Rayleigh-B\'enard convection of a model emulsion: anomalous heat-flux fluctuations and finite-size droplets effects

TL;DR

This study uses mesoscale simulations to analyze heat transfer and flux fluctuations in a 2D emulsion under Rayleigh-Bénard convection, revealing how finite-size droplets and non-Newtonian rheology influence non-steady heat flux dynamics.

Contribution

It introduces a detailed comparison between emulsion and single-phase systems, highlighting the role of droplet size and rheology in heat flux fluctuations and space correlations.

Findings

Finite-size droplets and non-Newtonian rheology enhance heat-flux fluctuations.

Local viscosity coarse-graining improves heat flux modeling.

Distant droplet correlations underpin flux fluctuations.

Abstract

We present mesoscale numerical simulations of Rayleigh-B\'enard (RB) convection in a two-dimensional model emulsion. The systems under study are constituted of finite-size droplets, whose concentration Phi_0 is systematically varied from small (Newtonian emulsions) to large values (non-Newtonian emulsions). We focus on the characterisation of the heat transfer properties close to the transition from conductive to convective states, where it is known that a homogeneous Newtonian system exhibits a steady flow and a time-independent heat flux. In marked contrast, emulsions exhibit a non-steady dynamics with fluctuations in the heat flux. In this paper, we aim at the characterisation of such non-steady dynamics via detailed studies on the time-averaged heat flux and its fluctuations. To understand the time-averaged heat flux, we propose a side-by-side comparison between the emulsion system and a single-phase (SP) system, whose viscosity is constructed from the shear rheology of the emulsion. We show that such local closure works well only when a suitable degree of coarse-graining (at the droplet scale) is introduced in the local viscosity. To delve deeper into the fluctuations in the heat flux, we propose a side-by-side comparison between a Newtonian emulsion and a non-Newtonian emulsion, at fixed time-averaged heat flux. This comparison elucidates that finite-size droplets and the non-Newtonian rheology cooperate to trigger enhanced heat-flux fluctuations at the droplet scales. These enhanced fluctuations are rooted in 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 function. The observed findings offer insights on heat transfer properties for confined systems possessing finite-size constituents.