Passive Mass Transport Processes in Cellular Membranes and their Biophysical Implications - Porous Media: Applications in Biological Systems and Biotechnology - page 308

where ∆ P=P 2 − c 1 ), and L pa , L pb are the filtration

coecients of both parts of the membrane. They are given as
L pa = J va
∆ P

P 1 ,∆Π= RT ( c 2 −

(8.41)

∆Π=0

L pb = J vb
∆ P

(8.42)

∆Π=0

The total volume flux across the membrane is obviously

J vM =( L pa + L pb )∆ P − L pa ∆Π=L p ∆ P − L p σ ∆Π (8.43)

where

L p = L pa + L pb (8.44)

is the total filtration coecient of the membrane. The quantity

σ = L pa
L p

(8.45)

which also satisfies

σ = ∆ P
∆Π

(8.46)

J vM =0

is called the reflection coecient, in analogy with the KK equations. If L pa =
L p , then σ = 1 and the membrane is semipermeable. If L pa = 0, then σ =0
(a permeable membrane). For L p >L pa > 0 the membrane is selective and
1 >σ> 0.

8.4.2 Equation for the Solute Flux
Contrary to water, the solute molecules permeate only through part (b) of the
membrane. The flux J vb is the sum of water and solute volume fluxes

J vb = J vwb + J vsb (8.47)

Each of these in turn can be written as the flux induced by the hydrostatic
pressure, ∆ P, and osmotic pressure, ∆Π

J vwb = J ∆ P

vwb + J ∆Π

(8.48)

vwb

J vsb = J ∆ P

vsb + J ∆Π

(8.49)

vsb

where the subscripts ∆ P and ∆Π denote the generating forces for the fluxes.
We consider two cases.