| The dissertation contains three projects. All three projects involve flows of two material phases with at least one phase being a granular material.; First, explicit constitutive relations for a binary mixture of nearly elastic disks are derived using a kinetic theory method called the Revised Enskog Theory. Comparison between the theoretical viscosity and viscosity found from numerical simulations is excellent up to moderate densities.; The second project involves a binary mixture of nearly elastic spheres. Existing constitutive relations derived from kinetic theory are corrected and then simplified for mixtures that differ only slightly in mass and diameter. A segregation study is then undertaken in a fully developed, steady, rectilinear flow. First, the thermal diffusion factor is defined and analyzed. It is a measure of local segregation and predicts that large particles tend to be in areas of low granular temperature. Following the local study, a boundary value problem is solved, giving a global picture of the segregation in a fully developed, steady, rectilinear flow between bumpy plates in relative motion. The results are compared with numerical simulations.; A specific model of a debris flow is considered in the third and last project. A two phase continuum model is devised for a mixture of an ideal fluid and uniformly sized particles. The constitutive relations for the particles are based on the idea of a bulk riding on a thin shear layer. The material behavior of the bulk is assumed to be governed by Mohr-Coulomb plasticity, but the shear layer is assumed to be a fully developed, steady, rectilinear flow with constitutive relations from kinetic theory. The shear layer determines the basal friction stress. A numerical solution of depth averaged equations shows some of the instabilities found in experiments. |
