Details

The molar flux at steady state is calculated using the analog of series resistances. The flux through each layer is:

feed:

,

membrane:

,

,

,

permeate:

,

where is the mass transfer coefficient, and are the feed and permeate concentrations, and are the concentrations at the interface, and are the concentrations at the surfaces, is diffusivity in the membrane, is membrane thickness and is the equilibrium constant.

The flux through the membrane can be written in terms of permeance :

,

.

Because the system is at steady state, is the same through all three layers:

.

Solving each equation for the concentration differences:

,

,

.

Adding these equations together and solving for gives the flux in terms of series resistances:

.

For more information on how these equations were derived, view the screencast videos [1, 2]. For an example problem, view the screencast video [3].

References

[1] University of Colorado Boulder. Membrane Transport: Series Resistances Part 1 [Video]. (Mar 20, 2017) www.youtube.com/watch?v=hlJA-St-x5w&t=36s.

[2] University of Colorado Boulder. Membrane Transport: Series Resistances Part 2 [Video]. (Mar 20, 2017) www.youtube.com/watch?v=xMl7_tXOSMQ.

[3] University of Colorado Boulder. Membrane Transport: Series Resistances Part 3 [Video]. (Mar 20, 2017) www.youtube.com/watch?v=NEroL-x_g-M.