Passive Mass Transport Processes in Cellular Membranes and their Biophysical Implications - Porous Media: Applications in Biological Systems and Biotechnology - page 312

j sMt = ω dt ∆Π+(1 − σ ) c s L pt ∆ P (8.76)

where the corrected coecients are defined as
L pt = J vtM
∆ P

(8.77)

∆Π=0

σ = ∆ P
∆Π

J vMt =0 ,J vM =0

ω dt = j sMt
∆Π

∆ P =0

Similarly, the 2P mechanistic equations can be corrected to a form:

J vMt = L pt ∆ P − L pt σ ∆Π (8.78)

j sMt =(1 − σ ) c s L pt (∆ P + ∆Π) (8.79)

since

ω dt =(1 − σ ) c s L pt (8.80)

Let us recall that the coecient L pt is defined as (Equation [8.37]):

A t
8 ηπ ∆ x

L pt =

but

A at
8 ηπ ∆ x +

A bt
8 ηπ ∆ x

L pt = L pta + L ptb =

where L pta and L ptb represent the total filtration coecients of pores n a and
n b , respectively. Then the reflection coecient is defined as

σ = A at
A t

(8.81)

8.4.6 Equivalence of KK and ME Equations
The KK equations are based on thermodynamics and the ME equations relay
on a specific model, a porous membrane, and allow at least partial micro-
scopic interpretation of the transport parameters. It is obvious, however, that
they should yield the same numerical results in situations where both are
applicable. The volume flux equations in both formalism, equations (8.19)
and (8.43) are formally identical but the transport parameters are defined
differently. In the KK formalism the reflection coecient, σ, is given by the
Staverman's definition, σ = L pD /L p , while in ME equations it is defined as

σ = σ M = L pa /L p . In the Staverman's definition the coecient L pD is nega-
tive, but if we put

−

| L pD | = L pa then both definitions are equivalent.