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The heat and mass transfer of deformable droplets in turbulent flows is crucial to a wide range of applications, such as cloud dynamics and internal combustion engines. This study investigates a single droplet undergoing phase change in isotropic turbulence using numerical simulations with a hybrid lattice Boltzmann scheme. Phase separation is controlled by a non-ideal equation of state and density contrast is taken into consideration. Droplet deformation is caused by pressure and shear stress at the droplet interface. The statistics of thermodynamic variables are quantified and averaged over both the liquid and vapour phases. The occurrence of evaporation and condensation is correlated to temperature fluctuations, surface tension variation and turbulence intensity. The temporal spectra of droplet deformations are analysed and related to the droplet surface area. Different modes of oscillation are clearly identified from the deformation power spectrum for low Taylor Reynolds number $Re_{\unicode[STIX]{x1D706}}$, whereas nonlinearities are produced with the increase of $Re_{\unicode[STIX]{x1D706}}$, as intermediate frequencies are seen to overlap. As an outcome, a continuous spectrum is observed, which shows a decrease in the power spectrum that scales as ${\sim}f^{-3}$. Correlations between the droplet Weber number, deformation parameter, fluctuations of the droplet volume and thermodynamic variables are also developed.

In this article, we present a modelling approach for rapid dynamic wetting based on the phase field theory. We show that in order to model this accurately, it is important to allow for a non-equilibrium wetting boundary condition. Using a condition of this type, we obtain a direct match with experimental results reported in the literature for rapid spreading of liquid droplets on dry surfaces. By extracting the dissipation of energy and the rate of change of kinetic energy in the flow simulation, we identify a new wetting regime during the rapid phase of spreading. This is characterized by the main dissipation to be due to a re-organization of molecules at the contact line, in a diffusive or active process. This regime serves as an addition to the other wetting regimes that have previously been reported in the literature.

Active feedback control was applied to suppress oscillations in thermocapillary convection in a half-zone liquid bridge. The experiment is on a unit-aspect-ratio liquid bridge where the most unstable azimuthal mode has wavenumber 2 when control is absent. Active control was realized by locally modifying the surface temperature using the local temperature measured at different locations fed back through a simple control law. The performance of the control process was quantified by analysing local temperature signals, and the flow structure was simultaneously identified by flow visualization. With optimal placement of sensors and heaters, proportional control can raise the critical Marangoni number by more than 40%. The amplitude of the oscillation can be suppressed to less than 30% of the initial value for a wide range of Marangoni number, up to 90% of the critical value. The proportional control was tested for a period-doubling state and it stabilized the oscillation to a periodic state. Weakly nonlinear control was applied by adding a cubic term to the control law to improve the performance of the control and alter the bifurcation characteristics.

The stability of the flow in a half-zone configuration is analysed with the aid of direct numerical simulation. The work is concentrated on the small Prandtl numbers relevant for typical semiconductor melts. The axisymmetric thermocapillary flow is found to be unstable to a steady non-axisymmetric state with azimuthal wavenumber 2, for a zone with aspect ratio 1. The critical Reynolds number for this bifurcation is 1960. This three dimensional steady solution loses stability to an oscillatory state at a Reynolds number of 6250. For small Prandtl numbers, both bifurcations are seen to be quite insensitive to changes in the Prandtl number, and are thus hydrodynamic in nature. An analogy to the instability of thin vortex rings is made. This analogy suggests a physical mechanism behind the instability and also gives an explanation of how the azimuthal wavenumber of the bifurcated solution is selected. The implications of this for the floating-zone crystal growth process are discussed.

We consider the problem of nonlinear thermal-solutal convection in the mushy zone accompanying unstable directional solidification of binary systems. Attention is focused on possible nonlinear mechanisms of chimney formation leading to the occurrence of freckles in solid castings, and in particular the coupling between the convection and the resulting porosity of the mush. We make analytical progress by considering the case of small growth Péclet number, δ, small departures from the eutectic point, and infinite Lewis number. Our linear stability results indicate a small O(δ) shift in the critical Darcy-Rayleigh number, in accord with previous analyses. We find that nonlinear two-dimensional rolls may be either sub- or supercritical, depending upon a single parameter combining the magnitude of the dependence of mush permeability on solids fraction and the variations in solids fraction owing to melting or freezing. A critical value of this combined parameter is given for the transition from supercritical to subcritical rolls. Three-dimensional hexagons are found to be transcritical, with branches corresponding to upflow and lower porosity in either the centres or boundaries of the cells. These general results are discussed in relation to experimental observations and are found to be in general qualitative agreement with them.

Spin-up from rest of a separating fluid–particle mixture is studied. A cylindrical container, filled with a stationary mixture of initially uniform particle volume fraction, is instantaneously set into rapid rotation. The viscous forces.on the walls introduce a secondary Ekman-layer circulation which causes the fluid motion to gradually approach a state of solid-body rotation. While the mixture acquires angular momentum, separation starts under the action of the local centrifugal effects: the dispersed particles – assumed here to be lighter than the fluid – tend to concentrate around the centre, leaving behind a peculiarly shaped domain of pure fluid. This process is simulated by a finite difference version of the ‘mixture model’ equations. The numerical results are in good agreement with previous asymptotical predictions but also illuminate some aspects of the flow field that have been covered by the analytical approach.

The time-dependent settling of a dilute monodisperse suspension in a centrifugal force field is considered. The settling takes place between two axisymmetric narrowly spaced conical disks that are rotating rapidly. Clear fluid and suspension are assumed to behave as Newtonian fluids of different densities. The viscosities are, for simplicity, assumed to be the same. All effects of the sediment are neglected. The fluid motion is assumed to be almost parallel with the disks and is computed by using lubrication theory. This leads to a nonlinear hyperbolic equation of first order for the location of the interface between clear fluid and suspension. Local multivaluedness of the solution is removed by inserting shocks. Such a shock is a model for a small region where the slope of the interface, as scaled in the lubrication approximation, is large. Two problems are solved: batch settling and a case where the suspension is pumped into a conical channel that is initially filled with clear fluid. In the batch-settling case, the solution is quite similar to that computed by Herbolzheimer & Acrivos for settling due to a constant gravity field in a narrow tilted channel. For large values of the Taylor number, it is found that the blocking of radial flow outside the Ekman layers leads to a somewhat slower separation process than expected. In the filling problem, the character of the solution is distinctly different for Taylor numbers of order unity and large values of this parameter.