Archimedes' law and its corrections for an active particle in a granular sea

TL;DR

This paper investigates buoyancy and its corrections for a particle in a shaken granular medium, revealing the effects of memory and excluded volume interactions through a lattice gas model.

Contribution

It introduces a theoretical model using asymmetric exclusion processes to explain buoyancy corrections and mutual attraction in granular media.

Findings

Archimedes' law holds in the fluid limit.

Memory effects oppose buoyancy before fluidization.

Excluded volume effects cause mutual attraction between particles.

Abstract

We study the origin of buoyancy forces acting on a larger particle moving in a granular medium subject to horizontal shaking and its corrections before fluidization. In the fluid limit Archimedes' law is verified; before the limit memory effects counteract buoyancy, as also found experimentally. The origin of the friction is an excluded volume effect between active particles, which we study more exactly for a random walker in a random environment. The same excluded volume effect is also responsible for the mutual attraction between bodies moving in the granular medium. Our theoretical modeling proceeds via an asymmetric exclusion process, i.e., via a dissipative lattice gas dynamics simulating the position degrees of freedom of a low density granular sea.