Taming the diffusiophoretic convective instability in colloidal suspensions

Abstract

A suspension of Brownian colloidal particles stabilised against aggregation is expected to be stable against convection when its density decreases monotonically with height. Surprisingly, a recent experimental investigation has shown that when colloidal particles are dispersed uniformly in a solvent with a stabilising stratification of a molecular solute, the system develops a convective instability under generic conditions [Anzivino \textit{et al., J. Phys. Chem. Lett.}, 2024, \textbf{15}, 9030]. This instability arises because the solute concentration gradient induces an upward diffusiophoretic motion of the colloidal particles, triggering a diffusiophoretic convective instability (DCI). In this work, we investigate the stability of the colloidal suspension against convection in the presence of a stable density stratification of the sample, with different initial conditions. In particular, we study the condition where both the colloid and the molecular solute are initially localized in the lower half of the sample prior to merging with the upper half made of pure water. This is unlike the previously studied setup where the colloid was initially present also in the upper half, suspended in water. We show that only when the concentration of glycerol exceeds a fairly large threshold value of approximately $0.3$w/w the system develops the convective instability. Hence, this new setup offers the possibility to tame DCI by changing the initial conditions. We model the experimental results by numerically solving the nonlinear double diffusion equations in the presence of a diffusiophoretic coupling to determine the time evolution of the base state of the system. The theoretical analysis allows us to elucidate the physical reason for the existence of the threshold value of the glycerol concentration and to establish that the interactions between the colloidal particles in do not play a significant role in the DCI.