Leidenfrost hydrogel spheres exhibit interfacial oscillations that inject energy and drive sustained bouncing. Using a computational model, we identify these oscillations as an evaporation-driven instability of elastic surface waves. The resulting dynamics conform to a classical engine cycle [S. R. Waitukaitis et al., Nat. Phys. 13, 1095 (2017)], even in the absence of vapor trapping at the solid surface previously proposed as the injection mechanism.

Over the past decade data-driven equation discovery emerged as a powerful alternative to first principles-based methodologies traditionally used in mathematical modelling cycles. The approach provides a promising path towards deep, physical insight into systems that have previously evaded rigorous mathematical derivation procedures, often due to intractable complexity. The strengths of such techniques have been successfully established for many problem classes described by systems of ordinary differential equations and continue to be extended, with their reach into partial differential equation systems gaining momentum, though comparatively nascent. Herein we tackle such a frontier: elucidating the dynamics of liquid film flows, a problem space providing a rich backdrop in terms of asymptotic analytical building blocks. By leveraging expert knowledge and the ability to carefully curate data, we establish a best-case scenario for identifying the underlying governing equations. Even here, multi-collinearity, stemming from the choice of monomial basis functions in our multi-scale flow configuration, introduces complex identifiability issues. Early-time transients compound this further, as the most dynamically rich behaviour carries the largest residuals in training data. Pinpointing such vulnerabilities allows us to better define the boundaries of current discovery techniques and paves the way for the next generation of more resilient, numerically stable algorithms.

The merging of two fluid drops is one of the fundamental topological transitions occurring in free surface flow. Its description has many applications, for example, in the chemical industry (emulsions, sprays, etc.), in natural flows driving our climate, and for the sintering of materials. After the reconnection of two drops, strongly localized surface tension forces drive a singular flow, characterized by a connecting liquid bridge that grows according to scaling laws. We review theory, experiment, and simulation of the coalescence of two spherical drops for different parameters and in the presence of an outer fluid. We then generalize to other geometries, such as drops spreading on a substrate and in Hele–Shaw flow, and we discuss other types of mass transport, apart from viscous flow. Our focus is on times immediately after reconnection and on the limit of initially undeformed drops at rest relative to one another.

Despite the large body of research on coalescence, firm agreement between experiment, theory, and computation has not been established for the very earliest times following the initial contact of two liquid volumes. Combining a range of experimental and computational modelling approaches, we have been able to elucidate the influence of the intervening gas, of the van der Waals forces and of thermal fluctuations on coalescence. For simple liquids, the gas influences both pre- and post-contact regimes, with a jump-to-contact the primary mode of merging. Subsequently, wave-like air pockets are observed. For a system with ultralow interfacial tension, that mimics nanodrop behaviour, the very first moments are governed by thermal fluctuations at the interfaces, with a nontrivial opening speed given by stochastic thermally driven motion.

Pectin is a major component of plant cells walls. The extent to which pectin chains crosslink with one another determines crucial properties including cell wall strength, porosity, and the ability of small, biologically significant molecules to access the cell. Despite its importance, significant gaps remain in our comprehension, at the molecular level, of how pectin cross-links influence the mechanical and physical properties of cell walls. This study employs a multidisciplinary approach, combining molecular dynamics simulations, experimental investigations, and mathematical modelling, to elucidate the mechanism of pectin cross-linking and its effect on cell wall porosity. The computational aspects of this work challenge the prevailing egg-box model, favoring instead a zipper model for pectin cross-linking, whilst our experimental work highlights the significant impact of pectin cross-linking on cell wall porosity. This work advances our fundamental understanding of the biochemistry underpinning the structure and function of the plant cell wall. This knowledge has important implications for agricultural biotechnology, informing us about the chemical properties of plant pectins that are best suited for improving crop resilience and amenability to biofuel extraction by modifying the cell wall.

