Flow-induced waterway in a heterogeneous granular material

In a heterogeneous granular material, viscous flow concentrates to regions with lower particle number density, or higher permeability region, denoted here by “macroscopic cavity”. This in turn enhances the normal stress toward the fluid region on the upstream boundary, which destroys the boundary if the local stress exceeds a certain magnitude. The latter may further enhance the concentration of flow into the cavity region, which is repeated to form a large scale fluidized region toward upstream direction. These processes have been elucidated in our previous experiment using glass beads layer confined between two parallel plane walls. In this paper, a numerical simulation taking into account of the global flow field on the basis of the generalized Darcy?s equation as well as the local stick-slip equation on the basis of the Newton?s equation of motion is performed. Our numerical simulation can successfully reproduce our experimental findings by imposing a suitable pressure gradient and frictional coefficient. The present numerical method can be applied to more general distribution of cavities, including three-dimensional ones, which may predict the formation of long underground waterways or creation of the passage of blood flows (angiogenesis).