Passive Mass Transport Processes in Cellular Membranes and their Biophysical Implications - Porous Media: Applications in Biological Systems and Biotechnology - page 311

Also, for dilute solutions

J ∆ P
vwb

≈ J vb =(1 − σ ) L p ∆ P (8.68)

Again, assuming ∆ P = − ∆Π we can write equation (8.66) in a form

L p σ ∆Π + J ∆Π

J vw = − L p ∆Π −

vwb

∆Π flux J ∆Π
vwb

J ∆Π When ∆ P = − satisfies |− L p ∆Π − L p σ ∆Π ||

vwb |

and can

be disregarded, yielding

J vw = − L p ∆Π − L p σ ∆Π (8.69)

Now from equations (8.62), (8.64), (8.65), and (8.69) we obtain the correlation
relation for membrane transport parameters, that is, equation (8.59).

8.4.4 2P Form of the Mechanistic Equations
Using the correlation relation (8.59) in transport equations (8.43) and (8.59)
we can reduce them to the following 2P form:

J vM = L p ∆ P − L p σ ∆Π (8.70)

j sM =(1 − σ ) c s L p (∆Π+∆ P ) (8.71)

The latter can also be written as the solute volume flux equation

− σ ) c s V s L p (∆Π+∆ P )

J svM =(1 (8.72)

8.4.5 Corrected Form of the Mechanistic Transport
Equations
In both the KK and the ME formalisms the volume and solute fluxes are
defined as J v = ∆ V

A ∆ t , j s = ∆ m A ∆ t , J vM = ∆ V A ∆ t , and j sM = ∆ m

A ∆ t , where A is the
active surface area of the membrane, that is, the area of the two-sided contact
of the membrane with solutions. However, porous membranes have pores in
otherwise totally impermeable matrix and transport takes place only through
the pores. The important thing is not the entire surface of the membrane but
the total cross-section area of the pores A t . Therefore the definition of fluxes
can be corrected as

∆ V
A t ∆ t

J vMt =

(8.73)

and

∆ m
A bt ∆ t

j sMt = (8.74)

where A tb is the total cross-section area of permeable pores, that is, pores in
part (b) of the membrane. The mechanistic transport equations can then be
written as

J vMt = L pt ∆ P − L pt σ ∆Π (8.75)