Suppression of the coffee ring effect is desirable in many industrial applications which utilize colloidal deposition from an evaporating liquid. Here we focus on the role of particle arrest at the liquid-air interface (surface capture) which occurs at high evaporation rates. It is known experimentally that this phenomenon inhibits particles from reaching the contact line, leading to a deposit which is closer to uniform. We are able to describe this effect using a simple 1D modeling framework and, utilizing asymptotic theory, parametrize our model by the ratio of the vertical advection and diffusion timescales. We show that our model is consistent with existing frameworks for small values of this parameter, but also predicts the surface layer formation seen experimentally at high evaporation rates. The formation of a surface layer leads to a deposit morphology which mimics the evaporative flux density and so is closest to uniform when evaporation has a constant strength across the liquid-air interface. Published by the American Physical Society 2024

Recent advances in experimental techniques have enabled remarkable discoveries and insight into how the dynamics of thin gas/vapour films can profoundly influence the behaviour of liquid droplets: drops impacting solids can “skate on a film of air”, so that they can “bounce off walls”; reductions in ambient gas pressure can suppress splashing and initiate the merging of colliding droplets; and evaporating droplets can levitate on their own vapour film (the Leidenfrost effect). Despite these advances, the precise physical mechanisms governing these phenomena remains a topic of debate. In this talk, I will overview our development of efficient computational models for the aforementioned droplet dynamics in the presence of gas nanofilms into which gas-kinetic, van der Waals and/or evaporative effects can be easily incorporated in order to address these open problems and stimulate new directions of research.

Thermally activated phenomena in physics and chemistry, such as conformational changes in biomolecules, liquid film rupture, or ferromagnetic field reversal, are often associated with exponentially long transition times described by Arrhenius' law. The associated subexponential prefactor, given by the Eyring-Kramers formula, has recently been rigorously derived for systems in detailed balance, resulting in a sharp limiting estimate for transition times and reaction rates. Unfortunately, this formula does not trivially apply to systems with conserved quantities, which are ubiquitous in the sciences: The associated zeromodes lead to divergences in the prefactor. We demonstrate how a generalised formula can be derived, and show its applicability to a wide range of systems, including stochastic partial differential equations from fluctuating hydrodynamics, with applications in rupture of nanofilm coatings and social segregation in socioeconomics.

In the last ten years, advances in experimental techniques have enabled remarkable discoveries of how the dynamics of thin gas films can profoundly influence the behavior of liquid droplets. Drops impacting onto solids can skate on a film of air so that they bounce off solids. For drop–drop collisions, this effect, which prevents coalescence, has been long recognized. Notably, the precise physical mechanisms governing these phenomena have been a topic of intense debate, leading to a synergistic interplay of experimental, theoretical, and computational approaches. This review attempts to synthesize our knowledge of when and how drops bounce, with a focus on ( a) the unconventional microscale and nanoscale physics required to predict transitions to/from merging and ( b) the development of computational models. This naturally leads to the exploration of an array of other topics, such as the Leidenfrost effect and dynamic wetting, in which gas films also play a prominent role.

A modeling framework for the complete evaporation of particle-laden droplets, including touchdown events where the air-liquid interface approaches the substrate, is presented. The inclusion of particle jamming into the model, creating a transition from free advection to an immobile porous plug, is essential to making realistic predictions for the deposit's dimensions. By removing the need to track jammed particle fronts explicitly, as often considered, we are able to run simulations until solute has jammed everywhere in the drop. This allows for valid comparisons with experimental findings on the dried deposit's topography. Our model can also be easily applied to general contact line geometries, allowing us to explore the influence of contact line curvature on the local deposit profile.

Whether colliding drops will merge with or bounce off each other is critical to numerous processes, and the physics involved is notoriously complex. In particular, experiments show that both sufficiently slow and fast head-on drop collisions lead to merging, but that there is often an intermediate regime in which bouncing is observed; these transitions in behaviour were recently discovered to be surprisingly sensitive to the radius of the drops and the ambient gas pressure. We show here that these transitions between bouncing and merging are governed by nanoscale phenomena; namely, gas-kinetic and disjoining pressure effects. To capture these crucial effects, a novel, open-source computational model is developed for the simulation of colliding drops. The model uses a hybrid approach, based on solving the Navier–Stokes equations in the drop with a lubrication approach for the unconventional physics of the gas film. Our simulations show remarkably good agreement with experiments of head-on collisions and also provide new experimentally verifiable predictions.

