Diffusioosmosis of Electrolyte Solutions in Fibrous Porous Media

The steady diffusioosmosis of electrolyte solutions in the fibrous medium constructed by a homogeneous array of parallel charged circular cylinders caused by constant concentration gradients imposed in the direction along the axes of the cylinders is theoretically investigated. The electric double layer surrounding each cylinder may have an arbitrary thickness relative to the radius of the cylinder. We employ a unit cell model to account for the effect of cylinders on each other. The study contains two parts. In the first part, the diffusioosmotic flow in the fibrous medium is analyzed for the case of low zeta potential. The electrostatic potential distribution in the fluid phase of a cell is obtained by solving the linearized Poisson-Boltzmann equation, and the macroscopic electric field induced by the imposed electrolyte concentration gradient is determined analytically as a function of the radial position with the constraint of no net electric current arising from the cocurrent diffusion of the electrolyte ions. A closed-form formula for the fluid velocity profile of the electrolyte solution due to the combination of electroosmotic and chemiosmotic contributions as a function of the porosity of the array of cylinders correct to the second order of their surface charge density or zeta potential is derived as the solution of a modified Navier-Stokes equation. In the other part, the diffusioosmotic flow in fibrous porous media with an arbitrary surface potential is examined, and the electrostatic potential distribution in the fluid phase is determined by an analytical approximation to the solution of the general Poisson-Boltzmann equation. Solving the 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 are obtained semianalytically as functions of the radial position in a self-consistent way. 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. The effects of the radial distribution in the induced macroscopic electric field and of the ionic convection in the electric double layer on the diffusioosmotic flow are found to be quite significant in practical situations.