The “avalanche effect” of an elasto-viscoplastic thixotropic material on an inclined plane

The so-called avalanche effect is one of the fingerprints of thixotropic materials. This self-reinforcing process where the decrease in viscosity, due to a rejuvenation process triggered by a stress field, induces a motion which in turn contributes to decrease the viscosity again, is well exemplified by the inclined plane problem. In this situation, the material in its fully-structured state is placed on an inclined plane with respect to the gravity force which is responsible for the beginning of the breakdown process. These thixotropic systems generally have a yield stress, a strength that must be overcome in order to induce rejuvenation. In addition, they exhibit elastic features, especially in the pre-yield state. In the present work we numerically solve the transient evolution of an elasto-viscoplastic thixotropic material subjected to the action of gravity on an inclined plane. In order to handle with the moving free-surface boundary condition encountered in the avalanche effect, we have used a combination of the Marker-And-Cell (MAC) method with the front-tracking scheme. This formulation was successfully employed for this kind of material in the recent paper of Oishi et al. (2016) [28]. In the present work, we have adapted our finite difference formulation to analyze the effects associated with an extended Herschel-Bulkley model in the simulation of a transient complex free surface flow. Concerning the parameters of the flow curve, it is shown that the dimensionless yield stress (plastic number) is the most significant one. However, for a fixed plastic number, different combinations of dimensionless consistency index and dimensionless Newtonian viscosity plateau can lead to a diversity of responses. The thixotropic equilibrium time had a significant impact on shifting the instant when the flow regime changes from an accelerating (when the front part of the material accelerates) to a retardation one (when this front part decelerates). Higher elasticity, as captured by the Weissenberg number, led to longer distances covered by the material.