Brinkman-medium resistance hampers periodic motions of sedimenting particles

Abstract

The dynamics of groups of non-touching particles settling under gravity in a crowded fluid medium are studied at the zero Reynolds number. It is assumed that the fluid velocity satisfies the Brinkman–Debye–Büche equations, and the particle dynamics are described in terms of the point-force model. The systems of particles at vertices of two or four horizontal regular polygons are considered that in the Stokes flow for a very long time do not destabilize, i.e., all the particles stay close to each other, performing periodic or quasiperiodic motions. It is known that such motions, as invariant manifolds, are essential for groups of particles at random initial positions to survive for a very long time and not destabilize. This work demonstrates that when the medium permeability is decreased, periodic motions cease to exist, and groups of particles split into smaller subgroups, moving away from each other. This mechanism seems to facilitate particle transport in a permeable medium.