James E. Sprittles

The University of Warwick · Warwick Mathematics Institute

Recent experiments on coating flows and liquid drop impact both demonstrate that wetting failures caused by air entrainment can be suppressed by reducing the ambient gas pressure. Here, it is shown that non-equilibrium effects in the gas can account for this behaviour, with ambient pressure reductions increasing the gas' mean free path and hence th...

The coalescence of two liquid drops surrounded by a viscous gas is considered in the framework of the conventional model. The problem is solved numerically with particular attention to resolving the very initial stage of the process which only recently has become accessible both experimentally and computationally. A systematic study of the paramete...

The formation of a single bubble from an orifice in a solid surface, submerged in an in- compressible, viscous Newtonian liquid, is simulated. The finite element method is used to capture the multiscale physics associated with the problem and to track the evolution of the free surface explicitly. The results are compared to a recent experimental an...

Surface engineering at the nanoscale is a rapidly developing field that promises to impact a range of applications including energy production, water desalination, self-cleaning and anti-icing surfaces, thermal management of electronics, microfluidic platforms, and environmental pollution control. As the area advances, more detailed insights of dyn...

The finite element simulation of dynamic wetting phenomena, requiring the computation of flow in a domain confined by intersecting a liquid-fluid free surface and a liquid-solid interface, with the three-phase contact line moving across the solid, is considered. For this class of flows, different finite element method (FEM) implementations have bee...

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...

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 b...

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 eigenmo...

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 eigenmo...

The effect of confining walls on the fluctuation of a nanoscale thin film's free surface is studied using the stochastic thin-film equations (STFE). Two canonical boundary conditions are employed to reveal the influence of the confinement: (i) an imposed contact angle and (ii) a pinned contact line. A linear stability analysis provides the wave eig...

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 In...

Formation of a splash crown and a cavity following the impact of a sphere on a body of liquid is a classical problem. In the related problem of a droplet splashing on a flat surface, it has been established that the properties of the surrounding gas can influence the splashing threshold. At lower impact speeds, this is due mainly to the influence o...

Formation of a splash crown and a cavity following the impact of a sphere on a body of liquid is a classical problem. In the related problem of a droplet splashing on a flat surface, it has been established that the properties of the surrounding gas can influence the splashing threshold. At lower impact speeds, this is due mainly to the influence o...

The moving contact line between a fluid, liquid and solid is a ubiquitous phenomenon, and determining the maximum speed at which a liquid can wet/dewet a solid is a practically important problem. Using continuum models, previous studies have shown that the maximum speed of wetting/dewetting can be found by calculating steady solutions of the govern...

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 descr...

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 c...

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 Toledano (2021) which we use as a benchmar...

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 nonuniform adaptive grids to study a series of nanoscale thin-film flows. The Fornberg scheme is used for high-resolution spatial discretization and a fully...

The Leidenfrost effect, where a drop levitates on a vapour film above a hot solid, is simulated using an efficient computational model that captures the internal flow within the droplet, models the vapour flow in a lubrication framework and is capable of resolving the dynamics of the process. The initial focus is on quasi-static droplets and the as...

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 vapor, traditional macroscopic approaches such as the Navier-Stokes-Fourier (NSF) equations become less accurate, and the use of highe...

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 high...

The moving-contact line between a fluid, liquid and a solid is a ubiquitous phenomenon, and determining the maximum speed at which a liquid can wet/dewet a solid is a practically important problem. Using continuum models, previous studies have shown that the maximum speed of wetting/dewetting can be found by calculating steady solutions of the gove...

Environmental structure describes physical structure that can determine heterogenous spatial distribution of biotic and abiotic (nutrients, stressors etc.) components of a microorganism’s micro-environment. This study investigated the impact of micrometre-scale structure on microbial stress sensing, using yeast cells exposed to copper in microfluid...

The formation of deformed liquid marbles via impact of drops onto powder beds is analysed using experimental and computational modelling approaches. Experimentally, particular attention is paid to determining a relationship between the maximum contact area of the spreading drops, which determines how much powder the drop's surface is able to harves...

The formation of deformed liquid marbles via impact of drops onto powder beds is analyzed using experimental and computational modeling approaches. Experimentally, particular attention is paid to determining a relationship between the maximum contact area of the spreading drops, which determines how much powder the drop's surface is able to harvest...

In this paper we compute the linear stability of similarity solutions of the breakup of viscous liquid threads, in which the viscosity and inertia of the liquid are in balance with the surface tension. The stability of the similarity solution is determined using numerical continuation to find the dominant eigenvalues. The stability of the first two...

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...

Determining physically admissible boundary conditions for higher moments in an extended continuum model is recognised as a major obstacle. Boundary conditions for the regularised 26-moment (R26) equations obtained using Maxwell's accommodation model do exist in the literature; however, we show in this article that these boundary conditions violate...

