Diffusiophoretic Motion of a Charged Spherical Particle in a Nanopore

The diffusiophoretic motion of a charged spherical particle in a nanopore, subjected to an axial electrolyte concentration gradient, is investigated using a continuum theory, which consists of the ionic mass conservation equations for the ionic concentrations, the Poisson equation for the electric potential in the solution, and the Stokes equations for the hydrodynamic field. With the concentration gradient imposed, the particle motion is induced by two different mechanisms: an electrophoresis generated by the induced electric field arising from the difference of ionic diffusivities and the double layer polarization (DLP) and a chemiphoresis by the resulting osmotic pressure gradient induced by the solute gradient in the electrical double layer around the particle. The particle diffusiophoretic velocity along the axis of the nanopore is computed as functions of the ratio of the particle size to the thickness of the electrical double layer, the ratio of the nanopore size to the particle size, the particle surface charge density, and the properties of the salt solution. The diffusiophoretic behavior of a particle comparable to the nanopore size is governed predominantly by the induced electrophoresis generated by the DLP-induced electric field, caused by the imposed concentration gradient and the double layer compression due to the presence of the impervious nanopore wall.