This paper studies numerically the convection of water vapour in snowpacks using an Eulerian–Eulerian two-phase approach. The convective water vapour transport in snow and its effects on snow density are often invoked to explain observed density profiles, e.g. of thin Arctic snow covers, but this process has never been numerically simulated and analysed in a systematic manner. Here, the impact of convection on the thermal and phase change regimes as a function of different snowpack depths, thermal boundary conditions and Rayleigh numbers is analysed. We find considerable impact of natural convection on the snow density distribution with a layer of significantly lower density at the bottom of the snowpack and a layer of higher density located higher in the snowpack or at the surface. We find that emergent heterogeneity in the snow porosity results in a feedback effect on the spatial organization of convection cells causing their horizontal displacement. Regions where the snowpack is most impacted by phase changes are found to be horizontally extended and vertically thin, ‘pancake’-like layers at the top and bottom of the snowpack. We further demonstrate that among the parameters important for natural convection, the snowpack depth has the strongest influence on the heat and mass transfer. Despite our simplifying assumptions, our study represents a significant improvement over the state of the art and a first step to accurately simulate snowpack dynamics in diverse regions of the cryosphere.

A novel flow instability emerging during a rheometric flow of a phase change material sheared in the vicinity of the melting point is reported. Right above the onset of the flow-induced crystallisation, the presence of the crystals in the flow leads to a primary bifurcation towards an oscillatory flow state. A further decrease of the temperature beyond this point leads to an increase of both the volume fraction and the size of the crystals, which ultimately triggers a fully developed chaotic flow. A full stability diagram as a function of the imposed deformation rate and the temperature is obtained experimentally. The systematic experimental observations reported herein could trigger further studies of the hydrodynamics of phase change materials and may find a number of interesting applications in polymer processing and thermal storage. The experimental findings are complemented by the analysis of a simple numerical model which provides further insights into the physical origins and mechanism of the instability.

Thermoacoustic instability – self-sustained pressure oscillations triggered by temperature gradients – has become an increasingly studied topic in the context of energy conversion. Generally, the process relies on conductive heat transfer between a solid and the fluid in which the generated pressure oscillations are sustained. In the present study, the thermoacoustic theory is extended to include mass transfer; specifically, the working fluid is modified so as to incorporate a ‘reactive’ gas, able to exchange phase with a solid/liquid boundary through a sorption process (or through evaporation/condensation), such that most heat is transferred in the form of latent heat rather than through conduction. A set of differential equations is derived, accounting for phase-exchange heat and mass transfer, and de-coupled via a small-amplitude asymptotic expansion. These equations are solved and subsequently manipulated into the form of a wave equation, representing the small perturbation on the pressure field, and used to derive expressions for the time-averaged, second-order heat and mass fluxes. A stability analysis is performed on the wave equation, from which the marginal stability curve is calculated in terms of the temperature difference, $\unicode[STIX]{x0394}T_{onset}$, required for initiation of self-sustained oscillations. Calculated stability curves are compared with published experimental results, showing good agreement. Effects of gas mixture composition are studied, indicating that a lower heat capacity of the inert component, combined with a low boiling temperature and high latent heat of the reactive component substantially lower $\unicode[STIX]{x0394}T_{onset}$. Furthermore, an increase in the average mole fraction of the reactive gas, $C_{m}$ strongly affects onset conditions, leading to $\unicode[STIX]{x0394}T_{onset}\sim 5\,^{\circ }\text{C}$ at the highest value of $C_{m}$ achievable under atmospheric pressure. An analysis of the system limit cycle is performed for a wide range of parameters, indicating a systematic decrease in the temperature difference capable of sustaining the limit cycle, as well as a significant distortion of the acoustic wave form as the phase-exchange mechanism becomes dominant. These findings, combined, reveal the underlying mechanisms by which a phase-exchange engine may produce more acoustic power than its counterpart ‘classical’ thermoacoustic system, while its temperature difference is substantially lower.

An explosive gas mixture of hydrogen and oxygen is introduced in liquid water between two horizontal walls, forming a flat cylindrical bubble. Ignition and explosion of the bubble lead to a large depressurized cavity that finally implodes. We investigate the dynamics of the bubble collapse, which is qualitatively similar to the collapse of a spherical bubble. It exhibits a slightly weaker singularity than for spherical bubbles. We also analyse the explosion process. Starting with an initial radius $R_{0}$, the bubble reaches a maximal radius $R_{max}$ that depends on the gap thickness $h$ between the two walls: for a thinner gap, the condensation of water vapour is more efficient, the overpressure consecutive to the combustion is weaker, and its duration is shorter. This leads to a smaller maximal radius $R_{max}$. An indirect measurement of the transport coefficient of hot water vapour can be inferred from this observation.

