Dynamical regimes of thermally convective emulsions

TL;DR

This study explores the complex behavior of emulsions under buoyancy-driven thermal convection, revealing how different emulsion rheologies influence convection regimes, droplet dynamics, and structural transformations through extensive numerical simulations.

Contribution

It provides the first detailed characterization of the dynamical regimes of emulsions in thermal convection, linking rheological properties with convection states and droplet size scaling laws.

Findings

Emulsions exhibit different convection states depending on volume fraction and Rayleigh number.

Droplet breakup and phase inversion are observed at high Rayleigh numbers.

Scaling laws for droplet size depend on the convection regime and emulsion rheology.

Abstract

Emulsions are paramount in various interdisciplinary topical areas, yet a satisfactory understanding of their behavior in buoyancy-driven thermal flows has not been established. In the present work, we unravel the dynamical regimes of thermal convection in emulsions by leveraging a large set of mesoscale numerical simulations. Emulsions are prepared with a given volume fraction of the initially dispersed phase, $\phi$, ranging from dilute (low values of $\phi$) to jammed emulsions (high values of $\phi$), resulting in different rheological responses of the emulsion, i.e., from Newtonian to non-Newtonian yield-stress behaviors, respectively. We then characterize the dynamics of the emulsions in the paradigmatic setup of the Rayleigh-B\'enard convection, i.e., when confined between two parallel walls at different temperatures under the effect of buoyancy forces, the latter encoded in the dimensionless Rayleigh number Ra. We thoroughly investigated the dynamics of the emulsion in the changing of $\phi$ and Ra. For a given $\phi$, at increasing Ra, we observe that the emulsion exhibits convection states, where structural changes may appear (i.e., droplet breakup, coalescence or phase inversion), which inevitably impact the emulsion rheology. For sufficiently high values of Ra, two states of convection are observed: for low/moderate values of $\phi$ (Newtonian emulsions), we observe breakup-dominated dynamics, whereas for high values of $\phi$ (non-Newtonian emulsions), we observe phase-inverted states. For both scenarios, the droplet size distribution depends on Ra, and scaling laws for the average droplet size are analyzed and quantified. Our results offer insights into the rich dynamics of emulsions under thermal convection, offering the first detailed characterization of the various dynamic regimes to be expected and their relation with structural changes occurring in such complex fluids.