Onset of Transition for Cohesive and Viscous Granular Flows

Abstract

A theory for determining the onset of rapid flow or termination of quasi-static flow in a cohesive granular material mixed in a viscous interstitial fluid is presented. This theory is based on a one-dimensional model introduced in an earlier paper. Linear stability analysis is used to find the combination of material properties and flow rate for which a quasi-static flow becomes unstable, indicating the onset of rapid flow. This theory yields a quantitative criterion to select appropriate constitutive laws for viscous and cohesive granular material. This criterion is a linear approximation of the theoretical result. While it provides the critical condition for quasi-static flow to terminate, it does not give the transitional constitutive law before a rapid flow is fully developed, for which a second power law dependence on the strain rate applies. Nonetheless, the analysis and modeling effort presented in this work are necessary first steps toward a general quantification of how granular materials, with identical physical composition, can behave in drastically different ways.