Experimental investigation of gravitational instabilities at the particle suspension-fluid interface

Abstract

Gravitational instabilities occurring at the interface between a suspension of granular particles and a clear fluid are studied experimentally using a sealed Hele–Shaw cell. Special attention is paid to the effects of particle Reynolds number (Re) and the initial particle packing on the growth of the interfacial perturbation. Glass beads are immersed in the glycerin–water mixture and are placed at the bottom of the cell initially. The mass content of the glycerin in fluid mixtures is varied to obtain the desired fluid viscosities and thus the Re value. The cell is then inverted to place the suspension above the fluid to trigger the gravitational instabilities. When the particle packing is dense, the distinct interface separating the fluid transforms progressively into an asymmetrical cusp-shaped structure. In contrast, when the packing is loose, the interface between the fluid and suspension takes on a symmetrical sinusoidal form initially and evolves into a mushroom-like pattern reminiscent of the canonical Rayleigh–Taylor instability. The growth rate of this symmetrical perturbation observed for loose packing surpasses that of its asymmetrical counterpart at the equivalent Re. Both types of perturbations exhibit larger growth rates with increasing Re. Linear stability analysis adapted to the loose packing configuration predicts a growth rate that is comparable to the observed rate during the initial growth of the symmetrical perturbation and suggests a similar dependence on Re.

Appendix: Late-time processes following the instabilities

Fig. 20

Representative snapshots for the experiment with $\text {Re}=7.3\times 10^{-3}$ and dense packing ($M>0.99$) subsequent to those shown in Fig. 7

In Fig. 20 in this appendix, we illustrate the progression of flow within the Hele–Shaw cell following the destruction of the initial suspension-fluid boundary. Figure 20a duplicates the final snapshot presented in Figs. 7, and  20b–f showcase the ensuing processes. Specifically, in Fig. 20b, the dilute fluid ‘bubble’ reaches the upper boundary of the cell; by Fig. 20c, a distinct gap emerges between the suspension and the top wall due to material depletion within this top layer. Throughout Fig. 20d–f, the process of hindered settling continues, leading to further consolidation of the material and a growing height of clear fluid layer within the cell.