Mathematical modeling of fluid-solid mixtures.

摘要

The flows of a mixture of solid particles and a fluid have relevance to several important technological applications. There are primarily two approaches that have been used for modeling such solid-fluid systems. In the first approach, the model is obtained by some kind of averaging of the equations of motion. In the second approach, the basic conservation laws are postulated and the ideas in continuum mechanics are used to arrive at appropriate constitutive relations. In this report we use this approach called mixture theory to derive the governing equations of motion for a steady one-dimensional fully developed pipe flow of a mixture of particles and a fluid. We present a brief historical account of the modeling of stress tensors for particles and the fluid. Finally, we discuss the importance of the boundary conditions. 24 refs.