When placed at the surface of a volatile liquid, a sphere of hot dense non-volatile material remains suspended until it cools sufficiently. The duration of this ‘inverse Leidenfrost’ phenomenon depends on the Nusselt number $Nu$ of the sphere, itself determined by flow in the film of vapour separating particle and liquid. It is shown that provided the Nusselt number is large, it can be calculated numerically using only the Laplace relation and the equations governing the thin film; patching to a solution for the outer thick film is not necessary. This method is demonstrated by using it to determine $Nu$ for a sphere sufficiently small that in the governing equations, the acceleration due to gravity is negligible except where multiplied by the density of the sphere. Numerical results giving $Nu$ as a function of a dimensionless measure of sphere weight are supplemented with analysis showing that, when the weight is of the order of the maximum supportable by surface tension alone, the film consists of a spherical bubble cap bounded by its contact rim. The solutions for these regions are coupled: although the apparent contact angle $\chi$ for the cap is determined within the rim, its value depends on the flow rate arriving from the cap as well as on the additional evaporation from the rim. The latter acts to reduce $\chi$ from the value it would otherwise have, thereby reducing the thickness of the entire cap. For the example treated here, the value of $Nu$ is doubled by this mechanism.

A phenomenological model is proposed to estimate the initial thickness of the liquid microlayer forming beneath a vapour bubble growing on a solid surface upon nucleate boiling. The model employs an analogy between the microlayer formation and the classic plate withdrawal problem. It calculates the microlayer thickness by considering it as a Landau–Levich film, where the thickness is a function of the meniscus speed and radius of curvature. Given the nearly hemispherical shape of the bubble during the early growth stage when the microlayer is first deposited, we assume that the meniscus speed can be approximated by the bubble expansion rate, and estimate the meniscus curvature using the Rayleigh equations. Unlike previous theories that assume that the bubble radius growth is proportional to the square root of time, the proposed model does not rely on any specific law of growth for vapour bubbles. The model is validated for predicting the microlayer thickness in water and ethanol, showing good agreement with experimental measurements and empirical correlations. Subsequent analyses of the microlayer interface profile address inconsistent reports – some described a wedge-like shape, whereas others reported a slight outward curvature with decreasing thickness in the outer region. This discrepancy is attributed to a reduction in the expansion rate of the microlayer's outer edge, particularly when the bubble reaches its maximum width. Our model provides insights into microlayer dynamics, essential to boiling heat transfer, as the evaporative heat flux through the microlayer is very sensitive to its initial thickness.

Saturated flow film boiling on a sphere has been numerically studied in this work for both vertical and horizontal flow configurations. The simulations were performed using a numerical methodology developed by the authors for boiling flows on three-dimensional unstructured meshes. For interface capturing, the coupled level set and volume of fluid method is used. The interface evolution, vapour wake dynamics and heat transfer have been thoroughly investigated by varying the saturated liquid flow velocity, sphere diameter and wall superheat. The relative importance of both the buoyancy and the inertial forces is described in terms of the Froude number $(Fr)$. The vapour bubble evolves periodically at low $Fr$ values, while a stable vapour column develops at high $Fr$ values. The interface evolution pattern obtained in the present work is in good agreement with the results of experimental studies available in the literature. For all the values of $Fr$, a stable vapour column develops for a large-diameter sphere and releases vapour bubbles of varying sizes. Furthermore, for a large-diameter sphere, surface capillary waves are observed at the interface, similar to the observations of some of the experimental studies available in the literature. The flow in the liquid and vapour wakes appears to be strongly coupled. The heat transfer in the present work is estimated using the spatially and temporally averaged Nusselt numbers. Finally, an fast Fourier transform analysis of the space-averaged Nusselt number reveals a strong interaction among the different forces.

Both experimental and theoretical studies of fast and microscale physical phenomena occurring during the growth of vapour bubbles in nucleate pool boiling are reported. The focus is on the liquid film of micrometric thickness (a ‘microlayer’) that can form between the heater and the liquid–vapour interface of a bubble. The microlayer strongly affects the macroscale heat transfer and is thus important to be understood. The microlayer appears as a result of the inertial forces that cause the hemispherical bubble shape. It is shown that the microlayer can be seen as the Landau–Levich film deposited by the bubble foot edge during its receding. Paradoxically, the deposition is controlled by viscosity and surface tension. The microlayer profile measured with white-light interferometry, the temperature distribution over the heater, and the bubble shape are observed with synchronised high-speed cameras. According to the numerical simulations, the microlayer consists of two regions: a dewetting ridge near the contact line, and a longer and flatter bumped part. It is shown that the ridge cannot be measured by interferometry because of its intrinsic limitation on the interface slope. The ridge growth is linked to the contact line receding. The simulated dynamics of both the bumped part and the contact line agrees with the experiment. The physical origin of the bump in the flatter part of microlayer is explained.

