Flow-induced waterway in a heterogeneous granular material

Recent investigations on the collapse and growth of macroscopic cavity regions in a granular material due to viscous flow have revealed the possible mechanism of the occurrence of natural disasters such as landslides, collapses of riverbanks and cliffs. We have already shown both theoretically and experimentally a significant effect of flow concentration into the macroscopic cavity regions in an otherwise homogeneous granular material, i.e., the volume flux into a two-dimensional circular cavity and the velocity at its center amount to 2 times and 3 times, respectively, (and 3 times and 6 times, respectively, in the case of a spherical cavity) compared to those without the cavity[1]. 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. The latter configuration change modifies the local flow field, which may enhance further destruction of the upstream cavity boundary. Repeated such processes may enlarge the cavity region or fluidized region toward upstream direction, leading to a long groundwater channel in the granular material. A similar situation can be found in an angiogenesis in biological tissues, where a new passage of blood flow or a capillary tube is created toward tumor or cancer cells. In this paper we shall confine our attention to the fundamental mesoscopic processes that bridge the gap between microscopic configuration changes due to viscous flow and the macroscopic fluidization. Initially spherical particles are introduced in almost densest packing, except the cavity region(s). The flow field and the particle motion are calculated by repeating the following procedures: (i) determine the local porosity for the given configuration of