To describe the velocities of particles such as ions, protein molecules and colloids dispersed or dissolved in a fluid, it is important to also describe the forces acting on the fluid, including pressure gradients and friction of the fluid with the particles and with the porous media through which the fluid flows. To account for this problem, the use of a two-fluid model is described, familiar in the field of fluid mechanics, extended to include osmotic effects. We show how familiar relationships follow in various situations and give examples of combined fluid/particle transport in neutral and charged membranes driven by a combination of electrostatic, diffusional and pressure forces. The analysis shows how the same modeling framework can be generally used both for multidimensional electrokinetic flow through macroscopic channels and around macroscopic objects, as well as for mean-field modeling of transport through porous media such as gels and membranes.
- irreversible thermodynamics
- nanofiltration membranes
- reverse electrodialysis
- neutral solute
Biesheuvel, P. M. (2011). Two-fluid model for the simultaneous flow of colloids and fluids in porous media. Journal of Colloid and Interface Science, 355(2), 389-395. https://doi.org/10.1016/j.jcis.2010.12.006