Fluid flow through an array of fixed particles (Q794529)

The author examines the slow flow of an incompressible viscous fluid in an array of a large number of small fixed solid particles. A general unsteady case has been investigated by using matched asymptotic expansions. The author considers the case of spherical and identical particles. It has been further generalized to the case of 3-dimensional particles of arbitrary shape. Assuming the particles size (\(\epsilon)\) and the distance between two neighbouring particles (\(\eta)\) such that \(\epsilon\leq \eta \leq 1\); it has been shown that Brinkman's law used for small volumic concentration is really applicable for a critical size of particles \(\epsilon /\eta^ 3=O(1).\) The investigations show that for large particles the fluid flow through porous media is governed by the Darcy's law and the smaller solid particles do not affect the flow. The 2-dimensional case has also been studied. The paper is interesting to read.