Coarsening dynamics of granular heaplets in tapped granular layers

A semi-continuum model is introduced to study the dynamics of the formation of granular heaplets in tapped granular layers. By taking into account the energy dissipation of collisions and screening effects due to avalanches, this model is able to reproduce qualitatively the pattern of these heaplets. Our simulations show that the granular heaplets are characterized by an effective surface tension which depends on the magnitude of the tapping intensity. Also, we observe that there is a coarsening effect in that the average size of the heaplets, V , grows as the number of taps k increases. The growth law at intermediate times can be fitted by a scaling function V ∼ k but the range of validity of the power law is limited by size effects. The growth exponent z appears to diverge as the tapping intensity is increased. In recent years, there has been increasing interest in the collective dynamics of granular materials. The dissipative nature of granular materials gives rise to properties distinct from those of solids and liquids. Many experimental and theoretical attempts have been made to seek a fundamental understanding of this granular state and especially pattern formation in driven granular layers. The experiments include vertically vibrated systems [1, 2], tapped or blown thin films of powders [3, 4] and electrostatically driven granular layers [5, 6]. Although many papers have been published to explain the experiments on tapped granular layers, most of them deal with either compactification of thick granular layers [7, 8], or static properties of granular heaplets on a thin granular layer [3]. The dynamical aspect of the heaping process in a tapped thin granular layer is still not well understood. This paper is concerned with the coarsening dynamics of granular heaplets in tapped granular layers from a theoretical point of view. This paper is organized as follows. First we introduce a simple model to study this fascinating system by considering the energy dissipation and screening effects during the tapping process. Despite its simplicity, this model is capable of capturing the essential phenomenology, reproducing various morphologies of the coarsening pattern, and showing the way in which New Journal of Physics 4 (2002) 81.1–81.9 PII: S1367-2630(02)52513-1 1367-2630/02/000081+9$30.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft