Effective modelling of the Rayleigh-B\'{e}nard convection of concentrated emulsions with finite-size droplets

TL;DR

This study uses mesoscale simulations to analyze heat transfer in concentrated emulsions with finite-size droplets under Rayleigh-Bénard convection, revealing heterogeneity effects and the importance of coarse-graining for system comparison.

Contribution

It introduces a method to compare heterogeneous emulsions with single-phase systems by coarse-graining local viscosity, highlighting the role of droplet-scale effects on heat transfer.

Findings

Heterogeneous flow causes concentration variations in the emulsion.

A suitable coarse-graining scale of droplet size aligns emulsion and single-phase heat transfer.

Quantitative matching is achieved with droplet-scale coarse-graining.

Abstract

We present mesoscale numerical simulations of Rayleigh-B\'{e}nard convection in a two-dimensional concentrated emulsion, confined between two parallel walls, heated from below and cooled from above, under the effect of buoyancy forces. The systems under study comprise finite-size droplets, whose concentration $\Phi_0$ is varied, ranging from the dilute limit up to the point where the emulsion starts to be packed and exhibits non-Newtonian rheology. We focus on the characterisation of the convective heat transfer properties close to the transition from conductive to convective states. The convective flow is confined and heterogeneous, which causes the emulsion to exhibit concentration heterogeneities in space $\phi_0(y)$, depending on the location in the wall-to-wall direction ($y$). With the aim of assessing quantitatively the heat transfer efficiency of such heterogeneous systems, we resort to a side-by-side comparison between the concentrated emulsion system and a single-phase (SP) system, whose local viscosity $\eta^{\mbox{SP}}(y)$ is suitably constructed from the shear rheology of the emulsion. Such comparison highlights that a suitable degree $\Lambda$ of coarse-graining needs to be introduced in the local viscosity $\eta_{\Lambda}^{\mbox{SP}}(y)$, in order for the single-phase system to attain the same heat transfer efficiency of the emulsion. Specifically, it is shown that a quantitative matching between the two systems is possible whenever the coarse-graining is performed over a scale of the order of the droplet size.