Two-layer Thermally Driven Turbulence: Mechanisms for Interface Breakup

It is commonly accepted that the breakup criteria of drops or bubbles in turbulence is governed by surface tension and inertia. However, also {\it{buoyancy}} can play an important role at breakup. In order to better understand this role, here we numerically study Rayleigh-B\'enard convection for two immiscible fluid layers, in order to identify the effects of buoyancy on interface breakup. We explore the parameter space spanned by the Weber number $5\leq We \leq 5000$ (the ratio of inertia to surface tension) and the density ratio between the two fluids $0.001 \leq \Lambda \leq 1$, at fixed Rayleigh number $Ra=10^8$ and Prandtl number $Pr=1$. At low $We$, the interface undulates due to plumes. When $We$ is larger than a critical value, the interface eventually breaks up. Depending on $\Lambda$, two breakup types are observed: The first type occurs at small $\Lambda \ll 1$ (e.g. air-water systems) when local filament thicknesses exceed the Hinze length scale. The second, strikingly different, type occurs at large $\Lambda$ with roughly $0.5 < \Lambda \le 1$ (e.g. oil-water systems): The layers undergo a periodic overturning caused by buoyancy overwhelming surface tension. For both types the breakup criteria can be derived from force balance arguments and show good agreement with the numerical results.Comment: 13 pages, 7 figure

Effect of Prandtl number on heat transport enhancement in Rayleigh-B\'enard convection under geometrical confinement

We study, using direct numerical simulations, the effect of geometrical confinement on heat transport and flow structure in Rayleigh-B\'enard convection in fluids with different Prandtl numbers. Our simulations span over two decades of Prandtl number $Pr$, $0.1 \leq Pr \leq 40$, with the Rayleigh number $Ra$ fixed at $10^8$. The width-to-height aspect ratio $\Gamma$ spans between $0.025$ and $0.25$ while the length-to-height aspect ratio is fixed at one. We first find that for $Pr \geq 0.5$, geometrical confinement can lead to a significant enhancement in heat transport as characterized by the Nusselt number $Nu$. For those cases, $Nu$ is maximal at a certain $\Gamma = \Gamma_{opt}$. It is found that $\Gamma_{opt}$ exhibits a power-law relation with $Pr$ as $\Gamma_{opt}=0.11Pr^{-0.06}$, and the maximal relative enhancement generally increases with $Pr$ over the explored parameter range. As opposed to the situation of $Pr \geq 0.5$, confinement-induced enhancement in $Nu$ is not realized for smaller values of $Pr$, such as $0.1$ and $0.2$. The $Pr$ dependence of the heat transport enhancement can be understood in its relation to the coverage area of the thermal plumes over the thermal boundary layer (BL) where larger coverage is observed for larger $Pr$ due to a smaller thermal diffusivity. We further show that $\Gamma_{opt}$ is closely related to the crossing of thermal and momentum BLs, and find that $Nu$ declines sharply when the thickness ratio of the thermal and momentum BLs exceeds a certain value of about one. In addition, through examining the temporally averaged flow fields and 2D mode decomposition, it is found that for smaller $Pr$ the large-scale circulation is robust against the geometrical confinement of the convection cell.Comment: 25 pages, 11 figures, and 1 table in main tex

A bouncing oil droplet in a stratified liquid and its sudden death

Droplets can self-propel when immersed in another liquid in which a concentration gradient is present. Here we report the experimental and numerical study of a self-propelling oil droplet in a vertically stratified ethanol/water mixture: At first, the droplet sinks slowly due to gravity, but then, before having reached its density matched position, jumps up suddenly. More remarkably, the droplet bounces repeatedly with an ever increasing jumping distance, until all of a sudden it stops after about 30 min. We identify the Marangoni stress at the droplet/liquid interface as responsible for the jumping: its strength grows exponentially because it pulls down ethanol-rich liquid, which in turn increases its strength even more. The jumping process can repeat because gravity restores the system. Finally, the sudden death of the jumping droplet is also explained. Our findings have demonstrated a type of prominent droplet bouncing inside a continuous medium with no wall or sharp interface.Comment: 6 pages, 4 figure

From zonal flow to convection rolls in Rayleigh-B\'enard convection with free-slip plates

