Fluid mechanical and electrostatic study on the osmotic flow through cylindrical pores

When two solutions differing in solute concentration are separated by a porous membrane, the osmotic pressure will generate a net volume flux of the suspending fluid across the membrane; this is termed osmotic flow. We consider the osmotic flow across a membrane with circular cylindrical pores when the solute and the pore walls are electrically charged, and the suspending fluid is an electrolytic solution containing small cations and anions. Under the condition in which the radius of the pores and that of the solute molecules greatly exceed those of the solvent as well as the ions, a fluid mechanical and electrostatic theory is introduced to describe the osmotic flow in the presence of electric charge. The interaction energy, including the electrostatic interaction between the solute and the pore wall, plays a key role in determining the osmotic flow. We examine the electrostatic effect on the osmotic flow and discuss the difference in the interaction energy determined from the nonlinear Poisson-Boltzmann equation and from its linearized equation (the Debye-Hückel equation).