Dynamics of a thin dewetting liquid film on a vertically oscillating substrate is considered. We assume moderate vibration frequency and large (compared to the mean film thickness) vibration amplitude. Using the lubrication approximation and the averaging method, we formulate the coupled sets of equations governing the pulsatile and the averaged fluid flows in the film, and then derive the nonlinear amplitude equation for the averaged film thickness. We show that there exists a window in the frequency-amplitude domain where the parametric and shear-flow instabilities of the pulsatile flow do not emerge. As a consequence, in this window the averaged description is reasonable and the amplitude equation holds. The linear and nonlinear analyses of the amplitude equation and the numerical computations show that such vibration stabilizes the film against dewetting and rupture.
We consider the dynamics of a thin liquid film in the attractive substrate potential and under the action of a longitudinal or a tilted vibration. Using a multiscale technique we split the film motion into the oscillatory and the averaged parts. The frequency of the vibration is assumed high enough for the inertial effects to become essential for the oscillatory motion. Applying the lubrication approximation for the averaged motion we obtain the amplitude equation, which includes contributions from gravity, van der Waals attraction, surface tension, and the vibration. We show that the longitud…
In this paper the lubrication-type dynamical model is developed of a molten, pulsed laser-irradiated metallic film. The heat transfer problem that incorporates the absorbed heat from a single beam or interfering beams is solved analytically. Using this temperature field, we derive the 3D long-wave evolution PDE for the film height. To get insights into dynamics of dewetting, we study the 2D version of the evolution equation by means of a linear stability analysis and by numerical simulations. The stabilizing and destabilizing effects of various system parameters, such as the peak laser beam in…
We study the deformation and dewetting of liquid films under impinging gas jets using experimental, analytical and numerical techniques. We first derive a reduced-order model (a thin-film equation) based on the long-wave assumption and on appropriate decoupling of the gas problem from that for the liquid. The model not only provides insight into relevant flow regimes, but is also used in conjunction with experimental data to guide more computationally prohibitive direct numerical simulations (DNS) of the full governing equations. A unique feature of our modelling solution is the use of an effi…
In this paper, we present a computationally efficient method for including fluid-solid interactions into direct numerical simulations of the Navier-Stokes equations. This method is found to be as powerful as our earlier formulation [J. Comp. Phys., vol. 249: 243 (2015)], while outperforming the earlier method in terms of computational efficiency. The performance and efficacy of the presented method are demonstrated by computing contact angles of droplets at equilibrium. Furthermore, we study the instability of films due to destabilizing fluid-solid interactions, and discuss the influence of co…
Macroscopic simulations of thin film wetting/dewetting using a precursor film model
State Key Laboratory of High Temperature Gas Dynamics, School of Engineering Science, University of Science and Technology of China（中国科学技术大学工程科学学院高温气体动力学国家重点实验室）
A gradient dynamics model based on an extended interface Hamiltonian is presented that is able to describe the dynamics of structuring processes in thin films of liquid mixtures, solutions and suspensions on solid substrates including coupled dewetting and decomposition. After discussing known limiting cases the model is employed to investigate the dewetting of thin films of liquid mixtures and suspensions under the influence of effective long-range van der Waals forces that depend on solute concentration. The occurring fluxes are discussed and it is shown that spinodal dewetting may be trigge…
Ultrathin polymer films on non-wettable substrates display dynamic features which have been attributed to either viscoelastic or slip effects. Here we show that in the weak and strong slip regime effects of viscoelastic relaxation are either absent or not distinguishable from slip effects. Strong-slip modifies the fastest unstable mode in a rupturing thin film, which questions the standard approach to reconstruct the effective interface potential from dewetting experiments.