Rayleigh-B\'enard (RB) convection with free-slip plates and horizontally periodic boundary conditions is investigated using direct numerical simulations. Two configurations are considered, one is two-dimension (2D) RB convection and the other one three-dimension (3D) RB convection with a rotating axis parallel to the plate. We explore the parameter range of Rayleigh numbers Ra from $10^7 to$10^9$and Prandtl numbers$Pr$from$1$to$100. We show that zonal flow, which was observed, for example, by Goluskin \emph{et al}. \emph{J. Fluid. Mech.} 759, 360-385 (2014) for \Gamma=2$, is only stable when$\Gamma$is smaller than a critical value, which depends on$Ra$and$Pr$. With increasing$\Gamma$, we find a second regime in which both zonal flow and different convection roll states can be statistically stable. For even larger$\Gamma$, in a third regime, only convection roll states are statistically stable and zonal flow is not sustained. For the 3D simulations, we fix$Ra=10^7$and$Pr=0.71$, and compare the flow for$\Gamma=8$and$\Gamma = 16$. We demonstrate that with increasing aspect ratio$\Gamma$, zonal flow, which was observed for small$\Gamma=2\pi by von Hardenberg \emph{et al}. \emph{Phys. Rev. Lett.} 15, 134501 (2015), completely disappears for \Gamma=16$. For such large$\Gamma$only convection roll states are statistically stable. In between, here for medium aspect ratio$\Gamma = 8$, the convection roll state and the zonal flow state are both statistically stable. What state is taken depends on the initial conditions, similarly as we found for the 2D case.Comment: 26 pages, 12 figure

Convection-dominated dissolution for single and multiple immersed sessile droplets

We numerically investigate both single and multiple droplet dissolution with droplets consisting of less dense liquid dissolving in a denser host liquid. In this situation, buoyancy can lead to convection and thus plays an important role in the dissolution process. The significance of buoyancy is quantified by the Rayleigh number , which is the buoyancy force over the viscous damping force. In this study, spans almost four decades from 0.1 to 400. We focus on how the mass flux, characterized by the Sherwood number , and the flow morphologies depend on. For single droplet dissolution, we first show the transition of the scaling from a constant value to , which confirms the experimental results by Dietrich et al. (J. Fluid Mech., vol. 794, 2016, pp. 45-67). The two distinct regimes, namely the diffusively and the convectively dominated regimes, exhibit different flow morphologies: when , a buoyant plume is clearly visible, which contrasts sharply with the pure diffusion case at low. For multiple droplet dissolution, the well-known shielding effect comes into play at low , so that the dissolution rate is slower as compared to the single droplet case. However, at high , convection becomes more and more dominant so that a collective plume enhances the mass flux, and remarkably the multiple droplets dissolve faster than a single droplet. This has also been found in the experiments by Laghezza et al. (Soft Matt., vol. 12 (26), 2016, pp. 5787-5796). We explain this enhancement by the formation of a single, larger plume rather than several individual plumes. Moreover, there is an optimal at which the enhancement is maximized, because the single plume is narrower at larger , which thus hinders the enhancement. Our findings demonstrate a new mechanism in collective droplet dissolution, which is the merging of the plumes, which leads to non-trivial phenomena, contrasting the shielding effect.</p

Convection-dominated dissolution for single and multiple immersed sessile droplets

We numerically investigate both single and multiple droplet dissolution with droplets consisting of lighter liquid dissolving in a denser host liquid. The significance of buoyancy is quantified by the Rayleigh number Ra which is the buoyancy force over the viscous damping force. In this study, Ra spans almost four decades from 0.1 to 400. We focus on how the mass flux, characterized by the Sherwood number Sh, and the flow morphologies depend on Ra. For single droplet dissolution, we first show the transition of the Sh(Ra) scaling from a constant value to $Sh\sim Ra^{1/4}$, which confirms the experimental results by Dietrich et al. (J. Fluid Mech., vol. 794, 2016, pp. 45--67). The two distinct regimes, namely the diffusively- and the convectively-dominated regime, exhibit different flow morphologies: when Ra>=10, a buoyant plume is clearly visible which contrasts sharply to the pure diffusion case at low Ra. For multiple droplet dissolution, the well-known shielding effect comes into play at low Ra so that the dissolution rate is slower as compared to the single droplet case. However, at high Ra, convection becomes more and more dominant so that a collective plume enhances the mass flux, and remarkably the multiple droplets dissolve faster than a single droplet. This has also been found in the experiments by Laghezza et al. (Soft Matter, vol. 12, 2016, pp. 5787--5796). We explain this enhancement by the formation of a single, larger plume rather than several individual plumes. Moreover, there is an optimal Ra at which the enhancement is maximized, because the single plume is narrower at larger Ra, which thus hinders the enhancement. Our findings demonstrate a new mechanism in collective droplet dissolution, which is the merging of the plumes, that leads to non-trivial phenomena, contrasting the shielding effect.Comment: 18 pages, 11 figures, submitted to JF

