Passive Mass Transport Processes in Cellular Membranes and their Biophysical Implications - Porous Media: Applications in Biological Systems and Biotechnology - page 307

∆ P=P 2 -P 1

P 2 > P 1

r w

(a)

J va =J vwa

r s

J vb =J vwb +J vsb

J vwb ∆ P

J vwb ∆ P

J vsd
J vsk

(b)

r N

C 2 > C 1

M

FIGURE 8.3
Membrane system ( M is the membrane; m is the stirrers; c 1 , c 2 are the con-
centrations; P 1 , P 2 are the pressures; J v is the volume fluxes of solute; J vw is
the volume fluxes of water; J vs is the volume fluxes of solute; J ∆ P , J ∆Π , are
the volume fluxes of water generated by ∆ P and ∆Π, respectively; J vsd , J vsk
is the volume fluxes of solute induced by ∆ P and ∆Π). The membrane pores
are arranged according to sizes from the smallest (at the top—part [a]) to the
largest (at the bottom—part [b] of the membrane).

same solute, with concentrations c 1 , c 2 ( c 1 <c 2 ) and under pressures P 1 , P 2
( P 1 <P 2 ). The membrane has N pores permeable to water. We assume the
pores are cylindrical, are perpendicular to the membrane surface, and are
ordered according to sizes, with the smallest pores in the top part of the
membrane. As described in the previous paragraph, for a given solute with
molecular radius r s the membrane can be divided into part (a) (top part in
Figure 8.3), containing only semipermeable pores, and part (b) (bottom part)
with only permeable pores.

8.4.1 Equation for the Volume Flux
The hydraulic pressure, ∆ P, and the osmotic pressure, ∆Π , across the mem-
brane generate volume fluxes, J va and J vb, in both parts of the membrane:

J va = L pa ∆ P − L pa ∆Π (8.39)

J vb = L pb ∆ P (8.40)