Passive Mass Transport Processes in Cellular Membranes and their Biophysical Implications - Porous Media: Applications in Biological Systems and Biotechnology - page 326

and solute flux density is

j s = P s ∆ c (8.116)

where P s = ω RT is the solute permeability. The solute flux equations are iden-
tical and the difference in volume flux equations appears to formally reduce to
a substitution σ = 1. However, as emphasized in Kleinhans (1998); Elmoazzen
et al. (2008), this would be incorrect since for σ = 1 there is no solute trans-
port. Equation (8.115) describes water flux only. To directly compare with
(8.113) one must compute the volume flux of water and solute (Elmoazzen
et al. 2008):

L p RT 1

∆ c

P s v s
L p RT

J v = J vw + J vs = − − (8.117)

Now equations (8.113) and (8.115) are almost identical. The only difference is
the expression 1 ( P s v s /L p RT ) instead of σ in the 2P equation. According

to the 2P formalism this expression is the upper limit of σ . It is reached when
water and solute permeate through separate pathways. In such case the 2P
and KK formalisms are equivalent.

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3. ME formalism (Kargol 2002; Kargol and Kargol 2003, 2006)

This formalism has been developed based on a specific microscopic model of
permeation, described in detail in the chapter. The transport equations are
given as (equations 8.43 and 8.59):

J vm = L p ∆ P − L p σ ∆Π (8.118)

j sM = ω d ∆Π+(1 − σ ) c s L p ∆ P (8.119)

where J vM is the volume flux density and j sM is the solute flux density. Both
fluxes are driven by pressure differences, ∆ P and ∆Π . Parameters L p , σ , and
ω d are defined as
L p = J vM
∆ P

,σ = ∆ P
∆Π

ω d = j sM
∆Π

, and

∆Π=0 J vM =0 ∆ P =0

where J vM = J va + J vb , L p = L pa + L pb , σ = L pa /L p , L pa =( J va / ∆ P ) ∆Π=0 ,
and L pb =( J vb / ∆ P ) ∆Π=0 . Different terms in (8.118-8.119) describe the phe-
nomena of filtration, osmosis, diffusion, and convection, respectively.
In the ME equations, the permeation coe cient is defined differently from
the KK formalism, and it refers to the diffusive solute permeation only. In
Section 8.4.6 we derived c orrelation relations f or the KK and ME formalisms
in the forms ω =(1 − σ 2 ) c s L p and ω d =(1 σ ) c s L p , respectively. Using these

relations one can show the equivalence of both formalisms (see Section 8.4.6).

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