Interaction of a Charged Spherical Particle with a Pore of a Charged Hydrophobic Membrane in an Electrolyte Solution

The problem on determining the equilibrium position of a spherical charged particle entering a pore of a charged hydrophobic membrane in an aqueous electrolyte solution has been considered. The dependence of the critical pressure gradient required to overcome the electrostatic repulsion force with allowance for the surface hydrophobicity of the membrane on the position of the center of the particle on the pore axis has been determined and plotted. The presence of the maximum on the plots, which indicates the presence of a force barrier located at the entrance to the pore that prevents the particle from passing to the permeate has been revealed. The height of the barrier depends on both physicochemical (ionic strength of the solution, solution viscosity, zeta potential of the interacting surfaces, slipping length) and geometrical (particle and pore radius, rounding of the pore entrance, pore influence zones) parameters. It has been shown that the membrane surface hydrophobicity increases the magnitude of the critical pressure gradient.