Bubble growth, departure and sliding in low-pressure flow boiling has received considerable attention in the past. However, most applications of boiling heat transfer rely on high-pressure flow boiling, for which very little is known, as experimental data are scarce and very difficult to obtain. In this work, we conduct an experiment using high-resolution optical techniques. By combining backlit shadowgraphy and phase-detection imaging, we track bubble shape and physical footprint with high spatial ($6\,\mathrm {\mu }{\rm m}$) and temporal ($33\,\mathrm {\mu }{\rm s}$) resolutions, as well as bubble size and position as bubbles nucleate and slide on top of the heated surface. We show that at pressures above 1 MPa bubbles retain a spherical shape throughout the growth and sliding process. We analytically derive non-dimensional numbers to correlate bubble velocity and liquid velocity throughout the turbulent boundary layer and predict the sliding of bubbles on the surface, solely from physical properties and the bubble growth rate. We also show that these non-dimensional solutions can be leveraged to formulate elementary criteria that predict the effect of pressure and flow rate on bubble departure diameter and growth time.

In this article, we present direct numerical simulation results for the expansion of spherical cap bubbles attached to a rigid wall due to a sudden drop in the ambient pressure. The critical pressure drop beyond which the bubble growth becomes unstable is found to match well with the predictions from classical theory of heterogeneous nucleation imposing a quasi-static bubble evolution. When the pressure drop is significantly higher than the critical value, a liquid microlayer appears between the bubble and the wall. In this regime, the interface outside the microlayer grows at an asymptotic velocity that can be predicted from the Rayleigh–Plesset equation, while the contact line evolves with another asymptotic velocity that scales with a visco-capillary velocity that obeys the Cox–Voinov law. In general, three distinctive regions can be distinguished: the region very close to the contact line where dynamics is governed by visco-capillary effects, an intermediate region controlled by inertio-viscous effects away from the contact line yet inside the viscous boundary layer, and the region outside the boundary layer dominated by inertial effects. The microlayer forms in a regime where the capillary effects are confined in a region much smaller than the viscous boundary layer thickness. In this regime, the global capillary number takes values much larger then the critical capillary number for bubble nucleation, and the microlayer height is controlled by viscous effects and not surface tension.

We report numerical simulations confirming the predictions in Gordillo & Riboux (J. Fluid Mech., vol. 941, 2022, A10), where we elucidated the lubrication mechanism by which a drop of a low-viscosity liquid impacting over a smooth solid substrate skates over a thin gas film that prevents contact with the wall. Moreover, with the purpose of explaining the so-called lift-off mechanism reported in Kolinski et al. (Phys. Rev. Lett., vol. 112, issue 13, 2014, 134501), we extend our previous findings and derive expressions for the time-varying thickness of the gas layer at the region where the distance to the wall is minimum, finding good agreement with the numerical results. In addition, we report that our predictions for the minimum thickness of the gas film separating a falling drop from a wall at room temperature follow closely the experimental values when gas kinetic effects are retained in the analysis, and also report that the analogous equation for the minimum thickness of the vapour layer formed after a drop impacts a superheated wall predicts well the experimental measurements.

Bentonites are candidate materials for encapsulating radioactive waste within barrier systems in crystalline rocks. In the ‘Alternative Buffer Material’ (ABM) test in the hard rock laboratory in Äspö, Sweden, six packages of eleven different buffer materials (mainly bentonites) with various exchangeable cation populations were packed vertically with an iron tube used as a heater in the center. After installation, the second ‘ABM package’ (ABM-II) was first allowed to saturate with water for approximately 2.5 years. The blocks were then exposed to a temperature of up to 141°C for approximately 3–4 years. The hypotheses for the present study were: (1) no horizontal gradient of the cation exchange population was present in the individual blocks of ABM-II because ABM-II had a longer reaction time in comparison to the ABM-I package, which did not have horizontal gradients; (2) the exchangeable cation Ca2+:Na+:Mg2+ ratio was equal in all blocks of ABM-II and was independent of block position in the package. As expected from ABM-I, all blocks in the ABM-II experiment showed large differences between the measured values of the reference materials and the reacted samples. The exchangeable Na+ and Mg2+ values in ABM-II were reduced by up to 55% to 59% in comparison to the reference material. Contrary to the first hypothesis, horizontal gradients were observed in ABM-II; and, contrary to the second hypothesis, the exchangeable cation ratios differed markedly in the different reacted buffer materials. The largest total Na+ loss was observed in the middle part (-67%), whereas Mg2+ values decreased by 79% in the upper part. The exchangeable Ca2+ values increased strongly in ABM-II, particularly in the upper part. The most useful parameter to distinguish between ion exchange equilibria of ABM-I and ABM-II was the Na+/Mg2+ ratio. This ratio was constant in ABM-I (3.0) and had a similar ratio (3.5) in the lower part of ABM-II; however, the ratio strongly increased (5–10) in the upper part of the ABM-II package. The large Na+/Mg2+ ratios in the upper part of ABM-II could possibly be explained by water loss into the rock (caused by a pressure drop and boiling) and subsequent water uptake.

