Transport through deformable matrices

Abstract

In order to induce and maintain a pressure gradient in a fluid mixture in steady state, the fluid has to pass through a solid-like matrix capable of generating and carrying an extra stress gradient. Frictional interactions between fluid components and the matrix then produce separations. Matrix deformation occurs and the implication of this is discussed. A general solution for multi component systems is given and then specialised to the case of three components - a deformable gel matrix component, a solvent and a macromolecular solute. A method is given for solving the system of equations and is applied in the steady state. Applications involving transendothelial flow and self-regulated selectivity are stressed in particular. The calculations are based on the Flory-Huggins equation, on the Flory gel deformation model and on ad hoc, very crude approximations to the concentration dependence of the three, pairwise defined friction coefficients between the three components involved.