Formation of a splash crown and a cavity following the impact of a sphere on a body of liquidis a classical problem. In the related problem of a droplet splashing on a flat surface, it has beenestablished that the properties of the surrounding gas can influence the splashing threshold. Atlower impact speeds, this is due mainly to the influence of g...

Determining physically admissible boundary conditions for higher moments in an extended continuum model is recognised as a major obstacle. Boundary conditions for the regularised 26-moment (R26) equations obtained using Maxwell's accommodation model do exist in the literature; however, we show in this article that these boundary conditions violate...

In this paper we compute the linear stability of similarity solutions of the breakup of viscous liquid threads, in which the viscosity and inertia of the liquid are in balance with the surface tension. The stability of the similarity solution is determined using numerical continuation to find the dominant eigenvalue of the correction problem. Stabi...

Classical continuum-based liquid vapour phase-change models typically assume continuity of temperature at phase interfaces along with a relation which describes the rate of evaporation at the interface (Hertz-Knudsen-Schrage, for example). However, for phase transitions processes at small scales, such as the evaporation of nanodroplets, the assumpt...

The well-known thermal capillary wave theory, which describes the capillary spectrum of the free surface of a liquid film, does not reveal the transient dynamics of surface waves, e.g. the process through which a smooth surface becomes rough. Here, a Langevin model is proposed that can capture this dynamics, goes beyond the long-wave paradigm which...

The relaxation dynamics of thermal capillary waves for nanoscale liquid films on anisotropic-slip substrates are investigated, using both molecular dynamics (MD) simulations and a Langevin model. The anisotropy of slip on substrates is achieved using a specific lattice plane of a face-centred cubic lattice. This surface's anisotropy breaks the simp...

Numerical solutions of the Enskog-Vlasov (EV) equation are used to determine the velocity distribution function of atoms spontaneously evaporating into near-vacuum conditions. It is found that an accurate approximation is provided by a half-Maxwellian including a drift velocity combined with different characteristic temperatures for the velocity co...

Thin-film evaporation from nanoporous membranes is a promising cooling technology employed for the thermal management of modern electronic devices. We propose an effective one-dimensional analytical approach that can accurately predict the temperature and density jump relations, and evaporation rates, for arbitrary nanoporous membrane configuration...

The well-known thermal capillary wave theory, which describes the capillary spectrum of the free surface of a liquid film, does not reveal the transient dynamics of surface waves, e.g., the process through which a smooth surface becomes rough. Here, a Langevin model is proposed that can capture these dynamics, goes beyond the long-wave paradigm whi...

In the Leidenfrost effect, drops levitate on a thin film of vapor generated by the evaporation of the liquid above a solid surface heated beyond the Leidenfrost temperature. A previous model [1] predicted the quasistatic shape of a Leidenfrost drop by using the lubrication approximation for the vapor but neglecting flow in the drop. We find that th...

In the Leidenfrost effect, drops levitate on a thin film of vapor generated by the evaporation of the liquid above a solid surface heated beyond the Leidenfrost temperature. A previous model [1] predicted the quasistatic shape of a Leidenfrost drop by using the lubrication approximation for the vapor but neglecting flow in the drop. We find that th...

The combined effects of thermal fluctuations and liquid-solid slip on nanoscale thin-film flows are investigated using stochastic lubrication equations (SLEs). The previous no-slip SLE for films on plates is extended to consider slip effects and a new SLE for films on fibers is derived, using a long-wave approximation to fluctuating hydrodynamics....

Numerical solutions of the Enskog-Vlasov equation are used to determine the velocity distribution function of atoms spontaneously evaporating into near-vacuum conditions. It is found that an accurate approximation is provided by a half-Maxwellian including a drift velocity combined with different characteristic temperatures for the velocity compone...

Cox–Voinov theory with slip - Volume 900 - Tak Shing Chan, Catherine Kamal, Jacco H. Snoeijer, James E. Sprittles, Jens Eggers

In immiscible liquid-liquid Newtonian flow through a porous medium, one phase often becomes trapped in corners or narrow regions by capillary forces as blobs (e.g. oil ganglia) deep within the matrix, whilst the second flow exhibits a steady and laminar flow (e.g. of water) that has negligible influence on the trapped liquid-liquid interfaces. Howe...

Next-generation processor-chip cooling devices and self-cleaning surfaces can be enhanced by a passive process that require little to no electrical input, through coalescence-induced nanodroplet jumping. Here, we describe the crucial impact thermal capillary waves and ambient gas rarefaction have on enhancing/limiting the jumping speeds of nanodrop...

The instability and rupture of nanoscale liquid threads is shown to strongly depend on thermal fluctuations. These fluctuations are naturally occurring within molecular dynamics (MD) simulations and can be incorporated via fluctuating hydrodynamics into a stochastic lubrication equation (SLE). A simple and robust numerical scheme is developed for t...

