Convective heat transfer of a model emulsion at the droplet scale

TL;DR

This study numerically investigates how droplet concentration and rheology in emulsions affect convective heat transfer and flow stability in Rayleigh-Bénard convection, revealing non-steady heat flux and droplet correlations.

Contribution

It uncovers the impact of droplet heterogeneity and non-Newtonian rheology on convection dynamics and heat transfer, highlighting phenomena not seen in homogeneous systems.

Findings

Increased droplet concentration leads to non-steady heat flux with fluctuations.

Heterogeneous emulsions exhibit space correlations among droplets.

Non-Newtonian emulsions show shear-thinning behavior affecting convection.

Abstract

We numerically study the Rayleigh-B\'enard (RB) convection in two-dimensional model emulsions confined between two parallel walls at fixed temperatures. The systems under study are heterogeneous, with finite-size droplets dispersed in a continuous phase. The droplet concentration is chosen to explore the convective heat transfer of both Newtonian (low droplet concentration) and non-Newtonian (high droplet concentration) emulsions, the latter exhibiting shear-thinning rheology, with a noticeable increase of viscosity at low shear rates. It is well known that the transition to convection of a homogeneous Newtonian system is accompanied by the onset of steady flow and time-independent heat flux; in marked contrast, the heterogeneity of emulsions brings in an additional and previously unexplored phenomenology. As a matter of fact, when the droplet concentration increases, we observe that the heat transfer process is mediated by a non-steady flow, with neat heat-flux fluctuations, obeying a non-Gaussian statistics. The observed findings are ascribed to the emergence of space correlations among distant droplets, which we highlight via direct measurements of the droplets displacement and the characterisation of the associated correlation functions.