Microbubble emission boiling (MEB), a phenomenon that occurs under highly subcooled boiling conditions, can achieve a high heat flux beyond critical heat flux. MEB has been observed to differ from nucleate boiling and is always accompanied by the emission of microbubbles from an oscillating bubble. The heat transfer mechanism of MEB differs from that of nucleate boiling and remains elusive. In this study, we measure the behaviour of a vapour bubble and its induced liquid flow simultaneously during subcooled boiling using the high-speed two-phase particle image velocimetry method. Different from nucleate boiling, we observe a rapid oscillating flow outside the bubble that constantly attaches on the heating surface in MEB. The spatially and temporally averaged velocity magnitude values under this oscillating flow, and their dependency on liquid subcooling and heat flux, are quantified. Then we derive a scaling law for the heat transfer of MEB as a function of Péclet and Jacob numbers. With such correlations, we suggest that the oscillating flow induced by bubble oscillations is important to MEB, thus elucidating a different heat transport process from nucleate boiling.

Nucleate boiling, a ubiquitous heat transfer mode, involves multiple vapour bubble nucleations on the heater surface and offers high heat transfer coefficients. The bubble growth process on a heating substrate involves the formation of microlayer, a thin liquid film trapped between the growing bubble and the heating substrate, and contributes to the bubble growth phenomenon through evaporation. Microlayer dynamics for a single bubble have been widely investigated in the pool and flow boiling conditions. However, the literature on multiple bubbles interactions and their associated microlayer information is scarce. Notably, in the case of flow boiling, where the microlayer dynamics are not symmetric due to the bubble's movement, the bubbles’ interaction and its influence on associated microlayer dynamics have never been reported. Therefore, microlayer and bubble dynamics in multiple interactions have been investigated experimentally using simultaneous application of thin-film interferometry and high-speed videography techniques in flow boiling with water as the working fluid. Our experimental investigation revealed that the secondary nucleation could cause a reduction in lift-off time and may assist or hinder the movement of the first bubble. The experimental results also demonstrated that the secondary nucleation could deplete the microlayer of the first bubble hydrodynamically even when the bubbles are far apart. Furthermore, it has been found that the microlayer depletion rate depends on the growth rate and the location of the secondary nucleation. Hence, this experimental study emphasises the need to consider the interaction of bubbles while modelling boiling flows to avoid overestimating the contribution of microlayer evaporation.

A theoretical model is developed for the forced convection film boiling phenomenon over a heated sphere moving vertically downwards in the water. Unprecedented compared with the previous analytical studies, this model accounts for the buoyancy effects while solving the momentum and energy equations in the vapour phase to obtain the velocity and the temperature distribution in terms of the vapour boundary layer thickness. To calculate the vapour boundary layer thickness, an energy balance is applied at the vapour–liquid interface. The flow of liquid around the sphere is considered to be governed by potential theory, and the energy equation in liquid is then solved for the known velocity distribution. We find that the vapour boundary layer thickness increases with an increase in the sphere temperature, the bulk water temperature and a decrease in the free stream velocity. This further results in a decrease in the film boiling heat transfer coefficient. The present study concludes that at low free stream velocities (${<}0.5\, {\rm m}\,{\rm s}^{-1}$) buoyancy becomes significant in delaying the separation, and when the velocity is further reduced the separation angle approaches $180^{\circ}$.

