Membrane processes

Membrane processes and driving forces

In many cases the permeation rate through the membrane is proportional to the driving forces, i.e. the flux-force relationship can be described by a linear phenomenological equation. Proportionality between the flux(J) and the driving force is given by

   J = - A dX/dx

Where A is called the phenomenological coefficient and (dX/dx) is the driving force, expressed as the gradient of X(temperature, concentration, pressure) along a coordinate x perpendicular to the transport barrier. Phenomenological equations can be used to describe mass flux, heat flux, volume flux, momentum flux and electrical flux.

As to syringe filters, its driving force is the pressure difference.

Phenomenological equations

mass flux           Jm  = - D dc/dx       (Fick)    D(the diffusion coeffient)

volume flux       Jv  = - Lp dP/dx      (Darcy)   Lp(permeability coeffient)

heat flux             Jh  = - λdT/dx      (Fourier)  λ(thermal diffusivity)

momentum flux Jn  = - υdv/dx      (Newton)  υ(=η/ρ kinematic viscosity)

electrical flux     Ji   = - l/R dE/dx     (Ohm)    l/R (electrical conductivity)

For a pure component permeating through a membrane , it is possible to employ linear relations to describe transport. However, when two or more components permeate simultaneously, such relations cannot be generally employed since coupling phenomena may occur in the fluxes and forces. These coupling phenomena can be described in terms of the formalism of non-equilibrium thermodynamics.