Heat transfer by large deformable drops in a turbulent flow is a complex and rich-in-physics system, in which drop deformation, breakage and coalescence influence the transport of heat. We study this problem by coupling direct numerical simulation (DNS) of turbulence with a phase-field method for the interface description. Simulations are run at fixed-shear Reynolds and Weber numbers. To evaluate the influence of microscopic flow properties, like momentum/thermal diffusivity, on macroscopic flow properties, like mean temperature or heat transfer rates, we consider four different values of the Prandtl number, which is the momentum to thermal diffusivity ratio: $Pr=1$, $Pr=2$, $Pr=4$ and $Pr=8$. The drop volume fraction is $\varPhi \simeq 5.4\,\%$ for all cases. Drops are initially warmer than the turbulent carrier fluid and release heat at different rates depending on the value of $Pr$, but also on their size and on their own dynamics (topology, breakage, drop–drop interaction). Computing the time behaviour of the drops and carrier fluid average temperatures, we clearly show that an increase of $Pr$ slows down the heat transfer process. We explain our results by a simplified phenomenological model: we show that the time behaviour of the drop average temperature is self-similar, and a universal behaviour can be found upon rescaling by $t/Pr^{2/3}$. Accordingly, the heat transfer coefficient $\mathcal {H}$ (respectively its dimensionless counterpart, the Nusselt number $Nu$) scales as $\mathcal {H}\sim Pr^{-2/3}$ (respectively $Nu\sim Pr^{1/3}$) at the beginning of the simulation, and tends to $\mathcal {H}\sim Pr^{-1/2}$ (respectively $Nu\sim Pr^{1/2}$) at later times. These different scalings can be explained via the boundary layer theory and are consistent with previous theoretical/numerical predictions.

This paper introduces a new modification to the convective Cahn–Hilliard equation and a lattice Boltzmann framework to simulate liquid–solid phase transitions in multicomponent systems. The model takes into account changes in properties, such as density, caused by solidification, which leads to volume expansion or contraction. After validating the proposed model against classical problems and experimental data, the solidification of a sessile droplet was investigated in detail. Results of numerical simulations suggest that the environmental conditions are as important as the surface condition in deciding the freezing time and the final shape of the droplet. The environmental properties can also affect the freezing time indirectly through interaction with surface wettability. It has been demonstrated that hydrophobic surfaces may lose their advantages over hydrophilic surfaces in terms of anti-icing performance when primary solidification is initiated from the interface between the droplet and the environment fluid. The deformations of droplets, either with contraction or expansion, were confirmed and compared in different environments. This study offers a new perspective on droplet solidification by exposing the strong influence of environmental conditions and meanwhile provides a useful numerical method to predict the phase change process.

The aim of the present study is to understand the role of steam/cold-air inhalation on the mucus layer dynamics in the proximal airways. We model these flows as a viscoelastic liquid (lining the inner side of a tube) sheared by a turbulent airflow and subjected to a radial heat flow. The linear stability analysis of the resulting flow is carried out using numerical and thin-film approaches. The air–mucus interface tension, coupled with the azimuthal curvature, leads to the previously predicted axisymmetric capillary mode responsible for airway closure in distal airways. The viscoelasticity of the mucus leads to axisymmetric and new non-axisymmetric elastic modes, with the former possessing a higher growth rate. The axisymmetric elastic and capillary modes merge to give rise to a new ‘elasto-capillary mode’ possessing a growth rate nearly equal to the combined growth rate of the elastic and capillary modes. The analysis predicts a strong stabilising effect of the thermocapillarity induced by steam inhalation on the elasto-capillary mode. Thus steam decreases airway resistance, which could explain the observed therapeutic effect of steam inhalation. The opposite is the case when the inhaled air is colder than the body temperature, in agreement with the observations. The theoretical predictions are corroborated by the physical mechanism explaining the suppression/amplification of the elasto-capillary mode due to thermocapillarity.

