Ambient air cushions the impact of drops on solid substrates, an effect usually revealed by the entrainment of a bubble, trapped as the air squeezed under the drop drains and liquid–solid contact occurs. The presence of air becomes evident for impacts on very smooth surfaces, where the gas film can be sustained, allowing drops to bounce without wetting the substrate. In such a non-wetting situation, Mandre & Brenner (J. Fluid Mech., vol. 690, 2012, p. 148) numerically and theoretically evidenced that two physical mechanisms can act to prevent contact: surface tension and nonlinear advection. However, the advection dominated regime has remained hidden in experiments as liquid–solid contact prevents rebounds being realised at sufficiently large impact velocities. By performing impacts on superheated surfaces, in the so-called dynamical Leidenfrost regime (Tran et al., Phys. Rev. Lett., vol. 108, issue 3, 2012, p. 036101), we enable drop rebound at higher impact velocities, allowing us to reveal this regime. Using high-speed total internal reflection, we measure the minimal gas film thickness under impacting drops, and provide evidence for the transition from the surface tension to the nonlinear inertia dominated regime. We rationalise our measurements through scaling relationships derived by coupling the liquid and gas dynamics, in the presence of evaporation.

When a liquid drop falls on a solid substrate, the air layer between them delays the occurrence of liquid–solid contact. For impacts on smooth substrates, the air film can even prevent wetting, allowing the drop to bounce off with dynamics identical to that observed for impacts on superamphiphobic materials. In this paper, we investigate similar bouncing phenomena, occurring on viscous liquid films, that mimic atomically smooth substrates, with the goal to probe their effective repellency. We elucidate the mechanisms associated with the bouncing to non-bouncing (floating) transition using experiments, simulations, and a minimal model that predicts the main characteristics of drop impact, the contact time and the coefficient of restitution. In the case of highly viscous or very thin films, the impact dynamics is not affected by the presence of the viscous film. Within this substrate-independent limit, bouncing is suppressed once the drop viscosity exceeds a critical value, as on superamphiphobic substrates. For thicker or less viscous films, both the drop and film properties influence the rebound dynamics and conspire to inhibit bouncing above a critical film thickness. This substrate-dependent regime also admits a limit, for low-viscosity drops, in which the film properties alone determine the limits of repellency.

Non-wetting substrates allow impacting liquid drops to spread, recoil and take-off, provided they are not too heavy (Biance et al., J. Fluid Mech., vol. 554, 2006, pp. 47–66) or too viscous (Jha et al., Soft Matt., vol. 16, no. 31, 2020, pp. 7270–7273). In this article, using direct numerical simulations with the volume of fluid method, we investigate how viscous stresses and gravity oppose capillarity to inhibit drop rebound. Close to the bouncing to non-bouncing transition, we evidence that the initial spreading stage can be decoupled from the later retraction and take-off, allowing us to understand the rebound as a process converting the surface energy of the spread liquid into kinetic energy. Drawing an analogy with coalescence-induced jumping, we propose a criterion for the transition from the bouncing to the non-bouncing regime, namely by the condition ${Oh}_{c} + {Bo}_{c} \sim 1$, where ${Oh}_{c}$ and ${Bo}_{c}$ are the Ohnesorge number and Bond number at the transition, respectively. This criterion is in excellent agreement with the numerical results. We also elucidate the mechanisms of bouncing inhibition in the heavy and viscous drop limiting regimes by calculating the energy budgets and relating them to the drop's shape and internal flow.

We report on the modification of the spectrum of a passive scalar inside a turbulent flow by the injection of large bubbles. Although the spectral modification through bubbles is well known and well analysed for the velocity fluctuations, little is known on how bubbles change the fluctuations of an approximately passive scalar, in our case temperature. Here we uncover the thermal spectral scaling behaviour of a turbulent multiphase thermal mixing layer. The development of a $-3$ spectral scaling is triggered. By injecting large bubbles (${Re}_{{bub}} = {O}(10^2)$) with gas volume fractions $\alpha$ up to 5 %. For these bubbly flows, the $-5/3$ scaling is still observed at intermediate frequencies for low $\alpha$ but becomes less pronounced when $\alpha$ further increases and it is followed by a steeper $-3$ slope for larger frequencies. This $-3$ scaling range extends with increasing gas volume fraction. The $-3$ scaling exponent coincides with the typical energy spectral scaling for the velocity fluctuations in high-Reynolds-number bubbly flows. We identify the frequency scale of the transition from the $-5/3$ scaling to the $-3$ scaling and show how it depends on the gas volume fraction.

