Construção de uma base de informações para a diferença de pressões arbitrárias em uma suspensão particulada

Abstract

The study of the motion of particulate suspensions is important both from a theoretical point of view and in many situations of practical interest. The accelerated fall movement of a particle in the fluid is a starting point for parameter information of a suspension, in particular a constitutive part of the interaction force. From the viewpoint of solid-fluid mixtures particulate suspension can be studied based on continuous theory mixtures without chemical reaction, because establishing the equations of the balances more generally, which is important for the analysis of constituent quantities, and when there is some type of restriction, arbitrary quantities. Depending on how these values are grouped, different forms of the equations of motion system of a particulate suspension with incompressibility constraint are obtained. The choice of this system shall be that easy to obtain exact solutions, the simplest possible, to be inserted in mathematical modeling. 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. Then, equations for the constituent parts of the force of interaction and of each strain tensor are proposed. Thus, the preliminary background information for studying the motion of a particulate suspension with an incompressibility constraint was established. Using the background information, the equation to calculate the difference in arbitrary pressures is determined. The numerical calculation results of the acceleration wave velocity, meeting point of the wave with the descending upper interface, the meeting point of the interfaces, of the parameters in the model equations and the difference in arbitrary pressures are reported in this paper.