Stagnant film model for concentration polarization in membrane systems

The stagnant film model is used almost universally to describe bulk mass transfer (concentration polarization) in pressure-driven membrane systems. However, the mathematical justification for this model, and in particular the logarithmic dependence on the solute concentration and the form of the mass transfer coefficient, remains a point of considerable confusion. This communication presents a more rigorous development of the stagnant film model, providing a much firmer mathematical justification for this approach as well as a more quantitative description of the limitations of this model. Specific calculations are provided for fully developed laminar flow in a parallel plate device and for unsteady mass transfer in an unstirred batch system. In addition, the effects of a concentration-dependent viscosity and diffusivity on the stagnant film analysis are examined, yielding new insights into the proper form of the stagnant film model under these conditions.