We numerically study the melting process of a solid layer heated from below such that a liquid melt layer develops underneath. The objective is to quantitatively describe and understand the emerging topography of the structures (characterized by the amplitude and wavelength), which evolve out of an initially smooth surface. By performing both two-dimensional (achieving Rayleigh number up to $Ra=10^{11}$) and three-dimensional (achieving Rayleigh number up to $Ra=10^9$) direct numerical simulations with an advanced finite difference solver coupled to the phase-field method, we show how the interface roughness is spontaneously generated by thermal convection. With increasing height of the melt the convective flow intensifies and eventually even becomes turbulent. As a consequence, the interface becomes rougher but is still coupled to the flow topology. The emerging structure of the interface coincides with the regions of rising hot plumes and descending cold plumes. We find that the roughness amplitude scales with the mean height of the liquid layer. We derive this scaling relation from the Stefan boundary condition and relate it to the non-uniform distribution of heat flux at the interface. For two-dimensional cases, we further quantify the horizontal length scale of the morphology, based on the theoretical upper and lower bounds given for the size of convective cells known from Wang et al. (Phys. Rev. Lett., vol. 125, 2020, 074501). These bounds agree with our simulation results. Our findings highlight the key connection between the morphology of the melting solid and the convective flow structures in the melt beneath.

We experimentally investigate the evaporation of very volatile liquid droplets (Novec 7000 Engineered Fluid, chemical name hydrofluoroethers HFE-7000) in a turbulent spray. Droplets with diameters of the order of a few micrometres are produced by a spray nozzle and then injected into a purpose-built enclosed dodecahedral chamber filled with air containing various amounts of water vapour. The ambient temperature and relative humidity in the chamber are carefully controlled. We observe water condensation on the rapidly evaporating droplet, both for the spray and for a single acoustically levitated millimetric Novec 7000 droplet. We further examine the effect of humidity, and reveal that a more humid environment leads to faster evaporation of the volatile liquid, as well as more water condensation. This is explained by the much larger latent heat of water as compared with that of Novec 7000. We extend an analytical model based on Fick's law to quantitatively account for the data.

Immiscible and incompressible liquid–liquid flows are considered in a Taylor–Couette geometry and analysed by direct numerical simulations coupled with the volume-of-fluid method and a continuum surface force model. The system Reynolds number $Re \equiv r_i \omega _i d / \nu$ is fixed to $960$, where the single-phase flow is in the steady Taylor vortex regime, whereas the secondary-phase volume fraction $\varphi$ and the system Weber number $We \equiv \rho r_i^2 \omega _i^2 d / \sigma$ are varied to study the interactions between the interface and the Taylor vortices. We show that different Weber numbers lead to two distinctive flow regimes, namely an advection-dominated regime and an interface-dominated regime. When $We$ is high, the interface is easily deformed because of its low surface tension. The flow patterns are then similar to the single-phase flow, and the system is dominated mainly by advection (advection-dominated regime). However, when $We$ is low, the surface tension is so large that stable interfacial structures with sizes comparable to the cylinder gap can exist. The background velocity field is modulated largely by these persistent structures, thus the overall flow dynamics is governed by the interface (interface-dominated regime). The effect of the interface on the global system response is assessed by evaluating the Nusselt number $Nu_{\omega }$ based on the non-dimensional angular velocity transport. It shows non-monotonic trends as functions of the volume fraction $\varphi$ for both low and high $We$. We explain how these dependencies are closely linked to the velocity and interfacial structures.

