Diffusioosmosis of Electrolyte Solutions around a Circular Cylinder at Arbitrary Zeta Potential and Double-Layer Thickness

Abstract

The steady diffusioosmotic flow of an electrolyte solution around a charged circular cylinder caused by a constant concentration gradient imposed in the direction along the axis of the cylinder is investigated theoretically. The cylinder can have either a constant surface potential or a constant surface charge density of an arbitrary value. The electric double layer surrounding the cylinder can have an arbitrary thickness, and its electrostatic potential distribution is determined by an analytical approximation to the solution of the Poisson-Boltzmann equation. Solving a modified Navier-Stokes equation with the constraint of no net electric current arising from the cocurrent diffusion, electric migration, and diffusioosmotic convection of the electrolyte ions, the macroscopic electric field and the fluid velocity along the axial direction induced by the imposed electrolyte concentration gradient are obtained semianalytically as functions of the radial position in a self-consistent manner. The direction of the diffusioosmotic flow relative to the concentration gradient is determined by the combination of the zeta potential (or surface charge density) of the cylinder, the properties of the electrolyte solution, and other relevant factors. For a prescribed concentration gradient of an electrolyte, the magnitude of the fluid velocity generally increases with increasing distance from the surface of the cylinder, but there are exceptions. The effects of the radial distribution of the induced macroscopic electric field and of the ionic convection in the double layer on the diffusioosmotic flow are quite significant in practical situations.