What is the final shape of a viscoplastic slump?

Abstract

The final shape of a two-dimensional viscoplastic slump is constructed assuming that the fluid yielded everywhere in its passage to the final state and that the yield stress dominates except in a viscous boundary layer at the base. These assumptions reduce the problem to a related one in plasticity theory. Two methods are presented. First, an asymptotic expansion based on small aspect ratio, ϵ , is used to build an analytical solution valid to third order in ϵ . Second, a slipline method is used to construct slump shapes for arbitrary aspect ratio. The slipline theory exposes flaws in the assumption that the fluid yields everywhere, and rigid plug zones must be inserted in the solution to match all the boundary conditions. The results are compared to a set of experiments with Carbopol in which fluid slumps down a channel. Care is taken to ensure that the width of the channel, any slip over the walls, and the mechanism of emplacement are not important. Despite this, the experiments and theory are not in particularly good agreement, suggesting that some of the theoretical assumptions are invalid.