap uf(t ) = (10) ri" ( RM + RL( t)) The layer resistance R L depends on the layer height and on the local cake resistance in the layer: RL(t) F (', "y)d (ll) = "l) rl( ~" The size of the particles influences the specific cake resistance. The specific cake resistance r L is estimated by the Carman-Kozeny equation: 160( l - e)2 rl -- "~. 3 (12) XST The porosity e of the layer was assumed as constant. XST is the Sauter diameter of the particles deposited on the layer in a certain height. 6" Q3 (x~it) XST =./(,'~'"q3(x)/xdx x~it is the maximum particle size which may deposit on the layer at a given filtration rate. The relation between x~,~t and the filtration rate v F is given by Eq. (9). The layer height can be calculated through the deposited mass on the membrane: m(t) fi;/n(7) d'r h(t) - = (14') p,.(l-e) p.,- (1-e) The mass transport to the membrane is related to the filtration rate. It is limited by the maximum particle size deposited on the layer x~,~t: p, c s /n( t) = uv( t) Q3 (-}"~rit) (15) p~ -- C s Eqs. (I0)-(16) do not allow an explicit solution of the filtrate flow and layer height versus time, therefore the system of equations is solved with a numerical method. 4. Comparison with experiments Fig. I I shows a good correspondence of the numerical calculated values with the experiments. The cake porosity was assumed to be 0.4. The typical behavior, that the layer height increases faster than the filtration rate decreases, can be described with this mode[ very well. Another way to check the suitability of the model is the comparison of the layer structure. Since an 8000" ~-E6000. E (1) "~4ooo" g 2000, LL E6OOO. ~4000' P, U- i 5kg/m ~ 1,0bar 1,5m/s 16 :~r~-.c. "=".; ~ : " "- ~ '02 0, : : : : : ', : : I I,I Time min 5kg/m' 1,5bar 1,5m/s / o, : : : : : : : : : : :,o Time rain t'- "06 ~ '04 t~l 1.8 E z= Fig. 11. Comparison of the theoretical and experimental results. 5

8 126 J. Altmann, S. Ripperger / Journal of Membrane Science 124 (1997) E+11 5E+11 ~_~ 4E+11 a) b) I-- 3E+11 oo u) ~ 2E+11 n" 1E+11 OE+O Layer height mm Fig. 12. Layer resistance versus layer height. 1.6 independent measurement of flux and layer height is possible, the total layer resistance can be shown as a function of the layer height (Fig. 13). The resistance is calculated according to: Ap Rtota I = R M + R L = - - 7' vf (16) Fig. 12 points to a strong asymmetrical layer structure. The bottom layer near the membrane shows a low resistance while the uppermost layer at the surface of the layer has a very high resistance. This high resistance is caused by the fine particles in upper layers (Fig. 12). The calculation describes the asymmetrical layer structure with a good correspondence. The experimental values show a higher increase of the cake resistance in the upper layers than the calculation. The reason for that is the assumption of a constant porosity in the layer. This assumption excludes the possibility of the deposition of fine particles into an existing particle structure. The asymmetrical layer structure at a filtration at constant transmembrane pressure could be proved by electron microscopical images. Fig. 13a shows a cross section of a layer of glass spheres. According to this theory it is possible to generate specific layer structures by varying the operating parameters during the filtration. The introduced model can be applied for the prediction of such specific structures. Fig. 13b shows as the result of an experiment a double asymmetric structure. Near the membrane the layer consists of fine particles, in -~- Membrane.~- Membrane Fig. 13. Cross section of a layer. (a) Filtration at constant trans membrane pressure. (b) Variable process parameters.