We study numerically the effect of thermal fluctuations and of variable fluid-substrate interactions on the spontaneous dewetting of thin liquid films. To this aim, we use a recently developed lattice Boltzmann method for thin liquid film flows, equipped with a properly devised stochastic term. While it is known that thermal fluctuations yield shorter rupture times, we show that this is a general feature of hydrophilic substrates, irrespective of the contact angle. The ratio between deterministic and stochastic rupture times, though, decreases with $θ$. Finally, we discuss the case of fluctuat…
We study the dewetting of liquid films capped by a thin elastomeric layer. When the tension in the elastomer is isotropic, circular holes grow at a rate which decreases with increasing tension. The morphology of holes and rim stability can be controlled by changing the boundary conditions and tension in the capping film. When the capping film is prepared with a biaxial tension, holes form with a non-circular shape elongated along the high tension axis. With suitable choice of elastic boundary conditions, samples can even be designed such that square holes appear.
The influence of wall slip on the instability of a non-wetting liquid film placed on a solid substrate is analyzed in the limit of negligible inertia. In particular, we focus on the stability properties of the film, comparing the performance of the three lubrication models available in the literature, namely the weak, intermediate and strong slip models, with the Stokes equations. Since none of the aforementioned leading-order lubrication models is shown to be able to predict the growth rate of perturbations for the whole range of slipping lengths, we develop a parabolic model able to accurate…
The spontaneous formation of droplets via dewetting of a thin fluid film from a solid substrate allows for materials nanostructuring, under appropriate experimental control. While thermal fluctuations are expected to play a role in this process, their relevance has remained poorly understood, particularly during the nonlinear stages of evolution. Within a stochastic lubrication framework, we show that thermal noise speeds up and substantially influences the formation and evolution of the droplet arrangement. As compared with their deterministic counterparts, for a fixed spatial domain, stochas…
We consider a porous solid covered with a water film (or with a drop) in situations where the liquid is pumped in, either spontaneously (if the porous medium is hydrophilic) or mechanically (by an external pump). The dynamics of dewetting is then strongly modified. We analyse a few major examples: a) horizontal films, which break at a certain critical thickness, b) the "modified Landau-Levich problem" where a porous plate moves up from a bath and carries a film: aspiration towards the plate limits the height H reached by the film, c) certain situation where the hysteresis of contact angles is …
This work presents a study of the interfacial dynamics of thin viscoelastic films subjected to the gravitational force and substrate interactions induced by the disjoining pressure, in two spatial dimensions. The governing equation is derived as a long-wave approximation of the Navier-Stokes equations for incompressible viscoelastic liquids under the effect of gravity, with the Jeffreys model for viscoelastic stresses. For the particular cases of horizontal or inverted planes, the linear stability analysis is performed to investigate the influence of the physical parameters involved on the gro…
The entrainment of air by advancing contact lines is studied by plunging a solid plate into a very viscous liquid. Above a threshold velocity, we observe the formation of an extended air film, typically 10 microns thick, which subsequently decays into air bubbles. Exploring a large range of viscous liquids, we find an unexpectedly weak dependence of entrainment speed on liquid viscosity, pointing towards a crucial role of the flow inside the air film. This induces a striking asymmetry between wetting and dewetting: while the breakup of the air film strongly resembles the dewetting of a liquid …
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 benchmark. We are able to interpret the maximum speed of dewetting $U^*_{\mathrm{crit}}$ as a fold bifurcation in the steady phase diagram and show that its dependence on the true contact angle $θ_{\mathrm{cl}}$ is quantitatively similar to that found using …
We revisit the fundamental problem of liquid-liquid dewetting and perform a detailed comparison of theoretical predictions based on thin-film models with experimental measurements obtained by atomic force microscopy (AFM). Specifically, we consider the dewetting of a liquid polystyrene (PS) layer from a liquid polymethyl methacrylate (PMMA) layer, where the thicknesses and the viscosities of PS and PMMA layers are similar. The excellent agreement of experiment and theory reveals that dewetting rates for such systems follow no universal power law, in contrast to dewetting scenarios on solid sub…