This work is devoted to the study of the conditions under which a drop directed normally towards a superheated or isothermal smooth substrate prevents the initial contact with the solid by skating over a micrometre-sized vapour or air layer. The results have been obtained analysing the gas flow at the spatio-temporal region where the maximum liquid pressure is attained, which is also where and when the minimum values of the film thickness are reached. For the common case in which $We St^{-1/6}\gtrsim 1$, where $We=\rho _l U^{2} R/\gamma$ and $St=\rho _l U R/\eta _a$ denote, respectively, the Weber and Stokes numbers, we find that capillary effects are negligible and the ratio between the minimum film thickness and the local drop radius of curvature is $h_m/R\propto St^{-7/6}$, with $\rho _l$, $\gamma$, $\eta _a$, $U$ and $R$ indicating the liquid density, interfacial tension coefficient, gas viscosity, impact velocity and drop radius, respectively. In contrast, when $We St^{-1/6}\lesssim 1$, capillary effects can no longer be neglected and $h_m/R\propto We^{-1/3} St^{-10/9}$. The predicted values of the minimum film thickness are compared with published experimental data, finding good agreement between predictions and measurements for the cases of both isothermal and superheated substrates. In addition, using mass conservation, we have also deduced an equation providing the minimum value of the substrate temperature for which a cylindrical central vapour bubble of constant height $h_d/R\propto St^{-2/3}$, with $h_d\gg h_m$, grows radially at the wetting velocity deduced in Riboux & Gordillo (Phys. Rev. Lett., vol. 113, 2014, 024507). The predicted values are in good agreement with the dynamic Leidenfrost temperatures reported by Shirota et al. (Phys. Rev. Lett., vol. 116, 2016, 064501).

This study presents computational simulations of multicomponent and multiphase flows to reproduce the physical phenomena in the secondary atomization of a droplet induced by a hot temperature environment. The computational fluid dynamics model is based on the geometric volume of fluid method, with piecewise linear interface calculation reconstruction for accurate determination of the curvature and evaporation fluxes at the interface. The purpose of the model was to faithfully reproduce complex physical processes, such as internal gas cavity formation, liquid–vapour interface instability, cavity collapse and liquid jet ejection, and the pinch-off of a secondary droplet, leading to the microexplosion phenomenon that greatly enhances the evaporation rate of non-volatile liquid droplets. The solver was validated against the analytical solution in benchmark cases, and experimental data with bicomponent droplets reported in the literature. The developed model was used to predict the atomization of heavy fuel oil exposed at high temperatures under microgravity conditions. Different atomization regimes were identified, depending on the initial size of the internal bubbles. While small bubbles led to simple gas ejections, cavity collapse caused the larger bubbles to produce a jet formation. When the ratio between the bubble and droplet volumes was bigger than 0.7, microexplosions occurred. The results were found to be consistent with cases of bubble burst on flat surfaces, showing a strong dependence on the Ohnesorge number ($Oh$). Key observable quantities, particularly jet velocity and bubble cap drainage velocity, were found to agree with correlations reported in other studies. The similarities were also supported by studies extending over a wide range of simulations (4000 cases) at different $Oh$. An inversion in the dependence of the jet velocity on $Oh$ (above a critical value $Oh_c$) was observed.

The dynamics of the microlayer beneath a growing bubble in nucleate boiling significantly impacts the heat-transfer characteristics of the process. The minute thickness of the microlayer motivates the use of direct numerical simulation (DNS) to model its behaviour if empirical models are to be avoided. In this work, we develop a computational strategy for utilising DNS to model nucleate boiling by resolving explicitly the microlayer, directly coupling, in a stable manner, the mass, momentum and energy conservation equations with the conjugate heat transfer between the solid and fluid domains. To this end, closure models for the treatment of interfacial heat transfer and the dynamic contact angle are introduced and substantiated. The computational procedure is validated against relevant experimental data recently measured at the Massachusetts Institute of Technology; it is shown that the main observed growth features and surface heat-transfer characteristics are well reproduced using our model. We go on to perform a sensitivity study of the dependence of the initial microlayer thickness distribution on the applied superheat and fluid properties. The results indicate that an equation derived from lubrication theory captures the observed trends well. Finally, a first demonstration of DNS of boiling with an explicitly resolved microlayer in three-dimensional Cartesian coordinates is presented in one of the appendices.

The phenomena of microlayer formation and its dynamic characteristics during the nucleate pool boiling regime have been widely investigated in the past. However, experimental works on real-time microlayer dynamics during nucleate flow boiling conditions are highly scarce. The present work is an attempt to address this lacuna and is concerned with developing a fundamental understanding of microlayer dynamics during the growth process of a single vapour bubble under nucleate flow boiling conditions. Boiling experiments have been conducted under subcooled conditions in a vertical rectangular channel with water as the working fluid. Thin-film interferometry combined with high-speed cinematography have been adopted to simultaneously capture the dynamic behaviour of the microlayer along with the bubble growth process. Transients associated with the microlayer have been recorded in the form of interferometric fringe patterns, which clearly reveal the evolution of the microlayer beneath the growing vapour bubble, the movement of the triple contact line and the growth of the dryspot region during the bubble growth process. While symmetric growth of the microlayer was confirmed in the early growth phase, the bulk flow-induced bubble deformation rendered asymmetry to its profile during the later stages of the bubble growth process. The recorded fringe patterns have been quantitatively analysed to obtain microlayer thickness profiles at different stages of the bubble growth process. For Re = 3600, the maximum thickness of the almost wedge-shaped microlayer was obtained as δ ~ 3.5 μm for a vapour bubble of diameter 1.6 mm. Similarly, for Re = 6000, a maximum microlayer thickness of δ ~ 2.5 μm was obtained for a bubble of diameter 1.1 mm.

