On the viscosity of a mixture of particulate solids and a fluid continuum
Abstract
In this work, the theory of interacting continua is used to formulate the governing equations of motion for each component and the mixture (a granular material and Newtonian fluid) as a whole. The fluid is assumed to be an incompressible viscous fluid and solid particles are treated as granular materials. Appropriate constitutive relations for stresses are proposed. Based on these, the stress tensor for the mixture is obtained, and in some ideal experiment where the velocities of the two phases are equal, a relationship among the viscosities of the two components and the viscosity of mixture exists. Based on these observations, simple experiments can be devised to obtain the viscosity of the solid particles. In Section 1, the importance of multicomponent flows is discussed. Section 2 provides a survey of literature on the stress tensors in twophase flows. In Section 3, the basics of the theory of interacting continua are discussed and equations of motion for the mixture are derived. In the final section, a few experiments are suggested that would help in measuring the material properties of the mixture.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 September 1990
 Bibcode:
 1990STIN...9112912M
 Keywords:

 Computational Fluid Dynamics;
 Continuum Mechanics;
 Incompressible Fluids;
 Newtonian Fluids;
 Two Phase Flow;
 Viscous Fluids;
 Equations Of Motion;
 Granular Materials;
 Mathematical Models;
 Particulates;
 Solids;
 Stress Tensors;
 Fluid Mechanics and Heat Transfer