By varying the oil volume fraction, the microscopic droplet size and the macroscopic rheology of emulsions are investigated in a Taylor–Couette turbulent shear flow. Although here oil and water in the emulsions have almost the same physical properties (density and viscosity), unexpectedly, we find that oil-in-water (O/W) and water-in-oil (W/O) emulsions have very distinct hydrodynamic behaviours, i.e. the system is clearly asymmetric. By looking at the micro-scales, the average droplet diameter hardly changes with the oil volume fraction for O/W or for W/O. However, for W/O it is about $50\,\%$ larger than that of O/W. At the macro-scales, the effective viscosity of O/W is higher when compared to that of W/O. These asymmetric behaviours are expected to be caused by the presence of surface-active contaminants from the walls of the system. By introducing an oil-soluble surfactant at high concentration, remarkably, we recover the symmetry (droplet size and effective viscosity) between O/W and W/O emulsions. Based on this, we suggest a possible mechanism responsible for the initial asymmetry and reach conclusions on emulsions where interfaces are fully covered by the surfactant. Next, we discuss what sets the droplet size in turbulent emulsions. We uncover a $-6/5$ scaling dependence of the droplet size on the Reynolds number of the flow. Combining the scaling dependence and the droplet Weber number, we conclude that the droplet fragmentation, which determines the droplet size, occurs within the boundary layer and is controlled by the dynamic pressure caused by the gradient of the mean flow, as proposed by Levich (Physicochemical Hydrodynamics, Prentice-Hall, 1962), instead of the dynamic pressure due to turbulent fluctuations, as proposed by Kolmogorov (Dokl. Akad. Nauk. SSSR, vol. 66, 1949, pp. 825–828). The present findings provide an understanding of both the microscopic droplet formation and the macroscopic rheological behaviours in dynamic emulsification, and connects them.

When a freely suspended liquid film ruptures, it retracts spontaneously under the action of surface tension. If the film is surrounded by air, the retraction velocity is known to approach the constant Taylor–Culick velocity. However, when surrounded by an external viscous medium, the dissipation within that medium dictates the magnitude of the retraction velocity. In the present work, we study the retraction of a liquid (water) film in a viscous oil ambient (two-phase Taylor–Culick retractions), and that sandwiched between air and a viscous oil (three-phase Taylor–Culick retractions). In the latter case, the experimentally measured retraction velocity is observed to have a weaker dependence on the viscosity of the oil phase as compared with the configuration where the water film is surrounded completely by oil. Numerical simulations indicate that this weaker dependence arises from the localization of viscous dissipation near the three-phase contact line. The speed of retraction only depends on the viscosity of the surrounding medium and not on that of the film. From the experiments and the numerical simulations, we reveal unprecedented regimes for the scaling of the Weber number ${We}_{f}$ of the film (based on its retraction velocity) or the capillary number ${Ca}_{s}$ of the surroundings versus the Ohnesorge number ${Oh}_{s}$ of the surroundings in the regime of large viscosity of the surroundings (${Oh}_{s} \gg 1$), namely ${We}_{f} \sim {Oh}_{s}^{-2}$ and ${Ca}_{s} \sim {Oh}_{s}^{0}$ for the two-phase Taylor–Culick configuration, and ${We}_{f} \sim {Oh}_{s}^{-1}$ and ${Ca}_{s} \sim {Oh}_{s}^{1/2}$ for the three-phase Taylor–Culick configuration.

Phase segregation triggered by selective evaporation can emerge in multicomponent systems, leading to complex physicochemical hydrodynamics. Recently, Li et al. (Phys. Rev. Lett., vol. 120, 2018, 224501) and Kim & Stone (J. Fluid Mech., vol. 850, 2018, pp. 769–783) reported a segregative behaviour (i.e. demixing) in an evaporating binary droplet. In this work, by means of experiments and theoretical analysis, we investigate the flow dynamics after the occurrence of the phase segregation. As example, we take the 1,2-hexanediol–water binary droplet system. First, we reveal experimentally the overall physicochemical hydrodynamics of the evaporation process, including the segregative behaviour and the resulting flow structure close to the substrate. By quantifying the evolution of the radial flow, we identify three successive life stages of the evaporation process. At Stage I, a radially outward flow is observed, driven by the Marangoni effect. At the transition to Stage II, the radial flow reverses partially, starting from the contact line. This flow breaks the axial symmetry and remarkably is driven by the segregation itself. Finally at Stage III, the flow decays as the evaporation ceases gradually. At this stage, the segregation has grown to the entire droplet, and the flow is again controlled by the Marangoni effect. The resulting Marangoni flow homogenizes the distribution of the entrapped volatile water over the whole droplet.

