Experimental study of competition between Rayleigh–Taylor and double-diffusive fingering when particles settle in the presence of a diffusing scalar in a Hele–Shaw cel1

Abstract

We investigate fluid instabilities in a Hele–Shaw cell driven by the combined effects of double diffusion (DD) and Rayleigh–Taylor (RT) mechanisms, focusing on the formation of vertical fingers and overturning plumes. These patterns emerge from the interplay between sediment settling and the diffusion of a scalar (dextrose). A novel experimental design is introduced in which particle sizes are selected so that their settling velocities are slower than, comparable to, or faster than the solute diffusion rate. This systematic variation allows the relative influence of settling and diffusion to be isolated and quantified. Two primary questions are addressed. First, under what conditions do fingering instabilities arise, as opposed to pure particle settling? We find that fingering is suppressed when the particle settling velocity exceeds the DD finger tip velocity. A predictive criterion is developed based on a dimensionless gravity parameter and the ratio of characteristic settling to diffusion times. Second, when instabilities are present, which mechanism—DD or RT—dominates? As expected, DD dominates when diffusion is rapid. A transition from DD to RT is observed when the settling-to-diffusion time ratio falls below approximately 0.2, using the gap width as the characteristic length scale. This work introduces a straightforward framework for exploring competing instability mechanisms in sediment-laden, diffusive flows in an experimentally accessible, previously uncharacterized parameter space.