A study on constitutive quantities and difference in arbitrary pressures in a particulate suspension with incompressibility constraint

Abstract

This work deals with porous media with incompressible constraints and is a study on constitutive quantities and difference in arbitrary pressures in a particulate suspension. In this study, two exact solutions of a system of motion equations of a particulate suspension were used. The solutions were employed in the mathematical modeling of the gravitational motion of particulate suspensions in a test tube. This modeling deals with sub-regions that vary with time and are bounded by moving interfaces and an acceleration wave. The exact solutions and the motions of waves and interfaces, along with experimental data on height versus time for the descending upper interface of the test tube, as obtained from literature, were used to calculate the parameters involved in the proposed equations for the constituent parts of the force of interaction and of each strain tensor. Thus, the difference in arbitrary pressures was determined. The numerical results of the parameters in the model equations obtained using the basic parameters of acceleration wave velocity, meeting point of the wave with the descending upper interface, and meeting point of interfaces are reported