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Downstream Processes BIE/CEE 5930/6930 Spring 2008 Ultrafiltration and Microfiltration • Microfiltration – 0.1 to 10 μm filter sizes – Used to separate cells • Ultrafiltration – MW range 2000 to 500,000 (2 to 500 kilo Daltons (kD)) – Used to concentrate or sieve proteins based on size – Anisotropic membranes • A thin membrane with small pores supported by a thicker membrane with larger pores • Low MW solutes pass through the filter and high MW solutes are retained • Pressure driven process – Can result in concentration polarization and gel formation at membrane surface Ultrafiltration and Microfiltration • At steady state: – Rate of convective transport of solute towards membrane = rate of diffusive transport of solute in opposite direction dC JC , where, dX De is the effective diffusivit y of solute in the liquid film (cm 2 /s) De J is the volumetri c filtration flux of the liquid (cm 3/cm 2 s) C is the concentrat ion of solute (mol/ cm 3 liquid ) Integratin g this equation with boundary conditions C CB at X 0 C CW at X J De ln CW C C k ln W k ln G CB CB CB Gel polarization equation where k is the mass transfer coefficien t (cm/s) k f( Re , Sc) Re dv / , Sc / De , Sh kd / De Ultrafiltration and Microfiltration Cross flow or tangential flow filtration • Pressure applied parallel to membrane instead of perpendicular to it • Fluid flows parallel to membrane and prevents accumulation of solute at the surface Ultrafiltration and Microfiltration Pressure drop given by: C2 LQ P Pi Po P Pi Po d4 C 4 fLQ2 d5 where C 4 , C2 are constants f is the fanning friction factor L is the length of fluid flow d is the diameter of the tube Q is the volumetri c flow rate is the viscocity Hagen-Poiseuille Equation for laminar flow in a pipe Modified Hagen-Poiseuille Equation for turbulent flow in a pipe These expressions relate pressure drop due to linear flow of fluid through the pipe Ultrafiltration and Microfiltration In addition to pressure drop due to flow throu gh the pipe, there is pressure drop across the membrane Average trans - membrane pressure drop Pi Po PM Pf 2 If Pf 0 (gage pressure or atmospheri c pressure), then PM Pi 0.5P Filtration flux can be related to gel (cake) and membrane resistance s (Darcy' s Law) J PM PM ( rG rM ) ( RG RM ) This equation is similar to the Darcy' s equation we used for filtration of particles dV PA dt ( rm rc ) Thus, J f ( PM , R ) and PM f ( Pi , P ) Ultrafiltration and Microfiltration • Filtration flux (J) is a function of – Transmembrane pressure drop (ΔPM) – Gel layer concentration (CG) – Mass transfer coefficient (K) – Bulk solute concentration (CB) • If no solute is present, then Flux is a function of ΔPM only. • If solute is present and RG is constant, flux still increases linearly with ΔPM • If gel polarization occurs, RG is not constant and flux will no longer be a function only of ΔPM } From Gel polarization eq. Ultrafiltration and Microfiltration • ΔPM may be applied in two ways – Increasing inlet pressure (Pi) – Decreasing ΔP by increasing Po (Backpressure) • Pi is constrained by pumps available or membrane properties • If Pi is constant, applying a little back pressure is good because we get higher ΔPM • If too much back pressure is applied, – ΔP decreases and thereby velocity – Gel polarization starts to occur – Lower velocity decreases mass transfer rate • If velocity is too high, we get high pressure drop (ΔP) and low ΔPM again resulting in low flux Ultrafiltration and Microfiltration