Preliminary background information for the study of the motion of a particulate suspension with incompressibility constraint

Abstract

This work dealt with porous media with incompressible constraints and is a study on the preparation of a preliminary background information to arbitrary and constitutive quantities of a particulate suspension. Two exact solutions of a system of motion equations for the particulate suspension were determined. The solutions were applied in the mathematical modeling of the gravitational motion of particulate suspensions in a test tube. The modeling considered sub-regions that varied with time and were bounded by moving interfaces and acceleration wave. One solution was embedded in the free sedimentation region, and the other, in the transition region. Motions of the wave and the interfaces were established by the compatibilization of the exact solution of the free sedimentation region with that of the transition region. The motions depend on the velocity parameters of the acceleration wave, meeting point of the wave with the descending upper interface, and meeting point of the interfaces. From the exact solutions and motions, two velocity functions were established, and these functions, along with the experimental data on height versus time of the descending upper interface of the test tube as obtained from literature, served as the basis for calculating the parameters. Thus, the preliminary background information for studying the motion of a particulate suspension with an incompressibility constraint was established. The numerical calculation results of the acceleration wave velocity, meeting point of the wave with the descending upper interface, and the meeting point of the interfaces are reported in this paper.