Sufficiently thin liquid films on solid surfaces are often unstable to intermolecular forces and it is commonly assumed that their rupture occurs via a linear instability mechanism in the so-called spinodal regime. Here, a theoretical framework is created for the experimentally observed thermal regime, in which fluctuation-induced nanowaves rupture linearly stable films. Molecular simulations in a quasi-2D geometry identify these regimes and are accurately reproduced by stochastic simulations based on fluctuating hydrodynamics. Rare-event theory is then applied to, and developed for, this field to provide exceptional computational efficiency and accuracy that allows us to extend calculations deep into the thermal regime. Analysis of the rare-event theory reveals a picture of how and when "rogue nanowaves" are able to provide a route to film rupture. Finally, future applications of the new theoretical framework and experimental verification is discussed.

Molecular simulations discover a new mode of dynamic wetting that manifests itself in the very earliest stages of spreading, after a droplet contacts a solid. The observed mode is a "rolling" type of motion, characterized by a contact angle lower than the classically assumed value of 180°, and precedes the conventional "sliding" mode of spreading. This motivates the development of a novel continuum framework that captures all modes of motion, allows the dominant physical mechanisms to be understood, and permits the study of larger droplets.

The effect of confining walls on the fluctuation of a nanoscale thin film's free surface is studied using stochastic thin-film equations (STFEs). Two canonical boundary conditions are employed to reveal the influence of the confinement: (1) an imposed contact angle and (2) a pinned contact line. A linear stability analysis provides the wave eigenmodes, after which thermal-capillary-wave theory predicts the wave fluctuation amplitudes. Molecular dynamics (MD) simulations are performed to test the predictions, and a Langevin diffusion model is proposed to capture oscillations of the contact lines observed in MD simulations. Good agreement between the theoretical predictions and the MD simulation results is recovered, and it is discovered that confinement can influence the entire film. Notably, a constraint on the length scale of wave modes is found to affect fluctuation amplitudes from our theoretical model, especially for 3D films. This opens up challenges and future lines of inquiry.

The elastic Leidenfrost effect occurs when a vaporizable soft solid is lowered onto a hot surface. Evaporative flow couples to elastic deformation, giving spontaneous bouncing or steady-state floating. The effect embodies an unexplored interplay between thermodynamics, elasticity, and lubrication: despite being observed, its basic theoretical description remains a challenge. Here, we provide a theory of elastic Leidenfrost floating. As weight increases, a rigid solid sits closer to the hot surface. By contrast, we discover an elasticity-dominated regime where the heavier the solid, the higher it floats. This geometry-governed behavior is reminiscent of the dynamics of large liquid Leidenfrost drops. We show that this elastic regime is characterized by Hertzian behavior of the solid's underbelly and derive how the float height scales with materials parameters. Introducing a dimensionless elastic Leidenfrost number, we capture the crossover between rigid and Hertzian behavior. Our results provide theoretical underpinning for recent experiments, and point to the design of novel soft machines.

The wetting and dewetting of solid surfaces is ubiquitous in physical systems across a range of length scales, and it is well known that there are maximum speeds at which these processes are stable. Past this maximum, flow transitions occur, with films deposited on solids (dewetting) and the outer fluid entrained into the advancing one (wetting). These new flow states may be desirable, or not, and significant research effort has focused on understanding when and how they occur. Up until recently, numerical simulations captured these transitions by focussing on steady calculations. This review concentrates on advances made in the computation of the time-dependent problem, utilising dynamical systems theory. Facilitated via a linear stability analysis, unstable solutions act as 'edge states', which form the 'point of no return' for which perturbations from stable flow cease decaying and, significantly, show the system can become unstable before the maximum speed is achieved.

