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We numerically investigate turbulent Rayleigh–Bénard convection with gas bubbles attached to the hot plate, mimicking a core feature in electrolysis, catalysis or boiling. The existence of bubbles on the plate reduces the global heat transfer due to the much lower thermal conductivity of gases as compared with liquids and changes the structure of the boundary layers. The numerical simulations are performed in three dimensions at Prandtl number 
$\mbox{Pr}=4.38$ (water) and Rayleigh number 
$10^7\leqslant \mbox{Ra}\leqslant 10^8$. For simplicity, we assume the bubbles to be equally sized and having pinned contact lines. We vary the total gas-covered area fraction 
$0.18 \leqslant S_0 \leqslant 0.62$, the relative bubble height 
$0.02\leqslant h/H \leqslant 0.05$ (where 
$H$ is the height of the Rayleigh–Bénard cell), the bubble number 
$40 \leqslant n \leqslant 144$ and their spatial distribution. In all cases, asymmetric temperature profiles are observed, which we quantitatively explain based on the heat flux conservation at each horizontal section. We further propose the idea of using an equivalent single-phase set-up to mimic the system with attached bubbles. Based on this equivalence, we can calculate the heat transfer. Without introducing any free parameter, the predictions for the Nusselt number, the upper and lower thermal boundary layer thicknesses and the mean centre temperature agree well with the numerical results. Finally, our predictions also work for the cases with much larger 
$\mbox{Pr}$ (e.g. 
$400$), which indicates that our results can also be applied to predict the mass transfer in water electrolysis with bubbles attached to the electrode surface or in catalysis.
We numerically investigate turbulent Rayleigh–Bénard convection through two immiscible fluid layers, aiming to understand how the layer thickness and fluid properties affect the heat transfer (characterized by the Nusselt number 
$\mbox {Nu}$) in two-layer systems. Both two- and three-dimensional simulations are performed at fixed global Rayleigh number 
$\mbox {Ra}=10^8$, Prandtl number 
$\mbox {Pr}=4.38$ and Weber number 
$\mbox {We}=5$. We vary the relative thickness of the upper layer between 
$0.01 \le \alpha \le 0.99$ and the thermal conductivity coefficient ratio of the two liquids between 
$0.1 \le \lambda _k \le 10$. Two flow regimes are observed. In the first regime at 
$0.04\le \alpha \le 0.96$, convective flows appear in both layers and 
$\mbox {Nu}$ is not sensitive to 
$\alpha$. In the second regime at 
$\alpha \le 0.02$ or 
$\alpha \ge 0.98$, convective flow only exists in the thicker layer, while the thinner one is dominated by pure conduction. In this regime, 
$\mbox {Nu}$ is sensitive to 
$\alpha$. To predict 
$\mbox {Nu}$ in the system in which the two layers are separated by a unique interface, we apply the Grossmann–Lohse theory for both individual layers and impose heat flux conservation at the interface. Without introducing any free parameter, the predictions for 
$\mbox {Nu}$ and for the temperature at the interface agree well with our numerical results and previous experimental data.
This numerical study presents a simple but extremely effective way to considerably enhance heat transport in turbulent wall-bounded multiphase flows, namely by using oleophilic walls. As a model system, we pick the Rayleigh–Bénard set-up, filled with an oil–water mixture. For oleophilic walls, 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 only of about 
$20\,\%$ as compared to pure water. The physical explanation of the heat transport increment for oleophilic walls is that thermal plumes detach from the oil-rich boundary layer and carry the heat with them. In the bulk, the oil–water interface prevents the plumes from mixing with the turbulent water bulk and to diffuse their heat. To confirm this physical picture, we show that the minimum amount of oil necessary 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 wall-bounded thermal turbulence. Moreover, the physical insight of how coherent structures are coupled with one of the phases of a two-phase system has very general applicability for controlling transport properties in other turbulent wall-bounded multiphase flows.