We study the impact and subsequent retraction dynamics of liquid droplets upon high-speed impact on hydrophobic surfaces. Performing extensive experiments, we show that the drop retraction rate is a material constant and does not depend on the impact velocity. We show that when increasing the Ohnesorge number, $\Oh=η/\sqrt{ρR_{\rm I} γ}$, the retraction, i.e. dewetting, dynamics crosses over from a capillaro-inertial regime to a capillaro-viscous regime. We rationalize the experimental observations by a simple but robust semi-quantitative model for the solid-liquid contact line dynamics inspir…
When a solid plate is withdrawn from a liquid bath, a receding contact line is formed where solid, liquid, and gas meet. Above a critical speed $U_{cr}$, a stationary contact line can no longer exist and the solid will eventually be covered completely by a liquid film. Here we show that the bifurcation diagram of this coating transition changes qualitatively, from discontinuous to continuous, when decreasing the inclination angle of the plate. We show that this effect is governed by the presence of capillary waves, illustrating that the large scale flow strongly effects the maximum speed of de…
When a liquid film lies on a non-wettable substrate, the configuration is unstable and the film then retracts from a solid substrate to form droplets. This phenomenon, known as dewetting, commonly leads to undesirable morphological changes. Nevertheless, recent works have demonstrated the possibility to harness dewetting by employing templated substrates with a degree of precision on par with advanced lithographic processes for high-performance nanophotonic applications. Since resonant behavior is highly sensitive to geometrical changes, predicting quantitatively dewetting dynamics is of high …
We present a computational investigation of thin viscoelastic films and drops on a solid substrate subject to the van der Waals interaction force, in two spatial dimensions. The governing equations are obtained within a long-wave approximation of the Navier-Stokes equations with Jeffreys model for viscoelastic stresses. We investigate the effects of viscoelasticity, Newtonian viscosity, and the substrate slippage on the dynamics of thin viscoelastic films. We also study the effects of viscoelasticity on drops that spread or recede on a prewetted substrate. For dewetting films, the numerical re…
When a solid substrate is withdrawn from a bath of simple, partially wetting, nonvolatile liquid, one typically distinguishes two regimes, namely, after withdrawal the substrate is macroscopically dry or homogeneously coated by a liquid film. In the latter case, the coating is called a Landau-Levich film. Its thickness depends on the angle and velocity of substrate withdrawal. We predict by means of a numerical and analytical investigation of a hydrodynamic thin-film model the existence of a third regime. It consists of the deposition of a regular pattern of liquid ridges oriented parallel to …
We have detected unique hydrodynamic topology in thin air film surrounding the central air dimple formed during drop impact on an immiscible liquid pool. The pattern resembles spinodal and finger-like structures typically found in various thin condensed matter systems. However, similar structures in thin entrapped gas films during drop impacts on solids or liquids have not been reported to date. The thickness profile and the associated dewetting dynamics in the entrapped air layer are investigated experimentally and theoretically using high-speed reflection interferometric imaging and linear s…
We consider a free surface thin film placed on a thermally conductive substrate and exposed to an external heat source in a setup where the heat absorption depends on the local film thickness. Our focus is on modeling film evolution while the film is molten. The evolution of the film modifies local heat flow, which in turn may influence the film surface evolution through thermal variation of the film's material properties. Thermal conductivity of the substrate plays an important role in determining the heat flow and the temperature field in the evolving film and in the substrate itself. In ord…
We study the combined effects of nonlocal elasticity and confinement induced ordering on the dynamics of thermomolecular pressure gradient driven premelted films bound by an elastic membrane. The confinement induced ordering is modeled using a film thickness dependent viscosity. When there is no confinement induced ordering, we recover the similarity solution for the evolution of the elastic membrane, which exhibits an infinite sequence of oscillations. However, when the confinement induced viscosity is comparable to the bulk viscosity, the numerical solutions of the full system reveal the con…
In this paper, we describe the optical grid deflection method used to reconstruct the 3D profile of liquid films deposited by a receding liquid meniscus. This technique uses the refractive properties of the film surface and is suitable for liquid thickness from several microns to millimeter. This method works well for strong interface slopes and changing in time film shape; it applies when the substrate and fluid media are transparent. The refraction is assumed to be locally unidirectional. The method is particularly appropriate to follow the evolution of parameters such as dynamic contact ang…
