Passive Mass Transport Processes in Cellular Membranes and their Biophysical Implications - Porous Media: Applications in Biological Systems and Biotechnology - page 303

The KK equations were derived from the laws of thermodynamics and
apply to generic membrane systems, without regard to the details of solute
and solvent permeation across the membrane. However, it has been shown
(Kleinhans 1998) that when water and solute permeate through membrane
pores, the role of the reflection coecient is to describe the mutual interac-
tion between water and solute fluxes in the same pores. When the fluxes flow
through separate pores, the KK formalism can be simplified; Kleinhans devel-
oped a 2P formalism requiring only the filtration and permeation coe cients.
It can be shown that both approaches agree in experiments where water and
solutes have distinct permeation mechanisms.
8.3 Porous Membranes
A membrane acts as a barrier to various chemical compounds and maintains a
difference of concentration, pressure, temperature, and the electric potential. If
the solutions on both sides are mixed well, then the gradients exist only across
the membrane. These gradients are the thermodynamic forces that generate
fluxes in the system. In a thermodynamic KK formalism described in the pre-
vious section, fluxes across the membrane are described from a macroscopic
point of view and we do not consider internal structure of the membrane and
the microscopic mechanisms of permeation. A membrane is considered homo-
geneous with respect to its transport properties, which can be summarized in
terms of three phenomenological parameters, that is, coecients of filtration
L p , reflection σ , and permeation ω .
Recently, our understanding of membrane structure and permeation mech-
anisms of both artificial and biological membranes has improved significantly.
Artificial membranes, porous and nonporous, can be manufactured by differ-
ent methods. By a porous membrane we mean a thin impermeable barrier
containing pores through which the solvent and, to a different degree, vari-
ous solutes can permeate. Typical examples are cellophane, ceramic, metal,
or polymer membranes that differ in the dimensions and geometry of their
pores. An example of a nonporous membrane can be, for instance, a gel mem-
brane on an appropriate support providing its stability. Such membranes do
not have stable pores, and permeation is based on dissolving and diffusion
of different solutes in the gel matrix. Biological membranes are phospholipid
cell membranes and organelle membranes. They allow the cells or organelles
to fulfill their physiological functions by controlling the exchange of various
substances with the external environment. This exchange may be active, that
is, requiring energy from some source, such as the ATP hydrolysis, or pas-
sive, where the transport is induced by thermodynamic forces, such as the
concentration or pressure gradient. The microscopic details of permeation vary
from the diffusion across the phospholipids bilayer to transport by specialized