Diffusioosmosis of nonelectrolyte solutions in a fibrous medium

The steady diffusioosmotic flow of a fluid solution of an uncharged solute in the fibrous porous medium constructed by a homogeneous array of parallel circular cylinders is analytically studied. The imposed solute concentration gradient is constant and can be oriented arbitrarily with respect to the axes of the cylinders. The range of the interaction between the solute molecules and the cylinder surfaces is assumed to be small relative to the radius of the cylinders and to the gap thickness between two neighboring cylinders, but the effect of polarization of the mobile solute in the thin diffuse layer surrounding each cylinder caused by the strong adsorption of the solute is taken into account. Through the use of a unit cell model, the appropriate equations of conservation of mass and momentum are solved for each cell, in which a cylinder is envisaged to be surrounded by a coaxial shell of the fluid solution. Analytical expressions for the diffusioosmotic velocity of the bulk fluid as functions of the porosity of the ordered array of cylinders are obtained for various cases. Comparisons of the results of the cell model with different conditions at the outer boundary of the cell are made. In the limit of maximum porosity, these results can be interpreted as the diffusiophoretic velocity of an isolated circular cylinder caused by the imposed solute concentration gradient.