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 investigate the counter-intuitive initial decrease and subsequent increase in the Nusselt number $Nu$ with increasing wall Reynolds number $Re_w$ in the sheared Rayleigh–Bénard (RB) system by studying the energy spectra of convective flux and turbulent kinetic energy for Rayleigh number $Ra = 10^{7}$, Prandtl number $Pr=1.0$ and inverse Richardson numbers $0 \leq 1/Ri \leq 10$. These energy spectra show two distinct high-energy regions corresponding to the large-scale superstructures in the bulk and small-scale structures in the boundary layer (BL) regions. A greater separation between these scales at the thermal BL height correlates to a higher $Nu$ and indicates that the BLs are more turbulent. The minimum $Nu$, which occurs at $1/Ri=1.0$, is accompanied by the smallest separation between the large- and small-scale structures at the thermal BL height. At $1/Ri=1.0$, we also observe the lowest value of turbulent kinetic energy normalized with the square of friction velocity within the thermal BL. Additionally, we find that the domain size has a limited effect on the heat and momentum transfer in the sheared RB system as long as the domain can accommodate the small-scale convective structures at the thermal BL height, signifying that capturing the large-scale superstructures is not essential to obtain converged values of $Nu$ and shear Reynolds number $Re_{\tau }$. When the domain is smaller than these small-scale convective structures, the overall heat and momentum transfer reduces drastically.

A scaling theory for the passive scalar transport in Couette flow, i.e. the flow between two parallel plates moving with different velocities, is proposed. This flow is determined by the bulk Reynolds number $Re_b$ and the Prandtl number $Pr$. In the turbulent regime, for moderate shear Reynolds number $Re_{\tau }$ and moderate $Pr$, we derive that the passive scalar transport characterised by the Nusselt number $Nu$ scales as $Nu \sim Pr^{1/2}Re_{\tau }^{2}Re_b^{-1}$. We then use the well-established scaling for the friction coefficient $C_f \sim Re_b^{-1/4}$ (corresponding to a shear Reynolds number $Re_{\tau } \sim Re_b^{7/8}$) which holds reasonably well within the range $3\times 10^{3} \leqslant Re_b \leqslant 10^{5}$, to obtain $Nu \sim Pr^{1/2}Re_b^{3/4}$ for the Nusselt number scaling. The theoretical results are tested against direct numerical simulations of Couette flows for the parameter ranges $81 \leqslant Re_b \leqslant 22361$ and $0.1 \leqslant Pr \leqslant 10$, finding good agreement. Analyses of the numerically obtained turbulent flow fields confirm logarithmic mean wall-parallel profiles of the velocity and the passive scalar in the inertial sublayer.

Solvent exchange is a process involving mixing between a good solvent with dissolved solute and a poor solvent. The process creates local oversaturation which causes the nucleation of minute solute droplets. Such ternary systems on a macro-scale have remained unexplored in the turbulent regime. We experimentally study the solvent exchange process by injecting mixtures of ethanol and trans-anethole into water, forming a turbulent buoyant jet in the upward direction. Locally, turbulent mixing causes oversaturation of the trans-anethole following turbulent entrainment. We optically measure the concentration of the nucleated droplets using a light attenuation technique and find that the radial concentration profile has a sub-Gaussian kurtosis. In contrast to the entrainment-based models, the spatial evolution of the oversaturation reveals continuous droplet nucleation downstream and radially across the jet, which we attribute to the limited mixing capacity of the jet. Although we are far from a full quantitative understanding, this work extends the knowledge on solvent exchange into the turbulent regime, and brings in a novel type of flow, broadening the scope of multicomponent, multiphase turbulent jets with phase transition.

We perform direct numerical simulations to study the effect of the gravity centre offset in spherical Rayleigh–Bénard convection. When the gravity centre is shifted towards the south, we find that the shift of the gravity centre has a pronounced influence on the flow structures. At low Rayleigh number $Ra$, a steady-state large-scale meridional circulation induced by the baroclinic imbalance, created by the misalignment of the gravity potentials and isotherms, is formed. At high $Ra$, an energetic jet is created on the northern side of the inner sphere that is directed towards the outer sphere. The large-scale circulation induces a strong co-latitudinal dependence in the local heat flux. Nevertheless, the global heat flux is not affected by the changes in the large-scale flow organization induced by the gravity centre offset.