Enhancing Heat Transport in Multiphase Rayleigh-B\'enard Turbulence by Changing the Plate-Liquid Contact Angles

This numerical study presents a simple but extremely effective way to considerably enhance heat transport in turbulent multiphase flows, namely by using oleophilic walls. As a model system, we pick the Rayleigh-B\'enard setup, filled with an oil-water mixture. For oleophilic walls, e.g. using only $10\%$ volume fraction of oil in water, we observe a remarkable heat transport enhancement of more than $100\%$ as compared to the pure water case. In contrast, for oleophobic walls, the enhancement is then only about $20\%$ as compared to pure water. The physical explanation of the highly-efficient heat transport for oleophilic walls is that thermal plumes detach from the oil-rich boundary layer and are transported together with the oil phase. In the bulk, the oil-water interface prevents the plumes to mix with the turbulent water bulk. To confirm this physical picture, we show that the minimum amount of oil to achieve the maximum heat transport is set by the volume fraction of the thermal plumes. Our findings provide guidelines of how to optimize heat transport in thermal turbulence. Moreover, the physical insight of how coherent structures are coupled with one phase of a two-phase system has very general applicability for controlling transport properties in other turbulent multiphase flows.Comment: 11 pages, 4 figue

Growth of respiratory droplets in cold and humid air

The ambient conditions surrounding liquid droplets determine their growth or shrinkage. However, the precise fate of a liquid droplet expelled from a respiratory puff as dictated by its surroundings and the puff itself has not yet been fully quantified. From the view of airborne disease transmission, such as SARS-CoV-2, knowledge of such dependencies are critical. Here we employ direct numerical simulations (DNS) of a turbulent respiratory vapour puff and account for the mass and temperature exchange with respiratory droplets and aerosols. In particular, we investigate how droplets respond to different ambient temperatures and relative humidity (RH) by tracking their Lagrangian statistics. We reveal and quantify that in cold and humid environments, as there the respiratory puff is supersaturated, expelled droplets can first experience significant growth, and only later followed by shrinkage, in contrast to the monotonic shrinkage of droplets as expected from the classical view by William F. Wells (1934). Indeed, cold and humid environments diminish the ability of air to hold water vapour, thus causing the respiratory vapour puff to super-saturate. Consequently, the super-saturated vapour field drives the growth of droplets that are caught and transported within the humid puff. To analytically predict the likelihood for droplet growth, we propose a model for the axial RH based on the assumption of a quasi-stationary jet. Our model correctly predicts super-saturated RH conditions and is in good quantitative agreement with our DNS. Our results culminate in a temperature-RH map that can be employed as an indicator for droplet growth or shrinkage.Comment: 7 pages, 6 figure

Extended lifetime of respiratory droplets in a turbulent vapour puff and its implications on airborne disease transmission

To quantify the fate of respiratory droplets under different ambient relative humidities, direct numerical simulations of a typical respiratory event are performed. We found that, because small droplets (with initial diameter of 10um) are swept by turbulent eddies in the expelled humid puff, their lifetime gets extended by a factor of more than 30 times as compared to what is suggested by the classical picture by William F. Wells, for 50% relative humidity. With increasing ambient relative humidity the extension of the lifetimes of the small droplets further increases and goes up to around 150 times for 90% relative humidity, implying more than two meters advection range of the respiratory droplets within one second. Employing Lagrangian statistics, we demonstrate that the turbulent humid respiratory puff engulfs the small droplets, leading to many orders of magnitude increase in their lifetimes, implying that they can be transported much further during the respiratory events than the large ones. Our findings provide the starting points for larger parameter studies and may be instructive for developing strategies on optimizing ventilation and indoor humidity control. Such strategies are key in mitigating the COVID-19 pandemic in the present autumn and upcoming winter.Comment: 7 pages, 4 figures, published in Phys. Rev. Let