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 theeffectivediffusivity of solut e in theliquid film (cm2 /s)
De
J is the volumetric filtrationflux of theliquid (cm3/cm2 s)
C is theconcentration of solut e (mol/cm3 liquid )
Integrating thisequation with boundary condit ions
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 themass transfercoefficient (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 fLQ 2
d5
where
C 4 , C2 are constant s
f is t hefanningfrictionfact or
L is t helength of fluid flow
d is t hediameterof t he t ube
Q is t he volumet ric flow rat e
 is t he 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 through thepipe,
thereis pressure drop across themembrane
Averagetrans- me mbranepre ssuredrop
Pi  Po
PM 
 Pf
2
If Pf  0 (gage pressure or atmospheric pressure), then
PM  Pi  0.5P
Filtrati onfl u xcan be relat ed to gel (cake)and membraneresist ances (Darcy's Law)
J
PM
PM

( rG  rM )  ( RG  RM )
T hisequat ionis similar tothe Darcy's equat ion we used for filtrationof particles
dV
PA

dt ( rm  rc ) 
T hus, 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