The calving of icebergs accounts for a significant fraction of the mass loss from both the Antarctic and Greenland ice sheets. Iceberg melting affects the water properties impacting sea ice formation, local circulation and biological activity. Laboratory experiments have investigated the effects of the Earth’s rotation on iceberg melting and the possible formation of Taylor columns (TCs) underneath icebergs. It is found that at high Rossby number, $Ro$, when rotation is weak compared to advection, iceberg melting is unaffected by the background rotation. As $Ro$ decreases, the melt rate shows an increasing trend, which is expected to reverse for very low $Ro$. This behaviour is explained by considering the integrated horizontal velocity at the base of the iceberg. For moderate $Ro$, a partial TC is formed and its effective blocking accelerates the flow under the remainder of the iceberg, which increases the melt rate since the melting is proportional to the flow velocity. It is expected that for very low $Ro$ the melt rate decreases because, with the expansion of the TC, the region of flow acceleration occurs away from the base of the iceberg. For low free stream velocity the freshwater produced by the ice melting introduces another dynamical effect. It is observed that there is a threshold free stream velocity below which the melt rate is constant. This is explained with the formation of a gravity current at the base of the iceberg that insulates it from the free flow and controls its melting.

The evaporation of sessile droplets is analysed when the influence of the thermal properties of the system is strong. We obtain asymptotic solutions for the evolution, and hence explicit expressions for the lifetimes, of droplets when the substrate has a high thermal resistance relative to the droplet and when the saturation concentration of the vapour depends strongly on temperature. In both situations we find that the lifetimes of the droplets are significantly extended relative to those when thermal effects are weak.

We consider finite-amplitude convection in a mushy layer during the primary solidification of a ternary alloy. Previous linear stability theories applied to ternary alloy primary-solidification models have identified an exceptional class of direct convective instability when all the individual stratifying agencies (one thermal and two solutal) were statically stabilizing. A reduced model, in which the effects of latent heat, solute rejection and background solidification are neglected, contains the essential interactions that admit qualitatively the same instability. We examine pattern selection for steady convection in this model. We find that roll, square or hexagonal convection patterns can be nonlinearly stable, depending on the relative importance of a number of physical effects, namely the solutal diffusion rates, the liquidus slopes and the background thermal and solutal density stratifications. The results for a special case are found to isolate a purely double-diffusive phase-change mechanism of pattern selection. Subcritical behaviour is identified inside the domain of individual static stability. A physical system is proposed that may be a promising one in which to experimentally identify these novel instabilities.

We study the evaporation rate from single drops as well as collections of drops on a solid substrate, both experimentally and theoretically. For a single isolated drop of water, in general the evaporative flux is limited by diffusion of water through the air, leading to an evaporation rate that is proportional to the linear dimension of the drop. Here, we test the limitations of this scaling law for several small drops and for very large drops. We find that both for simple arrangements of drops, as well as for complex drop size distributions found in sprays, cooperative effects between drops are significant. For large drops, we find that the onset of convection introduces a length scale of approximately 20 mm in radius, below which linear scaling is found. Above this length scale, the evaporation rate is proportional to the surface area.

In this article we investigate the importance of mass transfer effects in the effective acoustic properties of diluted bubbly liquids. The classical theory for wave propagation in bubbly liquids for pure gas bubbles is extended to capture the influence of mass transfer on the effective phase speed and attenuation of the system. The vaporization flux is shown to be important for systems close to saturation conditions and at low frequencies. We derive a general expression for the transfer function that relates bubble radius and pressure changes, solving the linear version of the conservation equations inside, outside and at the bubble interface. Simplified expressions for various limiting situations are derived in order to get further insight about the validity of the common assumptions typically applied in bubble dynamic models. The relevance of the vapour content, the mass transfer flux across the interface and the effect of variations of the bubble interface temperature is discussed in terms of characteristic non-dimensional numbers. Finally we derive the various conditions that must be satisfied in order to reach the low-frequency limit solutions where the phase speed no longer depends on the forcing frequency.

A new solver is developed to numerically simulate the melting phase change with natural convection. This solver was implemented on a single Nvidia GPU based on the CUDA technology in order to simulate the melting phase change in a 2D rectangular enclosure. The Rayleigh number is of the order of magnitude of 108 and Prandlt is 50. The hybrid thermal lattice Boltzmann method (HTLBM) is employed to simulate the natural convection in the liquid phase, and the enthalpy formulation is used to simulate the phase change aspect. The model is validated by experimental data and published analytic results. The simulation results manifest a strong convection in the melted phase and a different flow pattern from the reference results with low Rayleigh number. In addition, the computational performance is estimated for single precision arithmetic, and this solver yields 703.31MLUPS and 61.89GB/s device to device data throughput on a Nvidia Tesla C2050 GPU.

