Entropy-Driven Attraction of Heavy Spheres in a Harmonically Driven Bath of Poppy Seeds

Abstract

We develop the simplest possible theory that gives reason of the recent experimental observations that two heavy spheres, immersed into a mono-layer bath of poppy seeds, attract one another when shaken harmonically in a single horizontal direction. Their attraction is so strong that the two spheres remain bound during hundreds of driving periods. The paper consists of three independently readable Chapters, with only a few inter-chapter references. The first Chapter concerns itself with the the motion of a roller amidst a horizontally shaken sea of poppy seeds, under the Assumption of equal phase for rotational and translation velocities. The second Chapter details how this predicts the observed longitudinal diffusion of a single sphere in a bath of poppy seeds. The third Chapter shows how to retrieve all relevant physical parameters from experiment: viscosity of the seed bath, friction of the heavy spheres with the harmonically moving substrate, equilibrium rates for dissociation of bound pairs or binding of lone pairs, and the full Gibbs potential surface as a function of experimentally accessible parameters.