From industrial-scale production to small-scale fabrication of functional films, the blade coating method is used widely to apply a uniform thin liquid film on a moving substrate. However, conventional hydrodynamic models are inadequate for laboratory-scale low-speed blade coating, where capillary forces dominate. In this study, the low-speed blade coating of non-evaporative Newtonian fluids was investigated in experimental, computational and analytical approaches. The transient free boundary problem was solved utilizing a two-dimensional finite element method, and a simple viscocapillary model was developed to describe the viscous stress and capillary forces within the puddle, and predict the thickness of the wet film as a function of the speed of the substrate. Comparing the predicted film thickness with the computational results, and a flow visualization experiment of blade coating with silicone oil, respectively, confirmed the model's validity. The study indicates that the proposed model may be a useful tool for optimizing laboratory coating processes, as it provides a greater understanding of the low-speed blade coating system on a laboratory scale.

A classic lift decomposition (Von Kármán & Sears, J. Aeronaut. Sci., vol. 5, 1938, pp. 379–390) is conducted on potential flow simulations of a near-ground pitching hydrofoil. It is discovered that previously observed stable and unstable equilibrium altitudes are generated by a balance between positive wake-induced lift and negative quasi-steady lift while the added mass lift does not play a role. Using both simulations and experiments, detailed analyses of each lift component's near-ground behaviour provide further physical insights. When applied to three-dimensional pitching hydrofoils the lift decomposition reveals that the disappearance of equilibrium altitudes for ${A{\kern-4pt}R}\ {\rm (aspect\ ratio)} <1.5$ occurs due to the magnitude of the quasi-steady lift outweighing the magnitude of the wake-induced lift at all ground distances. Scaling laws for the quasi-steady lift, wake-induced lift and the stable equilibrium altitude are discovered. A simple scaling law for the lift of a steady foil in ground effect is derived. This scaling shows that both circulation enhancement and the velocity induced at a foil's leading edge by the bound vortex of its ground image foil are the essential physics to understand steady ground effect. The scaling laws for unsteady pitching foils can predict the equilibrium altitude to within $20\,\%$ of its value when $St\ {\rm (Strouhal\ number)} < 0.45$. For $St \ge 0.45$ there is a wake instability effect, not accounted for in the scaling relations, that significantly alters the wake-induced lift. These results not only provide key physical insights and scaling laws for steady and unsteady ground effects, but also for two schooling hydrofoils in a side-by-side formation with an out-of-phase synchronization.

We report an experimental investigation of the heat transport and flow field in a rectangular Rayleigh–Bénard convection (RBC) cell with two immiscible fluids: silicone oil and glycerol. The global heat transport of the system is divided into three ranges corresponding to the different flow structures formed in the glycerol layer. In range I, the glycerol layer is dominated by conduction, and no plume is formed over the interface. In range II, cellular rolls are formed in the glycerol layer and the horizontal motion of rolls causes an oscillation of temperature in the interface. In range III, the cellular pattern is time-independent, and the interface forms a group of wavelets with wave numbers consistent with the mode of the cellular pattern. In lower-thin glycerol, the Nusselt (Nu) grows from conduction to convection through an oscillating subcritical bifurcation at critical Rayleigh number $Ra_c$. The value of $Ra_c$ in the present work is smaller than the theoretical prediction of both-rigid boundaries and greater than the prediction of one-rigid and one-free boundaries. In the upper-thick silicone oil layer, $Nu$ increases with increasing $Ra$, but it is smaller than that of traditional RBC. For the silicone oil layer in two-layer RBC, the hot plumes emitting over the liquid–liquid interface showed different shape and different velocity from cold plumes emitting from the top rigid plate. This implies that the velocity boundary condition strongly influences the flow structure in turbulent convection.

Eukaryotic swimming cells such as spermatozoa, algae or protozoa use flagella or cilia to move in viscous fluids. The motion of their flexible appendages in the surrounding fluid induces propulsive forces that balance viscous drag on the cells and lead to a directed swimming motion. Here, we use our recently built database of cell motility (BOSO-Micro) to investigate the extent to which the shapes of eukaryotic swimming cells may be optimal from a hydrodynamic standpoint. We first examine the morphology of flexible flagella undergoing waving deformation and show that their amplitude-to-wavelength ratio is near that predicted theoretically to optimise the propulsive efficiency of active filaments. Next, we consider ciliates, for which locomotion is induced by the collective beating of short cilia covering their surface. We show that the aspect ratios of ciliates are close to that predicted to minimise the viscous drag of the cell body. Both results strongly suggest a key role played by hydrodynamic constraints, in particular viscous drag, in shaping eukaryotic swimming cells.