A two-phase thermomechanical theory for granular suspensions

In this paper, a two-phase thermomechanical theory for granular suspensions is presented. Our approach is based on a mixture-theoretic formalism and is coupled with a nonlinear representation for the granular viscous stresses so as to capture the complex non-Newtonian behaviour of the suspensions of interest. This representation has a number of interesting properties: it is thermodynamically consistent, it is non-singular and vanishes at equilibrium and it predicts non-zero granular bulk viscosity and shear-rate-dependent normal viscous stresses. Another feature of the theory is that the resulting model incorporates a rate equation for the evolution of the volume fraction of the granular phase. As a result, the velocity fields of both the granular material and the carrier fluid are divergent even for constant-density flows. Further, in this article we present the incompressible limit of our model which is derived via low-Mach-number asymptotics. The reduced equations for the important special case of constant-density flows are also presented and discussed. Finally, we apply the proposed model to two test cases, namely, steady shear flow of a homogeneous suspension and fully developed pressure-driven channel flow, and compare its predictions with available experimental and numerical results.