Passive Mass Transport Processes in Cellular Membranes and their Biophysical Implications - Porous Media: Applications in Biological Systems and Biotechnology - page 299

TABLE 8.1
List of Symbols

J Flux density

j s

Solute flux density

J v Volume flux density

J vw ,J vs Water/solute volume flux density

µ Chemical potential

ψ Dissipation function

V i Molar volume

P Hydrostatic pressure

Π

Osmotic pressure

c Concentration

L p ,L D ,L pD ,L Dp Onsager coecients

L p Filtration coecient

σ Reflection coecient

ω Permeation coecient (KK formalism)

ω d Permeation coecient (ME formalism)

v s , v w Velocities of molecules of solute and water

Subscript “a” Quantities referring to part (a) of the membrane (cf. Figure 8.3)

Subscript “b” Quantities referring to part (b) of the membrane (cf. Figure 8.3)

Subscript “M” Fluxes obtained in ME formalism

the membrane, the dissipation function for the entire membrane is

dx

∆ x ∆ x

µ i ) dx =
i

dµ i
dx

ψ ∆ x = J i grad( − J i −

i

0 0

= J i µ i − µ ∆ i =

i

J i ∆ µ i , (8.3)

where ∆ µ i = µ i i − µ ∆ i is the chemical potential difference across the mem-

brane. If we assume binary solutions (i.e., solutions consisting of the solvent
and one solute only), then we get

ψ ∆ x = j s ∆ µ s + j w ∆ µ w (8.4)

where j s , j w are the flux densities for the solute ( s ) and the solvent ( w ), and
∆ µ s ,∆ µ w are chemical potential differences for the two components of the
solution. In what follows we will refer to js as simply fluxes.