Shear-induced crystallization of a dense rapid granular flow: hydrodynamics beyond the melting point?

TL;DR

This paper models shear-induced crystallization in dense granular flows using hydrodynamics, predicting complex layered flow structures and analyzing their stability, with implications for understanding granular phase transitions beyond melting.

Contribution

It introduces a hydrodynamic model for dense granular flows that predicts multi-layer shear structures and analyzes their stability, extending understanding of shear-induced crystallization.

Findings

Prediction of multi-layer shear flow structures with sharp boundaries.

Identification of conditions for uniform and non-uniform shear flows.

Linear stability analysis suggests possible bifurcations and complex flow regimes.

Abstract

We investigate shear-induced crystallization in a very dense flow of mono-disperse inelastic hard spheres. We consider a steady plane Couette flow under constant pressure and neglect gravity. We assume that the granular density is greater than the melting point of the equilibrium phase diagram of elastic hard spheres. We employ a Navier-Stokes hydrodynamics with constitutive relations all of which (except the shear viscosity) diverge at the crystal packing density, while the shear viscosity diverges at a smaller density. The phase diagram of the steady flow is described by three parameters: an effective Mach number, a scaled energy loss parameter, and an integer number m: the number of half-oscillations in a mechanical analogy that appears in this problem. In a steady shear flow the viscous heating is balanced by energy dissipation via inelastic collisions. This balance can have different forms, producing either a uniform shear flow or a variety of more complicated, nonlinear density, velocity and temperature profiles. In particular, the model predicts a variety of multi-layer two-phase steady shear flows with sharp interphase boundaries. Such a flow may include a few zero-shear (solid-like) layers, each of which moving as a whole, separated by fluid-like regions. As we are dealing with a hard sphere model, the granulate is fluidized within the "solid" layers: the granular temperature is non-zero there, and there is energy flow through the boundaries of the "solid" layers. A linear stability analysis of the uniform steady shear flow is performed, and a plausible bifurcation diagram of the system, for a fixed m, is suggested. The problem of selection of m remains open.