A dynamical model is proposed to describe the coupled decomposition and profile evolution of a free surface film of a binary mixture. An example is a thin film of a polymer blend on a solid substrate undergoing simultaneous phase separation and dewetting. The model is based on model-H describing the coupled transport of the mass of one component (convective Cahn-Hilliard equation) and momentum (Navier-Stokes-Korteweg equations) supplemented by appropriate boundary conditions at the solid substrate and the free surface. General transport equations are derived using phenomenological non-equilibr…
We develop and analyze a model for ratchet-driven macroscopic transport of a continuous phase. The transport relies on a field-induced dewetting-spreading cycle of a liquid film with a free surface based on a switchable, spatially asymmetric, periodic interaction of the liquid-gas interface and the substrate. The concept is exemplified using an evolution equation for a dielectric liquid film under an inhomogeneous voltage. We analyse the influence of the various phases of the ratchet cycle on the transport properties. Conditions for maximal transport and the efficiency of transport under load …
Theory and numerical simulations of the Navier-Stokes equations are used to unravel the inertia-driven dewetting dynamics of an ultrathin film of Newtonian liquid deposited on a solid substrate. A classification of the film thinning regimes at finite Ohnersorge numbers is provided, unifying previous findings. We reveal that, for Ohnesorge numbers smaller than one, the final approach to the rupture singularity close to the molecular scales is controlled by a balance between liquid inertia and van der Waals forces leading to a self-similar asymptotic regime with $h_{\text{min}} \propto τ^{2/5}$,…
Thin liquid films are ubiquitous in natural phenomena and technological applications. They have been extensively studied via deterministic hydrodynamic equations, but thermal fluctuations often play a crucial role that needs to be understood. An example of this is dewetting, which involves the rupture of a thin liquid film and the formation of droplets. Such a process is thermally activated and requires fluctuations to be taken into account self-consistently. In this work we present an analytical and numerical study of a stochastic thin-film equation derived from first principles. Following a …
We propose a novel approach to the numerical simulation of thin film flows, based on the lattice Boltzmann method. We outline the basic features of the method, show in which limits the expected thin film equations are recovered and perform validation tests. The numerical scheme is applied to the viscous Rayleigh-Taylor instability of a thin film and to the spreading of a sessile drop towards its equilibrium contact angle configuration. We show that the Cox-Voinov law is satisfied, and that the effect of a tunable slip length on the substrate is correctly captured. We address, then, the problem…
We present a theoretical study of wetting phenomena and interactions between liquid-vapor interfaces based on the density functional theory. The focus is mostly on the impact of long-range van der Waals interactions both within the fluid and between the fluid and substrate. For the latter, we consider two models-hard wall and soft wall approximations-differing by the role of steric effects and leading to a qualitatively different character of phase transitions. We compute numerically the disjoining and conjoining potentials (which are important dynamically for spreading, spinodal dewetting, an…
Solitary-like surface waves that originate from the spatio-temporal evolution of falling liquid films have been the subject of theoretical and experimental research due to their unique properties that are not readily observed in the physical system of other nature. Here we investigate, experimentally and theoretically, the dynamics of solitary-like surface waves in a liquid layer on an inclined plane that is subjected to a harmonic low-frequency vibration in the range from 30 to 50 Hz. We demonstrate that the vibration results in a decrease in the average and peak amplitude of the long solitar…
The liquid film motor (LFM) is a simple device which serves as a laboratory to conduct experimental research in basic theoretical studies of electrohydrodynamics (EHD). In addition the LFM can play an important role in technological applications such as micro mixers and washers. In this paper we initially performed experiments to examine the theory regarding rotation and vibration of an AC LFM. While many theoretical predictions are in agreement with our experimental data, but in the threshold of vibration there is an obvious disagreement; we showed that no threshold exists and oscillation is …
We present the results of large scale simulations of 4th order nonlinear partial differential equations of dif- fusion type that are typically encountered when modeling dynamics of thin fluid films on substrates. The simulations are based on the alternate direction implicit (ADI) method, with the main part of the compu- tational work carried out in the GPU computing environment. Efficient and accurate computations allow for simulations on large computational domains in three spatial dimensions (3D) and for long computational times. We apply the methods developed to the particular problem of in…
