Viscous flow through macroscopic spherical cavities in an arbitrary configuration in a granular material

Viscous flow through macroscopic spherical cavities in a granular material is theoretically investigated. Number, size and configuration of the cavities are arbitrary, except that cavities are sufficiently distant to allow asymptotic analysis on their interaction, which is taken into account up to O(a/l)3 , where a and l are the characteristic radius and inter-cavity distance, respectively. Dependence of the flow field, flux into respective cavities and stress field etc on the cavity size, separation distance and orientation are analyzed. As further examples, 1D-, 2D-, and 3D-array of equal size cavities are examined, by which onset of the collapse of cavity and development of the collapsed region are elucidated. The latter may predict landslides and other flow-induced catastrophic changes in the material with quasi-equilibrium solid structure, as well as microscale waterway formation in human tissue known as angiogenesis.