A viscoplastic slump on a horizontally oscillating plate

Abstract

A thin, two-dimensional deposit of viscoplastic fluid is studied as it slumps atop a horizontal plate exhibiting in-plane oscillations. Numerical results are reported for a range of Bingham and oscillatory Reynolds numbers, and comparison is made with asymptotic results obtained for low oscillatory Reynolds numbers. When inertia is small, these flows become arrested as time t→∞, and approach a symmetric state where the maximum basal stress in a period of oscillation balances with the yield stress. An exact expression for this final shape is obtained. The deposit slumps further across the plate at small Bingham numbers and results in a thinner profile. The arrested shape is equivalent to the ..