The aim of this study is to provide a better insight into the heat transfer mechanisms involved in single bubble growth in forced convection. In a set-up with vertical upflow of demineralized water under saturation conditions special bubble generators (BGs) were embedded at various positions in the plane wall. Power to a BG, local mean wall temperature and high-speed camera recordings from two viewing angles were measured synchronously. An accurate contour analysis is applied to reconstruct the instantaneous three-dimensional bubble volume. Interface topology changes of a vapour bubble growing at a plane wall have been found to be dictated by the rapid growth and by fluctuations in pressure, velocity and temperature in the approaching fluid flow. The camera images have shown a clear dry spot under the bubbles on the heater surface. A micro-layer under the bubble is experimentally shown to exist when the bubble pins to the wall surface and is therefore dependent on roughness and homogeneity of the wall. The ratio of heat extracted from the wall to the total heat required for evaporation was found to be around 30 % at most and to be independent of the bulk liquid flow rate and heat provided by the wall. When the bulk liquid is locally superheated this ratio was found to decrease to 20 %. Heat transfer to the bubble is also initially controlled by diffusion and is unaffected by the convection of the bulk liquid.

We report on new patterns in high-speed flows of granular materials obtained by means of extensive numerical simulations. These patterns emerge from the destabilization of unidirectional flows upon increase of mass holdup and inclination angle, and are characterized by complex internal structures, including secondary flows, heterogeneous particle volume fraction, symmetry breaking and dynamically maintained order. In particular, we evidenced steady and fully developed ‘supported’ flows, which consist of a dense core surrounded by a highly energetic granular gas. Interestingly, despite their overall diversity, these regimes are shown to obey a scaling law for the mass flow rate as a function of the mass holdup. This unique set of three-dimensional flow regimes raises new challenges for extending the scope of current granular rheological models.

We examine the dissolution of a vertical solid surface in the case where the heat and mass transfer is driven by turbulent compositional convection. A theoretical model of the turbulent dissolution of a vertical wall is developed, which builds on the scaling analysis presented by Kerr (J. Fluid Mech., vol. 280, 1994, pp. 287–302) for the turbulent dissolution of a horizontal floor or roof. The model has no free parameters and no dependence on height. The analysis is tested by comparing it with laboratory measurements of the ablation of a vertical ice wall in contact with salty water. The model is found to accurately predict the dissolution velocity for water temperatures up to approximately 5–$6\,^{\circ }\text{C}$, where there is a transition from turbulent dissolution to turbulent melting. We quantify the turbulent convective dissolution of vertical ice bodies in the polar oceans, and compare our results with some field observations.

The effect of high-energy electropulsing treatment (EPT) on the microstructure evolution, mechanical properties, and fracture behavior of as-treated Ti–6Al–4V alloy strips was investigated. EPT was found to accelerate phase transition and microstructure evolution of quasi-single-phase titanium alloy strips at a relatively low temperature, and obtain characteristic duplex microstructure and Widmanstatten microstructure. The EPT-induced microstructural changes increased elongation-to-failure remarkably with a slight decrease in tensile strength. Fracture surface observation and three-dimensional analysis showed that transition from small-shallow dimple colony to big-deep colony fracture took place with an increase in frequency of EPT. The rapid phase change of the Ti–6Al–4V alloy strip under EPT was attributed to the enhancement of nucleation rate and atomic diffusion resulting from the coupling of the thermal and athermal effects. It is supposed that EPT can provide a highly efficient method for the intermediate-softening annealing of titanium alloy sheet/strips.

We analyse the stability of a mushy layer during the directional solidification of a ternary alloy. Our model includes diffusive and convective transport of heat and solutes, coupled by an equilibrium thermodynamic constraint of the ternary phase diagram. The model contains phase change effects due to latent-heat release, solute rejection and background solidification. We identify novel convective instabilities, both direct and oscillatory, which are present under statically stable conditions. We examine these instabilities asymptotically by simplifying to a thin mushy layer with small growth rates. We also discuss numerical results for the full problem, confirming the asymptotic predictions and providing the stability characteristics outside the small-growth-rate approximation. A physical explanation for these instabilities in terms of parcel arguments is proposed, indicating that the instability mechanisms generally involve different rates of solute diffusion, different rates of solute rejection and different background solute distributions induced by the initial alloy composition.

