Rayleigh-Bénard thermal convection in emulsions: a short review

TL;DR

This paper surveys how thermally driven emulsions behave in Rayleigh-Bénard convection, emphasizing the coupling between concentration-dependent rheology and buoyancy-driven flows. It relies on 2D multicomponent lattice Boltzmann simulations with disjoining-pressure stabilization to resolve finite-sized droplets and interfacial dynamics, analyzing macroscopic heat transfer via the Nusselt number $\overline{\operatorname{Nu}}$, and droplet-scale transport through $\operatorname{Nu}_{\mathrm{drop}}$ and droplet displacements. Key findings show that droplet stabilization and high volume fractions induce non-Newtonian and yield-stress rheology, trigger phase-inversion phenomena, and promote intermittent convection with bursts linked to microstructural rearrangements, while finite-sized droplets amplify localized heat-transfer fluctuations and cooperative effects near boundaries. The study highlights the essential role of interfacial physics in thermal convection of soft materials and outlines a path toward experimental validation and 3D simulations to extend these insights.

Abstract

Thermally driven emulsions arise in a broad range of natural and industrial contexts, yet their fundamental physical understanding remains only partially established. Emulsions exhibit a complex, concentration-dependent rheology, ranging from Newtonian (dilute emulsions) to yield-stress (concentrated emulsions). In buoyancy-driven flows, the complex structure and rheology of the emulsion are strongly coupled to convective flows, giving rise to fascinating and non-trivial phenomena involving stability, transient dynamics, and morphological evolution of the system. We review recent progress on thermally driven emulsions in the celebrated Rayleigh-Bénard configuration, offering new perspectives on the behaviour of soft materials in thermal convection.

Figures (4)

• Figure 1: Panel (a): Snapshots of oil-in-water emulsions with different values of the volume fraction of the initially dispersed phase, $\phi$. Panel (b): rheological curve relating the shear stress to the shear rate for emulsions shown in panel (a). Panel (c): Snapshots of stabilised (i.e., proper emulsions, left column) and non-stabilised (right column) liquid-liquid dispersions at $\phi<0.5$ (top row) and $\phi>0.5$ (bottom row). Panel (d): oil-in-water emulsion in a 2D RB cell, confined between a lower hot and an upper cold wall and under the effect of buoyancy forces. Light blue arrows highlight droplet displacements, $\mathrm{\bf d} (x,z,t)$, at a given time during convective dynamics, marking the convective rolls. The corresponding thermal plume is also shown.
• Figure 2: Analysis of heat transfer at macroscopic scales. Panel (a): time evolution of the Nusselt number $\operatorname{Nu}(t)$, highlighting the time average of the Nusselt number $\overline{\operatorname{Nu}}$ over the statistically steady state [see Eq. \ref{['eq:Nu']}]. Data refer to an emulsion with $\phi=0.16$ for a value of the Rayleigh number $\operatorname{Ra} \approx 4 \times 10^6$. Time is reported in simulation units. Panel (b): $\overline{\operatorname{Nu}}$, as a function of $\operatorname{Ra}$ [see Eq. \ref{['eq:Ra']}] for $\phi = 0.16$ and $\phi = 0.84$. We report cases of stabilised (i.e., proper emulsions) and non-stabilised liquid-liquid dispersions.
• Figure 3: Analysis of heat transfer at the droplet scale. Panel (a): Log-lin plot of the PDF of the droplet Nusselt number $\operatorname{Nu}_{\mathrm{drop}}$ [see Eq. \ref{['eq:NuDrop']}], computed over all droplets and time frames. Values are expressed in units of the standard deviation, $\sigma_{\operatorname{Nu}}$, relatively to the mean $\overline{\operatorname{Nu}_{\mathrm{drop}}}$. Different symbols (colors) refer to different values of $\phi$ ($\overline{\operatorname{Nu}}$). We also report zoomed snapshots of displacement fluctuations $\delta \mathrm{\bf d}(x,z,t)$ [see Eq. \ref{['eq:displ_fluct']}] of droplets contributing to positive and negative PDF tails. Panel (b): Spatio–temporal map of the absolute value of the $x$–averaged displacement fluctuations, $\tilde{\delta \mathrm{\bf d}}(z,t)$ [see Eq. \ref{['eq:displ_fluct']}].
• Figure 4: Time evolution of the average heat transfer $\operatorname{Nu}(t)$ of a jammed emulsion with $\phi = 0.79$ and $\operatorname{Ra} \approx 4 \times 10^5$. Dotted black line marks the conductive regime ($\operatorname{Nu} = 1$), while upper panels show maps of density (first row) and temperature (second row) for some selected configurations [panels (a)–(d)]. Time is reported in simulation units.