By William K. Wang
This article information the connection among membrane know-how and bioprocesses, discussing purposes. This moment version refines and optimizes key beneficial properties of the 1st version - and contours new illustrative case reports. The e-book examines merits and drawbacks of utilizing ordinary and new membrane applied sciences; analyzes quite a lot of purposes, together with phone tradition harvesting and product and procedure validation thoughts; and extra.
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Extra resources for Membrane Separations in Biotechnology, Second Edition, (Biotechnology and Bioprocessing)
25] found that the time needed to reach steady state was, roughly, inversely proportional to Lp. 25 ϫ 10Ϫ13 m was attained in about 2 h; hence, at the same ICS flow and in the same reactor geometry but at L p ϭ 6 ϫ 10Ϫ15 m, as used by Koska et al. , steady state would be reached in approximately 42 h. Reduction of L p by several orders of magnitude was found to have little influence on the steady-state protein distribution, except to diminish slightly the large axial concentration gradient that exists at the boundary between the protein-rich and protein-free zones .
As in the analogous Krogh cylinder models, the coupled fluid flow and protein transport equations are solved numerically, with the hydrodynamic solution lagged one time step behind the concentration solution. It can easily be shown that, in the absence of radial gradients and with the axial hydraulic permeabilities calculated from expressions derived using the Krogh cylinder approach, the one-dimensional PMM and KCM become identical. However, there is a notable difference between the two-dimensional KCM and PMM: in the former, the radial dimension is considered only on the microscale of a single fiber, while in the latter it accommodates the whole HFBR cartridge.
26 Labecki et al. For example, the algebraic forms of the velocities for a closed-shell HFBR are as follows: Ά · u L (z, r) ϭ u0 1 Ϫ (r/R L )2 cosh[λ(z/L Ϫ 1/2)] 1 ϩ 1 ϩ 1/γ cosh(λ/2) γ u S (z, r) ϭ u0 r 2 Ϫ R 2F Ϫ 2R 2K ln (r/R F ) cosh[λ(z/L Ϫ 1/2)] Ϫ1 R 2L (1 ϩ γ) cosh(λ/2) Ά v L (z, r) ϭ Ϫu0r[2 Ϫ (r/R L )2] v S (z, r) ϭ Ϫu0rλΦ(r) √ Lp sinh[λ(z/L Ϫ 1/2)] R 3L (1 ϩ 1/γ) cosh(λ/2) √ Lp sinh[λ(z/L Ϫ 1/2)] R 3L γ(1 ϩ γ) cosh(λ/2) (9) · (10) (11) (12) where µ0 is the inlet centerline lumen velocity, λ ϭ 4L √ L p (1 ϩ 1/γ) R 3L (13) and ΄ Φ(r) ϭ 2R 2K Ϫ 2R 2F ϩ r 2 Ϫ 3 ϩ4 R 4K R 2KR 2F ϩ 2 r2 r2 ΅R R 4K ln(RK /R F ) Ϫ 4R 2K ln(r/R F ) r2 (14) 2 L It should be noted that the Krogh cylinder approach assumes that the fluid in open-shell operations enters or exits the ECS axially at either end of the annular space; in reality, the inflow or outflow occurs radially through the ECS manifold, which extends over a finite distance along the outer circumference of the module and typically offers a much larger surface area for the incoming or outgoing flow.
Membrane Separations in Biotechnology, Second Edition, (Biotechnology and Bioprocessing) by William K. Wang