Recent directional solidification experiments with aqueous suspensions of alumina particles (Anderson & Worster, Langmuir, vol. 28 (48), 2012, pp. 16512–16523) motivate a model for freezing colloidal suspensions that builds upon a theoretical framework developed by Rempel et al. (J. Fluid Mech., vol. 498, 2004, pp. 227–244) in the context of freezing soils. Ice segregates from the suspension at slow freezing rates into discrete horizontal layers of particle-free ice, known as ice lenses. A portion of the particles is trapped between ice lenses, while the remainder are pushed ahead, forming a layer of fully compacted particles separated from the bulk suspension by a sharp compaction front. By dynamically modelling the compaction front, the growth kinetics of the ice lenses are fully coupled to the viscous flow through the evolving compacted layer. We examine the periodic states that develop at fixed freezing rates in a constant, uniform temperature gradient, and compare the results against experimental observations. Congruent with the experiments, three periodic regimes are identified. At low freezing rates, a regular periodic sequence of ice lenses is obtained; predictions for the compacted layer thickness and ice-lens characteristics as a function of freezing rate are consistent with experiments. At intermediate freezing rates, multiple modes of periodic ice lenses occur with a significantly diminished compacted layer. When the cohesion between the compacted particles is sufficiently strong, a sequence of mode-doubling bifurcations lead to chaos, which may explain the disordered ice lenses observed experimentally. Finally, beyond a critical freezing rate, the regime for sustained ice-lens growth breaks down. This breakdown is consistent with the emergence of a distinct regime of ice segregation found experimentally, which exhibits a periodic, banded structure that is qualitatively distinct from ice lenses.

The complete description of the lifetime of a droplet on a solid substrate evaporating in a ‘stick–slide’ mode is obtained. The unexpectedly subtle relationship between the lifetime of such a droplet and the lifetimes of initially identical droplets evaporating in the extreme modes (namely the constant contact radius and constant contact angle modes) is described and summarised in an appropriate master diagram. In particular, it is shown that the lifetime of a droplet is not, in general, constrained by the lifetimes of the extreme modes.

The thermodynamic effects associated with the growth and collapse of a single cavitation bubble are investigated in the present paper by an experimental approach. The study focuses on the temperature variations in the liquid surrounding the bubble. Experiments are conducted in a cylinder partially filled with water at an ambient temperature and atmospheric pressure. The bubble growth results from the expansion of an initial air bubble, due to the pressure wave generated by a so-called ‘tube-arrest’ method. Several locations of the bubble, at different distances from the bottom wall of the cylinder, are considered. The bottom wall is made of sapphire, which is transparent to both the visible and infrared light spectra which enables temperature measurements by a high-speed thermovision camera at a wavelength of 3–$5~\unicode[.5,0][STIXGeneral,Times]{x03BC} \mathrm{m} $. Water is opaque to the infrared light spectrum, hence only temperatures in the boundary layer and on the liquid vapour interface could be determined. A temperature decrease of ${\sim }3$ K was recorded during the bubble growth while an increase up to 4 K was detected during the collapse. Experimental results are compared to the predictions of the ‘thermal delay’ model based on the assumption that the bubble growth and collapse are due to phase changes only. In this approach, the temperature variations are related to the latent heat exchanges during the vapourization and condensation processes. On the basis of these results, the respective effects of phase change and air dilatation/compression in the bubble dynamics are discussed.

We model buoyancy-driven convection with chimneys – channels of zero solid fraction – in a mushy layer formed during directional solidification of a binary alloy in two dimensions. A large suite of numerical simulations is combined with scaling analysis in order to study the parametric dependence of the flow. Stability boundaries are calculated for states of finite-amplitude convection with chimneys, which for a narrow domain can be interpreted in terms of a modified Rayleigh number criterion based on the domain width and mushy-layer permeability. For solidification in a wide domain with multiple chimneys, it has previously been hypothesized that the chimney spacing will adjust to optimize the rate of removal of potential energy from the system. For a wide variety of initial liquid concentration conditions, we consider the detailed flow structure in this optimal state and derive scaling laws for how the flow evolves as the strength of convection increases. For moderate mushy-layer Rayleigh numbers these flow properties support a solute flux that increases linearly with Rayleigh number. This behaviour does not persist indefinitely, however, with porosity-dependent flow saturation resulting in sublinear growth of the solute flux for sufficiently large Rayleigh numbers. Finally, we consider the influence of the porosity dependence of permeability, with a cubic function and a Carman–Kozeny permeability yielding qualitatively similar system dynamics and flow profiles for the optimal states.