Granular Rayleigh-Taylor Instability: Experiments and Simulations

A granular instability driven by gravity is studied experimentally and numerically. The instability arises as grains fall in a closed Hele-Shaw cell where a layer of dense granular material is positioned above a layer of air. The initially flat front defined by the grains subsequently develops into a pattern of falling granular fingers separated by rising bubbles of air. A transient coarsening of the front is observed right from the start by a finger merging process. The coarsening is later stabilized by new fingers growing from the center of the rising bubbles. The structures are quantified by means of Fourier analysis and quantitative agreement between experiment and computation is shown. This analysis also reveals scale invariance of the flow structures under overall change of spatial scale.

Figure 1

(a) Experimental image and (b) numerical snapshot of a vertical Hele-Shaw cell where polystyrene beads (in black) of $140\mu \mathrm{m}$ in diameter displace air (in white). The cells are 56 mm wide and were rotated 0.2 s ago.

Figure 2

(a),(d) Interfaces superposed on the snapshots ($t=0.20\mathrm{s}$) from Fig. 1. (b),(e) Spatiotemporal evolution of the air-grain interface from $t=0.00\mathrm{s}$ (bottom) to $t=0.29\mathrm{s}$ (top). (c),(f) Temporal evolution of the power spectrum of the interfaces. The circles indicate the location of the maximum wave number.

Figure 3

Mean wave number $⟨k⟩$ and standard deviation ${\sigma }_k$ (inset) for two experiments and one simulation, all using polystyrene beads of $140\mu \mathrm{m}$ in diameter.

Figure 4

Data-collapse plot of $d⟨k⟩$ for a series of (a) simulations using glass beads and (b) experiments using polystyrene beads. The grain diameters $d$ are given in the legend box. The inset shows the evolution of $⟨k⟩$.