Structures and chaotic fluctuations of granular clusters in a vibrated fluid layer

Abstract

Particles that oscillate with respect to a background fluid experience a long-range attraction and a short-range repulsion that give rise to clustering at a preferred separation. We have studied the structure and dynamics of these clusters for both small (2<N<7) and large (N=25 or 48) clusters. For small clusters, the particles often form well-defined structures with chaotic fluctuations about the mean particle positions. However, for a given N , there are generally several different structures, e.g., both isosceles and equilateral triangles. The nearest neighbor spacings grow systematically with the dimensionless driving acceleration Gamma. Large clusters are less rigid, and show much larger velocity fluctuations than do small clusters, for sufficiently large Gamma. The fluctuation amplitude grows systematically with Gamma for large clusters, but not for small ones. The instantaneous particle velocity is typically largest when a particle moves through a region where its probability density is low. Some of the observed phenomena suggest a variational model in which particles seek minima in an effective potential, and are perturbed by dynamically generated noise arising from the nonlinear interactions between particles. However, pairwise forces cannot account for all of the results. We discuss the nature of the fluctuations, including the low apparent dimension of the occupied set in configuration space for clusters of modest size.