Mathematical modeling of fluidsolid mixtures
Abstract
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 solidfluid 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 onedimensional 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.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 March 1990
 Bibcode:
 1990STIN...9022007R
 Keywords:

 Equations Of Motion;
 Flow Theory;
 Mathematical Models;
 Mixtures;
 Particles;
 Pipe Flow;
 Pipes (Tubes);
 Two Phase Flow;
 Coal;
 Conservation Laws;
 Stress Tensors;
 Fluid Mechanics and Heat Transfer