Moderate rotation and moderate horizontal confinement similarly enhance the heat transport in Rayleigh–Bénard convection (RBC). Here, we systematically investigate how these two types of flow stabilization together affect the heat transport. We conduct direct numerical simulations of confined-rotating RBC in a cylindrical set-up at Prandtl number $\textit {Pr}=4.38$, and various Rayleigh numbers $2\times 10^{8}\leqslant {\textit {Ra}}\leqslant 7\times 10^{9}$. Within the parameter space of rotation (given as inverse Rossby number $0\leqslant {\textit {Ro}}^{-1}\leqslant 40$) and confinement (given as height-to-diameter aspect ratio $2\leqslant \varGamma ^{-1}\leqslant 32$), we observe three heat transport maxima. At lower $ {\textit {Ra}}$, the combination of rotation and confinement can achieve larger heat transport than either rotation or confinement individually, whereas at higher $ {\textit {Ra}}$, confinement alone is most effective in enhancing the heat transport. Further, we identify two effects enhancing the heat transport: (i) the ratio of kinetic and thermal boundary layer thicknesses controlling the efficiency of Ekman pumping, and (ii) the formation of a stable domain-spanning flow for an efficient vertical transport of the heat through the bulk. Their interfering efficiencies generate the multiple heat transport maxima.

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.

We report on the mobility and orientation of finite-size, neutrally buoyant, prolate ellipsoids (of aspect ratio $\varLambda =4$) in Taylor–Couette flow, using interface-resolved numerical simulations. The set-up consists of a particle-laden flow between a rotating inner and a stationary outer cylinder. The flow regimes explored are the well-known Taylor vortex, wavy vortex and turbulent Taylor vortex flow regimes. We simulate two particle sizes $\ell /d=0.1$ and $\ell /d=0.2$, $\ell$ denoting the particle major axis and $d$ the gap width between the cylinders. The volume fractions are $0.01\,\%$ and $0.07\,\%$, respectively. The particles, which are initially randomly positioned, ultimately display characteristic spatial distributions which can be categorised into four modes. Modes (i) to (iii) are observed in the Taylor vortex flow regime, while mode (iv) encompasses both the wavy vortex and turbulent Taylor vortex flow regimes. Mode (i) corresponds to stable orbits away from the vortex cores. Remarkably, in a narrow $\textit {Ta}$ range, particles get trapped in the Taylor vortex cores (mode (ii)). Mode (iii) is the transition when both modes (i) and (ii) are observed. For mode (iv), particles distribute throughout the domain due to flow instabilities. All four modes show characteristic orientational statistics. The focus of the present study is on mode (ii). We find the particle clustering for this mode to be size-dependent, with two main observations. Firstly, particle agglomeration at the core is much higher for $\ell /d=0.2$ compared with $\ell /d=0.1$. Secondly, the $\textit {Ta}$ range for which clustering is observed depends on the particle size. For this mode (ii) we observe particles to align strongly with the local cylinder tangent. The most pronounced particle alignment is observed for $\ell /d=0.2$ at around $\textit {Ta}=4.2\times 10^5$. This observation is found to closely correspond to a minimum of axial vorticity at the Taylor vortex core ($\textit {Ta}=6\times 10^5$) and we explain why.

A sequence of two- and three-dimensional simulations are conducted for the double-diffusive convection (DDC) flows in the diffusive regime subjected to an imposed shear. For a wide range of control parameters, and for sufficiently strong perturbation of the conductive initial state, staircase-like structures spontaneously develop, with relatively well-mixed layers separated by sharp interfaces of enhanced scalar gradient. Such staircases appear to be robust even in the presence of strong shear over very long times, with early-time coarsening of the observed layers. For the same set of control parameters, different asymptotic layered states, with markedly different vertical scalar fluxes, can arise for different initial perturbation structures. The imposed shear significantly spatio-temporally modifies the vertical transport of the various scalars. The flux ratio $\gamma ^*$ (i.e. the ratio between the density fluxes due to the total salt flux and the total heat flux) is found, at steady state, to be essentially equal to the square root of the ratio of the salt diffusivity to the thermal diffusivity, consistent with the physical model proposed by Linden & Shirtcliffe (J. Fluid Mech., vol. 87, 1978, pp. 417–432) and the variational arguments presented by Stern (J. Fluid Mech., vol. 114, 1982, pp. 105–121) for unsheared double-diffusive convection.