A continuum model for the bulldozing of an immersed granular material in a confined geometry #

Liam Morrow, Chris MacMinn, Oliver Paulin, Matthew Hennessy, Duncan Hewitt

11:10 Wednesday in 4Q07.

Part of the Granular and multiphase flows session.

Abstract #

The flow of immersed granular materials in confined geometries is difficult to characterise due to the complex interactions among the grains, between the grains and the ambient liquid, and between both materials and the walls. Here, we present a reduced-order continuum model for the bulldozing of an immersed, sedimented granular material by a rigid piston in a fluid-filled gap between two parallel plates. This scenario has been studied previously using ad-hoc models and discrete-element simulations. In our continuum approach, the granular pile and the overlying fluid layer evolve as coupled thin films. We model the solid phase as a dense, viscous porous material that experiences Coulomb-like friction along the walls. Conservation of mass and momentum lead to a linear elliptic equation for the local velocity of the grains that is coupled with a nonlinear conservation law for the height of the granular pile. We solve our model numerically for a variety of different scenarios in order to develop insight into the interactions between wall friction, internal viscous-like stresses, and fluid flow both above and through the pile. Further, we validate our model against experimental results.