On the polar nature and invariance properties of a thermomechanical theory for continuum-on-continuum homogenization

This paper makes a rigorous case for considering the continuum derived by the homogenization of extensive quantities as a polar medium in which the balances of angular momentum and energy contain contributions due to body couples and couple stresses defined in terms of the underlying microscopic state. The paper also addresses the question of invariance of macroscopic stress and heat flux and form-invariance of the macroscopic balance laws.

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.