Role of interfacial stabilization in the Rayleigh-Bénard convection of liquid-liquid dispersions

TL;DR

This study addresses how interfacial stabilization, modeled via a positive disjoining pressure, influences Rayleigh-Bénard convection in liquid-liquid dispersions using mesoscale lattice Boltzmann simulations. By comparing stabilized emulsions with non-stabilized dispersions across varying volume fractions $\phi$ and Rayleigh numbers $\mathrm{Ra}$, the authors quantify both global heat transfer and mesoscale fluctuations through the Nusselt number $\mathrm{Nu}$, its mesoscale counterpart $\mathrm{Nu}_{\mathrm{mes}}$, and an interface indicator $I$. They find that while the total heat transfer $\overline{\mathrm{Nu}}$ is largely insensitive to interfacial details, stabilized systems exhibit stronger mesoscale heat-flux fluctuations with a pronounced, non-monotonic dependence on $\phi$ (maximizing near $0.1<\phi<0.2$) due to persistent velocity fluctuations coupled to interfacial dynamics. The work highlights that interfacial physics can control small-scale energy redistribution in complex fluids without necessarily changing global transport, suggesting avenues for tuning heat transfer in emulsions through interfacial engineering.

Abstract

Based on mesoscale lattice Boltzmann numerical simulations, we characterize the Rayleigh-Bénard (RB) convective dynamics of dispersions of liquid droplets in another liquid phase. Our numerical methodology allows us to modify the droplets' interfacial properties to mimic the presence of an emulsifier (e.g., a surfactant), resulting in a positive disjoining pressure that stabilizes the droplets against coalescence. To appreciate the effects of this interfacial stabilization on the RB convective dynamics, we carry out a comparative study between a proper emulsion, i.e., a system where the stabilization mechanism is present (stabilized liquid-liquid dispersion), and a system where the stabilization mechanism is absent (non-stabilized liquid-liquid dispersion). The study is conducted by systematically changing both the volume fraction, $φ$, and the Rayleigh number, Ra. We find that the morphology of the two systems is dramatically different due to the different interfacial properties. However, the two systems exhibit similar global heat transfer properties, expressed via the Nusselt number Nu. Significant differences in heat transfer emerge at smaller scales, which we analyze via the Nusselt number defined at mesoscales, Nu$_{\mathrm{mes}}$. In particular, stabilized systems exhibit more intense mesoscale heat flux fluctuations due to the persistence of fluid velocity fluctuations down to small scales, which are instead dissipated in the interfacial dynamics of non-stabilized dispersions. For fixed Ra, the difference in mesoscale heat flux fluctuations depends non-trivially on $φ$, featuring a maximum in the range $0.1 < φ< 0.2$. Taken all together, our results highlight the role of interfacial physics in mesoscale convective heat transfer of complex fluids.

Figures (11)

• Figure 1: Representative snapshots of the dynamics of the Rayleigh-Bénard (RB) thermal convection of stabilized and non-stabilized liquid-liquid dispersions. Systems are confined between a lower hot and an upper cold wall at a distance $H$, thus undergoing a temperature difference $\Delta T = T_{\mathrm{hot}} - T_{\mathrm{cold}}$. A buoyancy force is applied due to the gravity ${\bm g}$. Convective states are analyzed by investigating the hydrodynamical fields of density $\rho (x,z,t)$, velocity ${\bm u}(x,z,t)$, and temperature $T (x,z,t)$. Snapshots refer to systems with a volume fraction $\phi=0.28$ and Rayleigh number $\operatorname{Ra} \approx 1.6 \times 10^{7}$.
• Figure 2: Comparison between stabilized and non-stabilized liquid-liquid dispersions at varying volume fractions $\phi$. The selected values of $\phi$ are chosen in such a way that $|\phi - \bar{\phi}| \approx 0.1$, with $\bar{\phi}=0.5$. While non-stabilized systems exhibit morphological symmetry under the exchange of continuous and dispersed phases, stabilized liquid-liquid dispersions break this symmetry due to the presence of a disjoining pressure. All snapshots correspond to simulations at $\operatorname{Ra} \approx 1.6 \times 10^{6}$.
• Figure 3: Density map snapshots for different volume fractions $\phi$ and different Rayleigh numbers $\operatorname{Ra}$, featuring both stabilized and non-stabilized liquid-liquid dispersions. $\operatorname{Ra}$ increases from left to right.
• Figure 4: Time evolution of the Nusselt number $\operatorname{Nu}$ (cfr. Eq. \ref{['eq:Nusselt']}) and the interface indicator $\operatorname{I}$ (cfr. Eq. \ref{['eq:II']}), normalized with its initial value $\operatorname{I}_0$, for stabilized and non-stabilized liquid-liquid dispersions. Left panels refer to cases with a volume fraction $\phi=0.17$. Right panels refer to the case with $\phi=0.39$. Different values of the Rayleigh number $\operatorname{Ra}$ (different colors) are considered. To facilitate readability, data for $\operatorname{Nu}$ are vertically shifted by a quantity $\delta$ which depends on $\operatorname{Ra}$: $\delta = 0$ for $\operatorname{Ra} \approx 1.6 \times 10^{6}$, $\delta=10$ for $\operatorname{Ra} \approx 8 \times 10^{6}$, $\delta = 35$ for $\operatorname{Ra} \approx 1.2 \times 10^{7}$, while $\delta = 70$ for $\operatorname{Ra} \approx 1.6 \times 10^{7}$.
• Figure 5: Steady-state averages in time of the Nusselt number $\overline{\operatorname{Nu}}$ (panels (a)-(c)), and the interface indicator $\bar{\operatorname{I}}$ (panels (d)-(f)) as a function of the volume fraction $\phi$, for different values of the Rayleigh number $\operatorname{Ra}$. Data for both stabilized (red circles) and non-stabilized (grey diamonds) liquid-liquid dispersions are shown.