Fluxes and Driving Forces in Membrane Separation Processes

The transport rate of a component through a membrane is determined by the permeability of the membrane and by the driving force. Generally, the flux through a membrane can be described by

$$ \mathrm{J}=-P\frac{dX}{dz} $$

(1)

where J is a flux, P is a phenomenological coefficient expressing the permeability of the membrane, and $\frac{dX}{dz}$ is the driving force. The flux through the membrane can be defined as volume flux (J_v) expressed in volume per time (m.s⁻¹), mass flux (J_m) expressed in mass per time (kg.m⁻².s⁻¹), molar flux (J_n) expressed in mole per time (mol.m⁻².s⁻¹), electrical flux (J_e) expressed in Faraday per time (A.m⁻²), and heat flux (J_q) expressed in heat per time (J.m⁻².s⁻¹).

The driving forces in membrane processes are gradients in the chemical potential, the electrical potential, and the hydrostatic pressure, which could result in a diffusion of individual molecules, a migration of ions, and a convection of mass, respectively. The function of the membrane is...