9 J. Altmann, S. Ripperger / Journal of Membrane Science ) middle layers of very large particles and on the top again of fine particles. This structure was generated by an alternating low-high-low filtration rate. 5. Conclusions The balance between the lift force and the drag force of the filtrate flow determines the particle transport to the layer. Particles can be deposited if the drag force of the filtrate flow is higher than the lift force. Since the lift force increases with the third power of the particle size and the drag force increases with the first power of the particle size, small particles can attach to the layer much easier than large ones. Because of this effect, the stationary filtration rate is determined by the fine material of the particle system. The adhesion and friction forces are sometimes higher than the hydrodynamic forces. Therefore particle deposition on the layer is mostly an irreversible process. Only large particles, agglomerates and layer fragments can be detached from the layer. The introduced model explains the crossflow filtration on a physical basis and allows to predict the filtrate flow and layer growth during the instationary filtration periods and at the stationary state. The model shows, that the instationary period is influenced by the whole particle size distribution, while the stationary state especially depends on the fine material of the particle system. The structure of the layer depends on the start-up period of the filtration. In the case of filtration at constant transmembrane pressure the layer shows an asymmetric structure. By changing the operating parameters during the filtration process other structures can be realized. On this way it could be possible to generate definite structures, e.g. highly asymmetric layers for anorganic ceramic membranes. The model can predict necessary operating conditions to generate such layer structures. 6. Notation a adhesive distance (0.4 nm) F~ adhesive forces F n drag force of the crossflow F F friction force F L lift force F,. drag force of the filtrate flow h layer height q3 mass density distribution of the particle system Q3 cumulative mass sistribution of the particle system m deposited mass on the membrane R L layer resistance r L specific layer resistance R M membrane resistance t time c L lilt velocity t, F filtration rate, filtrate flow, flux w crossflow velocity x particle size v distance from the layer/membrane Ap transmembrane pressure drop r/ dynamic fluid viscosity p,~ solid density p fluid density p~ friction coefficient porosity of the layer q~, volume concentration r,. shear stress /i~ Lifschitz-van der Waals constant References [1] H. Bechhold, Kolloidstudien mit der Filtratioosmelhode, Z. Phys. Chem., 60 (1907) [2] M.C. Porter. Concentration polarization with inembrane ultrafiltralion, Ind. Eng. Chem. Prod. Res. Develop., 11(3) (1972) [3] A.L. Zydney and C.K. Colton, A concentration polarization model for the filtrate flux in cross-flow microfihration of particulate suspensions, Chem. Eng. Commun., 47 (1986) [4] A.G. Fane, Ultrafiltration of suspensions, J. Membrane Sci., 20 (1984) [5] F.W. Ahena and G. Belfort, ]Lateral migration of spherical particles in porous flow channels: Application to membrane filtration, Chem. Eng. Sci., 39 (1984) [6] G. Schock. Mikrofiltration an iiberstr~imten Membranen, Dis sertation. Ttt Aachen, [7] S. Ripperger, Mikrofiltration mit Membranen, VCH, Weinhelm, [8] C. Tam, The drag on a cloud of spherical particles in low Reynold number flow, J. Fluid Mech., 38(3) (1969) [9] H.C. Brinkman, A calculation of the viscous force exerted by

10 128 J. Altmann, 5". Ripperger/ Journal of Membrane Science 124 (1997) a flowing on a dense swarm of particles, Appl. Sci. Res., A 1 (1947) 27. [10] P.G. Saffmann, The lift on a small sphere in a slow shear flow, J. Fluid Mech., 22 (1965) ; corrigendum, 31 (1968) 624. [11 ] G. Rubin, Widerstands- und Auftriebsbeiwerte von ruhenden kugelf6rmigen Partikeln in stationmen, wandnahen laminaren Grenzschichten, Dissertation, TH Karlsruhe, [12] J.B. McLaughlin, The lift on a small sphere in wall bounded linear shear flows, J. Fluid Mech., 246 (1993) [13] H. Nirschl, Das strismungstechnische Verhalten einzelner Partikel in wandnahen, laminaren Grenzschichten, Preprints GVC-Jahrestreffen Stral3bourg, [14] J.S. Halow, Incipient rolling sliding and suspension of particles in horizontal and inclined turbulent flow, Chem. Eng. Sci., 28 (1973) 1-12.

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