Slow relaxation in granular compaction

Abstract

Experimental studies show that the density of a vibrated granular material evolves from a low density initial state into a higher density final steady state. The relaxation towards the final density value follows an inverse logarithmic law. We propose a simple stochastic adsorption-desorption process which captures the essential mechanism underlying this remarkably slow relaxation. As the system approaches its final state, a growing number of beads have to be rearranged to enable a local density increase. In one dimension, this number grows as N = ρ/(1 − ρ), and the density increase rate is drastically reduced by a factor e −N . Consequently, a logarithmically slow approach to the final state is found ρ∞ − ρ(t) ∼ = 1/ ln t.

Production of Dry Powder Clots Using Piezoelectric Drop Generator

“…We have demonstrated that the piezoelectric liquid drop generation technique, originally used for searching for free fractional charge particles in liquids [30,32], The interval corresponds to thousands of high voltage pulses (consistent with the "inverse logarithmically slow" density relaxation in a vibrated granular material discussed for instance in [39,40]) and the clot generation process resembles water dripping from a slightly open tap. The most puzzling question that remains is the origin of forces which bind the powder particles in the clot.…”

“…The reiterative vibration pulses applied to the container tend to compact the particles to the steady state value of the volume fraction η 0.64 (see, e.g. [39,40] …”

Novel experimentally observed phenomena in soft matter

“…The dynamics are therefore driven not by entropy, but by the imposition of external forces. Granular packings exhibit a logarithmically slow approach to the steady state upon external forcing [170]. In contrast to colloidal suspensions, solvent-mediated interactions are not important in granular systems.…”

Entropy for Relaxation Dynamics in Granular Media

“…In their turn these effects induce the need of complex cooperative rearrangements which account for the very slow relaxation dynamics of these systems. At high densities (or very low temperatures for thermal systems) the system remains trapped in a local minimum and exhibits a non-ergodic behavior as well as very slow relaxations: the logarithmic compaction in granular media [3][4][5][6][7] or the Kohlrausch-Williams-Watts (KWW) relaxations in glassy systems [8].In this paper we try to elucidate the role that the concept of entropy can play in the dynamics of these systems. In particular we show how, in the framework of a meanfield model introduced for the compaction phenomenon, there exists a free-energy-like functional which decreases along the trajectories of the dynamics and which allows to account for the asymptotic behavior: e.g.…”

“…For instance in the problems of parking of r-mers (i.e. segments of length r) on a line, under the hypothesis of an exponential distribution for the lengths of the empty (or filled) intervals, the probability for each r-mer to find a sufficient space to land is exp(−r/(1 − ρ)), where ρ is the occupation density on the line [5]. The question we want to address is whether there exists a variational principle driving the relaxation phenomena in this system and in general in granular media.…”