A model is developed for liquid drop impact on a solid surface that captures the thin film gas flow beneath the drop, even when the film’s thickness is below the mean free path in the gas so that gas kinetic effects (GKE) are important. Simulation results agree with experiments, with the impact speed threshold between bouncing and wetting reproduce...

Evaporation is an effective cooling mechanism widely exploited in the thermal management of modern electronic devices, with a growing interest in the evaporation process in thin-film-based nanoporous membrane technologies. At such scales, classical approaches fail and one requires solutions of the Boltzmann equation; these are obtained here using t...

A transition from a d2 to a d law is observed in molecular dynamics (MD) simulations when the diameter (d) of an evaporating droplet reduces to the order of the vapor’s mean free path; this cannot be explained by classical theory. This Letter shows that the d law can be predicted within the Navier-Stokes-Fourier (NSF) paradigm if a temperature-jump...

A transition from a d^2-to a d-law is observed in molecular dynamics (MD) simulations when the diameter (d) of an evaporating droplet reduces to the order of the vapor's mean free path; this cannot be explained by classical theory. This Letter shows that the d-law can be predicted within the Navier-Stokes-Fourier (NSF) paradigm if a temperature-jum...

The instability of a thin liquid film on a solid surface is studied both by molecular dynamics simulations (MD) and a stochastic thin-film equation (STF), which models thermal fluctuations with white noise. A linear stability analysis of the STF allows us to derive a power spectrum for the surface fluctuations, which is quantitatively validated aga...

The classical notion of the coalescence of two droplets of the same radius R is that surface tension drives an initially singular flow. In this Letter we show, using molecular dynamics simulations of coalescing water nanodroplets, that after single or multiple bridges form due to the presence of thermal capillary waves, the bridge growth commences...

We consider the linearized form of the regularized 13-moment equations (R13) to model the slow, steady gas dynamics surrounding a rigid, heat-conducting sphere when a uniform temperature gradient is imposed far from the sphere and the gas is in a state of rarefaction. Under these conditions, the phenomenon of thermophoresis, characterized by forces...

We study air entrainment by a solid plate plunging into a viscous liquid, theoretically and numerically. At dimensionless speeds $Ca=U\unicode[STIX]{x1D702}/\unicode[STIX]{x1D6FE}$ of order unity, a near-cusp forms due to the presence of a moving contact line. The radius of curvature of the cusp’s tip scales with the slip length multiplied by an ex...

The theoretical framework developed by Rayleigh and Plateau in the 19th century has been remarkably accurate in describing macroscale experiments of liquid cylinder instability. Here we re-evaluate and revise the Rayleigh–Plateau instability for the nanoscale, where molecular dynamics experiments demonstrate its inadequacy. A new framework based on...

Evaporation of a binary liquid into near-vacuum conditions has been studied using numerical solutions of a system of two coupled Enskog-Vlasov equations. Liquid-vapor coexistence curves have been mapped out for different liquid compositions. The evaporation process has been investigated at a range of liquid temperatures sufficiently lower than the...

Macroscopic models based on moment equations are developed to describe the transport of mass and energy near the phase boundary between a liquid and its rarefied vapour due to evaporation and hence, in this study, condensation. For evaporation from a spherical droplet, analytic solutions are obtained to the linearised equations from the Navier–Stok...

Fundamental solutions (Green’s functions) are derived for the regularised 13-moment system (R13) of rarefied gas dynamics, for small departures from equilibrium; these solutions show the presence of Knudsen layers, associated with exponential decay terms, that do not feature in the solution of lower-order systems (e.g. the Navier–Stokes–Fourier equ...

The maximum speed at which a liquid can wet a solid is limited by the need to displace gas lubrication films in front of the moving contact line. The characteristic height of these films is often comparable to the mean free path in the gas so that hydrodynamic models do not adequately describe the flow physics. This Letter develops a model which in...

We report studies of the coalescence of pairs of picolitre aerosol droplets manipulated with holographic optical tweezers, probing the shape relaxation dynamics following coalescence by simultaneously monitoring the intensity of elastic backscattered light (EBL) from the trapping laser beam (time resolution on the order of 100 ns) while recording h...

Computations of the breakup of a liquid bridge are used to establish the limits of applicability of similarity solutions derived for different breakup regimes. These regimes are based on particular viscous–inertial balances, that is, different limits of the Ohnesorge number $Oh$ . To accurately establish the transitions between regimes, the minim...

The interface formation model is applied to describe the initial stages of the coalescence of two liquid drops in the presence of a viscous ambient fluid whose dynamics is fully accounted for. Our focus is on understanding (a) how this model's predictions differ from those of the conventionally used one, (b) what influence the ambient fluid has on...

We examine the dynamics of two coalescing liquid drops in the `inertial regime', where the effects of viscosity are negligible and the propagation of the bridge front connecting the drops can be considered as `local'. The solution fully computed in the framework of classical fluid-mechanics allows this regime to be identified and the accuracy of th...