An electrostatic model for osmotic flow through circular cylindrical pores is developed to describe the reflection coefficient for the membrane transport in the presence of surface charges on the pore wall and the solute. For a spherical solute placed at an arbitrary radial position in the pore, the electrical potential was computed by a spectral element method applied to the Poisson-Boltzmann equation together with the condition of electrical neutrality. The interaction energy between the surface charges was used to estimate the osmotic reflection coefficient. The proposed model predicts that even for a small Debye length compared to the pore radius, the repulsive electrostatic interaction between the surface charges could significantly increase the osmotic flow through the pore.
Akinaga, T., Sugihara-Seki, M., & Itano, T. (2008). Electrical charge effect on osmotic flow through pores. Journal of Physical Society of Japan, 77(5), . https://doi.org/10.1143/JPSJ.77.053401