Collapse and growth of cavity regions in granular media due to viscous flow

Abstract

Experimental studies of viscous flow are made on the effect of macroscopic cavity regions in an otherwise homogeneous granular material. The presence of such cavity regions enhances local velocity, which can accelerate the collapse of their boundaries. At the same time, the mobilized regions grow toward the upstream direction. In a continuation of our previous paper [Kaneko and Sano, Phys. Fluids 17, 033102 (2005)], we focus our attention on the latter processes in this paper. For a certain configuration of two interacting cavities, mobilized regions spread faster and in larger scale, which is likely to play an important role in the network formation of a water channel and the onset of a landslide. A numerical simulation based on the two-fluid model is also performed, and is compared with our experimental results.

Viscous flow and collapse of macroscopic cavities in a granular material in terms of a Darcylet

“…We show some examples of the streamlines in figure 3. The present asymptotic model agrees considerably well with (a) our experiment (see the detail in [9,10]) and (b) numerical calculation (see the detail in [11]). We also show the dependence of the flow field on the distance l and orientation α in figure 4.…”

“…On the basis of our present approximation, we calculate the volume flux into the downstream cavity Q 2 . The contourlines of Q 2 are shown in figure 5a, which agrees with our previous experimental results [9,11] and our numerical calculation [11]. For smaller l and α, the volume flux Q 2 is larger than the single cavity case Q s , because some additional fluid volume that flows into upstream cavity C 1 then flows into the downstream cavity C 2 , as is illustrated in figure 5b.…”

“…Flow concentration enhances the local stress on the upstream-side boundary of the cavity, so that the grains of that part will be eroded and carried to the downstream-side boundary if it exceeds certain criteria. This process effectively causes the migration of the cavity towards the upstream direction, or a narrow waterway formation in the medium as was previously shown [10][11][12][13][14][15]. In this paper, we reformulate the analysis on the fundamental flow through a single cavity, and apply it to the interaction of two cavities.…”

Report of the Symposium on Interactions for Dispersed Systems in Newtonian and Viscoelastic Fluids, Guanajuato, Mexico, 2006

“…Osamu Sano ͑Tokyo University of Agriculture and Technology, Japan͒ described an experimental and numerical study of the collapse of cavities in a porous medium or granular flow. 35 The experiments considered were prepared by laying down a layer of granular material on a plate with one or two cylinders placed in the layer to maintain a cavity or cavities, followed by removal of the cylinder͑s͒ and sandwiching the layer by a second glass plate. A pressure-driven flow was imposed through the material.…”

Flow-induced waterway in a heterogeneous granular material

“…These effects are enhanced if more than two such cavity regions interact [2]. Consequent increase of stresses on the boundary of the cavity can destroy the local equilibrium configuration of particles [2,3]. Particles, which detach the upstream-side boundary of the macroscopic cavity region, will be carried downstream, until another local equilibrium configuration is realized.…”