Complex behavior in compressible nonisochoric granular flows

Granular flow models are typically examined within steady isochoric systems where velocity divergence equals zero and properties are uniform along streamlines. Within these flows dilatancy and packing variations can be, and are, neglected. However, there exists a broad range of flows that are nonisochoric, where these variations cannot be ignored. In this paper we examine different nonisochoric systems using discrete element simulations. We first demonstrate that nonisochoric granular flows do not exhibit a simple relationship between stress and packing and that the alignment criterion relating stress to strain rate apply only to well-agitated regions of the flow. Subsequently, the discrete simulation results are used to test the velocity divergence and stress in several compressible granular flow models. We demonstrate that the models are able to capture key features of the nonisochoric flows, though none fully describe the observed behavior. We show that in some cases the predictions of the models can be improved by redefining the equilibrium condition. Finally, we discuss the challenges faced with extending these compressible models into dense regions, where granular flows require nonlocal descriptions of the rheology.