We theoretically and numerically investigate the instabilities driven by diffusiophoretic flow, caused by a solutal concentration gradient along a reacting surface. The important control parameters are the Péclet number 
$Pe$, which quantifies the ratio of the solutal advection rate to the diffusion rate, and the Schmidt number 
$Sc$, which is the ratio of viscosity and diffusivity. First, we study the diffusiophoretic flow on a catalytic plane in two dimensions. From a linear stability analysis, we obtain that for 
$Pe$ larger than 
$8{\rm \pi}$ mass transport by convection overtakes that by diffusion, and a symmetry-breaking mode arises, which is consistent with numerical results. For even larger 
$Pe$, nonlinear terms become important. For 
$Pe > 16{\rm \pi}$, multiple concentration plumes are emitted from the catalytic plane, which eventually merge into a single larger one. When 
$Pe$ is even larger (
$Pe \gtrsim 603$ for Schmidt number 
$Sc=1$), there are continuous emissions and merging events of the concentration plumes. The newly found flow states have different flow structures for different 
$Sc$: for 
$Sc\geqslant 1$, we observe the chaotic emission of plumes, but the fluctuations of concentration are only present in the region near the catalytic plane. In contrast, for 
$Sc<1$, chaotic flow motion occurs also in the bulk. In the second part of the paper, we conduct three-dimensional simulations for spherical catalytic particles, and beyond a critical Péclet number again find continuous plume emission and plume merging, now leading to a chaotic motion of the phoretic particle. Our results thus help us to understand the experimentally observed chaotic motion of catalytic particles in the high 
$Pe$ regime.
It is commonly accepted that the breakup criteria of drops or bubbles in turbulence is governed by surface tension and inertia. However, also buoyancy can play an important role at breakup. In order to better understand this role, here we numerically study two-dimensional Rayleigh–Bénard 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 
$5\leqslant We \leqslant 5000$ (the ratio of inertia to surface tension) and the density ratio between the two fluids 
$0.001 \leqslant \varLambda \leqslant 1$, 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 
$\varLambda$, two breakup types are observed. The first type occurs at small 
$\varLambda \ll 1$ (e.g. air–water systems) when local filament thicknesses exceed the Hinze length scale. The second, strikingly different, type occurs at large 
$\varLambda$ with roughly 
$0.5 < \varLambda \leqslant 1$ (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.
We perform a numerical study of the heat transfer and flow structure of Rayleigh–Bénard (RB) convection in (in most cases regular) porous media, which are comprised of circular, solid obstacles located on a square lattice. This study is focused on the role of porosity 
$\unicode[STIX]{x1D719}$ in the flow properties during the transition process from the traditional RB convection with 
$\unicode[STIX]{x1D719}=1$ (so no obstacles included) to Darcy-type porous-media convection with 
$\unicode[STIX]{x1D719}$ approaching 0. Simulations are carried out in a cell with unity aspect ratio, for Rayleigh number 
$Ra$ from 
$10^{5}$ to 
$10^{10}$ and varying porosities 
$\unicode[STIX]{x1D719}$, at a fixed Prandtl number 
$Pr=4.3$, and we restrict ourselves to the two-dimensional case. For fixed 
$Ra$, the Nusselt number 
$Nu$ is found to vary non-monotonically as a function of 
$\unicode[STIX]{x1D719}$; namely, with decreasing 
$\unicode[STIX]{x1D719}$, it first increases, before it decreases for 
$\unicode[STIX]{x1D719}$ approaching 0. The non-monotonic behaviour of 
$Nu(\unicode[STIX]{x1D719})$ originates from two competing effects of the porous structure on the heat transfer. On the one hand, the flow coherence is enhanced in the porous media, which is beneficial for the heat transfer. On the other hand, the convection is slowed down by the enhanced resistance due to the porous structure, leading to heat transfer reduction. For fixed 
$\unicode[STIX]{x1D719}$, depending on 
$Ra$, two different heat transfer regimes are identified, with different effective power-law behaviours of 
$Nu$ versus 
$Ra$, namely a steep one for low 
$Ra$ when viscosity dominates, and the standard classical one for large 
$Ra$. The scaling crossover occurs when the thermal boundary layer thickness and the pore scale are comparable. The influences of the porous structure on the temperature and velocity fluctuations, convective heat flux and energy dissipation rates are analysed, further demonstrating the competing effects of the porous structure to enhance or reduce the heat transfer.
