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.
All Science Journal Classification (ASJC) codes
- Materials Science(all)
- Physical and Theoretical Chemistry
- Filtration and Separation