When a volatile drop impacts on a superheated solid, air drainage and vapour generation conspire to create an intermediate gas layer that delays or even prevents contact between the liquid and the solid. In this article, we use high-speed synchronized reflection interference and total internal reflection imaging to measure the short-time dynamics of the intermediate gas film and to probe the transition between levitation and contact. We observe that the substrate temperature strongly affects the vertical position of the liquid–gas interface and that the dynamic Leidenfrost transition is influenced by both air and vapour drainage (i.e. gas drainage), and evaporation, the latter giving rise to hitherto unreported vertical oscillations of the gas film that can trigger liquid–solid contact. We first derive scaling relations for the height of the gas film trapped under the drop's centreline, called the dimple height, and the minimum film thickness at short times. The former is set by a competition between gas drainage and liquid inertia, similarly as for isothermal impacts, while the latter strongly depends on the vapour production. The gas pressure, at the location where the minimum thickness is reached, is determined by liquid inertia and vapour production and ultimately balanced by the increasing interfacial curvature, determining the minimum thickness. We show that, in the low impact velocity limit, the transient stability of the draining gas film remarkably makes dynamic levitation less demanding than static levitation. We characterize the vertical gas film oscillations by measuring their frequency and monitoring their occurrence in the parameter space spanned by surface temperature and impact velocity. Finally, we model the occurrence of these oscillations and account for their frequency through a hydrodynamic mechanism.

During the impact of a liquid droplet on a sufficiently heated surface, bubble nucleation reduces the contact area between the liquid and the solid surface. Using high-speed imaging combined with total internal reflection, we measure and report how the contact area decreases with time for a wide range of surface temperatures and impact velocities. We also reveal how formation of the observed fingering patterns contributes to a substantial increase in the total length of the contact line surrounding the contact area.

Formation of a microlayer in nucleate boiling results in substantial changes to the heat-transfer dynamics of the process, and establishing a criterion to distinguish between the microlayer and contact-line regimes encountered is necessary to obtain a quantitative description of the nucleate-boiling phenomenon. In this work, we describe microlayer formation as a dewetting transition in the presence of phase change. We derive a specific criterion for modelling the transition based on a synthesis of existing theoretical, experimental and numerical data. As a result, a new formulation of the transition criterion is developed, and applied to (i) reference data from a dewetting experiment of a volatile liquid, and (ii) results derived from a high-resolution direct numerical simulation of nucleate boiling. In both cases, very good agreement is found for Jakob numbers $\lesssim$75, a range which covers many important boiling situations.

Saturated film boiling over an elliptical heater is investigated in the mixed regime considering both aiding and orthogonal liquid flow configurations relative to gravity. A computational framework developed for phase change problems on unstructured grids based on a coupled level set and volume of fluid interface capturing method is used to characterize interface evolution and vapour wake dynamics alongside quantifying heat transfer at low values of the Froude number (Fr). The influence of hydrodynamic and thermal conditions along with cross-flow direction for a fixed heater geometry manifests in the form of varied wake profiles with the quasi-steady nature of film boiling lost as Fr increases. Additionally, while the heater aspect ratio affects the rate of vapour infusion into the wake, the heater orientation significantly affects the film boiling behaviour. With horizontal cross-flow, higher angles of incidence entail a lower influence of flow inertia while augmenting buoyancy-driven vapour removal leading to enhanced heat transfer compared to aiding flow under certain cases, and adding a further dimension to the interplay between buoyancy and inertia. Similarly an anomalous impairment of heat transfer with an increase in cross-flow velocity arises from a competing influence of buoyancy and drag as an artefact of heater and cross-flow configurations. The mutual coupling of liquid and vapour wakes is also discussed in detail under such conditions. Finally, a shape factor $(\psi )$ is proposed to comprehensively predict the heat transfer in conjunction with correlations for a circular heater, and determined based on the effect of the elliptical geometry in the mixed regime.