Thin-film-based nanoporous membrane technologies exploit evaporation to efficiently cool microscale and nanoscale electronic devices. At these scales, when domain sizes become comparable to the mean free path in the vapour, traditional macroscopic approaches such as the Navier-Stokes-Fourier (NSF) equations become less accurate, and the use of higher-order moment methods is called for. Two higher-order moment equations are considered; the linearised versions of the Grad 13 and Regularised 13 equations. These are applied to the problem of nanoporous evaporation, and results are compared to the NSF method and the method of direct simulation Monte Carlo (i.e. solutions to the Boltzmann equations). Linear and non-linear versions of the boundary conditions are examined, with the latter providing improved results, at little additional computational expense, compared to the linear form. The outcome is a simultaneously accurate and computationally efficient method, which can provide simulation-for-design capabilities at the nanoscale.

The effects of thermal fluctuations on nanoscale flows are captured by a numerical scheme that is underpinned by fluctuating hydrodynamics. A stochastic lubrication equation (SLE) is solved on non-uniform adaptive grids to study a series of nanoscale thin-film flows. The Fornberg scheme is used for high-resolution spatial discretisation and a fully-implicit time-marching scheme is designed for numerical stability. The accuracy of the numerical method is verified against theoretical results for thermal capillary waves during the linear stage of their development. The framework is then used to study the nonlinear behaviour of three bounded thin-film flows: (i) droplet spreading, where new power laws are derived; (ii) droplet coalescence, where molecular dynamics results are reproduced by the SLE at a fraction of the computational cost and it is discovered that thermal fluctuations decelerate the process, in contrast to previously investigated phenomena; and (iii) thin-film rupture, where, in the regime considered, disjoining pressure dominates the final stages of rupture.

We develop a novel boundary integral formulation for the steady linearized form of Grad's 13-moment (G13) equations applied to a uniform flow of rarefied gas past solid objects at low Mach numbers. Changing variables leads to a system of boundary integral equations that combines integral equations from Stokes flow and potential theory. The strong coupling between the stress deviator and heat flux featured by the G13 equations demands adding a boundary integral equation for the pressure. We specialize the integral equations for an axisymmetric flow with no swirl and derive the axisymmetric fundamental solutions for the pressure equation, seemingly absent in the Stokes-flow literature. Using the boundary element method to achieve a numerical solution, we apply this formulation to streaming flow of rarefied gas past prolate or oblate spheroids with their axis of symmetry parallel to the free stream, considering various aspect ratios and Knudsen numbers—the ratio of the molecules' mean free path to the macroscopic length scale. After validating the method, we obtain the surface profiles of the deviations from the unperturbed state of the traction, heat flux, pressure, temperature, and slip velocity, as well as the drag on the spheroid, observing convergence with the number of elements. Rarefaction phenomena, such as temperature jump and polarization, Knudsen effects in the drag, and velocity slippage, are predicted. This method opens a new path for investigating other gas non-equilibrium phenomena that can be modeled by the same set of equations, such as thermophoresis, and has application in nano- and microfluidics.

We report a molecularly augmented continuum-based computational model of dynamic wetting and apply it to the displacement of an externally driven liquid plug between two partially wetted parallel plates. The results closely follow those obtained in a recent molecular dynamics (MD) study of the same problem (Fernández-Toledano et al. , J. Colloid Interface Sci. , vol. 587, 2021, pp. 311–323), which we use as a benchmark. We are able to interpret the maximum speed of dewetting $U^*_{{crit}}$ as a fold bifurcation in the steady phase diagram and show that its dependence on the true contact angle $\theta _{{cl}}$ is quantitatively similar to that found using MD. A key feature of the model is that the contact angle is dependent on the speed of the contact line, with $\theta _{{cl}}$ emerging as part of the solution. The model enables us to study the formation of a thin film at dewetting speeds $U^*>U^*_{{crit}}$ across a range of length scales, including those that are computationally prohibitive to MD simulations. We show that the thickness of the film scales linearly with the channel width and is only weakly dependent on the capillary number. This work provides a link between matched asymptotic techniques (valid for larger geometries) and MD simulations (valid for smaller geometries). In addition, we find that the apparent angle, the experimentally visible contact angle at the fold bifurcation, is not zero. This is in contrast to the prediction of conventional treatments based on the lubrication model of flow near the contact line, but consistent with experiment.