The flow of thin liquid films on inclined or vertical surfaces is one of immense importance, with applications spanning many types of process industries, due to the increased mass and heat transfer brought about by the presence of waves on film surfaces. While extensive research has been carried out in this area, many outstanding questions remain due to the complexity of the problem - a result of the extremely large aspect ratio and the three-dimensional nature. In this study, the evolution process of both naturally forming and forced waves on these thin liquid films is numerically studied using a hybrid front-tracking/level-set hybrid method which has the advantage of a distinct and accurate capture of the interface topology without being affected by the issues of mass conservation, numerical diffusion or spurious interface profiles. The simulation is conducted on an infinite domain specification through the imposition of periodic boundary conditions at the film outlet. The obtained results show the growth, step-wise progression, and eventual transition of natural waves from the two-dimensional state to three-dimensional disordered structures. Finally, three-dimensional simulations of artificially forced waves are carried out while different parameters/features of these waves are compared with the existing two-dimensional benchmark cases in the literature with excellent agreement found.
Keywords: falling films, thin films, solitary waves, three-dimension, forcing, interface tracking
The interaction that occurs between a light solid object and a horizontal soap film of a bamboo foam contained in a cylindrical tube is simulated in 3D. We vary the shape of the falling object from a sphere to a cube by changing a single shape parameter as well as varying the initial orientation and position of the object. We investigate in detail how the soap film deforms in all these cases, and determine the network and pressure forces that a foam exerts on a falling object, due to surface tension and bubble pressure respectively. We show that a cubic particle in a particular orientation exp…
We report that liquids perform self-propelled motion when they are placed in contact with hot surfaces with asymmetric (ratchet-like) topology. The pumping effect is observed when the liquid is in the film-boiling regime, for many liquids and over a wide temperature range. We propose that liquid motion is driven by a viscous force exerted by vapor flow between the solid and the liquid.
When a liquid drop falls on a solid substrate, the air layer in between them delays the occurrence of liquid--solid contact. For impacts on smooth substrates, the air film can even prevent wetting, allowing the drop to bounce off with dynamics identical to that observed for impacts on superamphiphobic materials. In this article, we investigate similar bouncing phenomena, occurring on viscous liquid films, that mimic atomically smooth substrates, with the goal to probe their effective repellency. We elucidate the mechanisms associated to the bouncing to non-bouncing (floating) transition using …
Flowing menisci: coupled dynamics and liquid exchange with soap films
Université Côte d’Azur（蔚蓝海岸大学）；CNRS（法国国家科学研究中心）；INPHYNI（物理化学与界面研究所）；Université de Rennes（雷恩大学）；IPR (Institut de Physique de Rennes)（雷恩物理研究所）；Institut Universitaire de France (IUF)（法兰西学院）
We study the time evolution of a thin liquid film coating the outer surface of a sphere in the presence of gravity, surface tension and thermal gradients. We derive the fourth-order nonlinear partial differential equation that models the thin film dynamics, including Marangoni terms arising from the dependence of surface tension on temperature. We consider two different imposed temperature distributions with axial or radial thermal gradients. We analyze the stability of a uniform coating under small perturbations and carry out numerical simulations in COMSOL for a range of parameter values. In…
We have observed that a rotating liquid soap film generates electricity when placed between two non-contact electrodes with a sufficiently large potential difference. In our experiments suspended liquid film (water + soap film) is formed on the surface of a circular frame, which is forced to rotate in the $x-y$ horizontal plane by a motor. This system is located at the center of two capacitor-like vertical plates to apply an external electric voltage difference in the $x-$direction. The produced electric current is collected from the liquid film using two conducting electrodes that are separat…
We study a horizontal streaming excited by means of a low frequency and intensity acoustic wave in 2D freely suspended film of thermotropic smectic liquid crystal. Acoustic pressure induces fast periodic transverse oscillations of the film, which produce in-plane stationary couples of vortices slowly rotating in opposite directions owing to hydrodynamic nonlinearity. The parameters of vortices are measured using a new method, based on tracking disk-shaped island defects. The horizontal motion occurs only when the amplitude of acoustic pressure exceeds threshold value, which can be explained by…
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 $h_{\text{min}} \propto τ^{2/5}$,…
We present experiments to study the relaxation of a nano-scale cylindrical perturbation at one of the two interfaces of a thin viscous free-standing polymeric film. Driven by capillarity, the film flows and evolves towards equilibrium by first symmetrizing the perturbation between the two interfaces, and eventually broadening the perturbation. A full-Stokes hydrodynamic model is presented which accounts for both the vertical and lateral flows, and which highlights the symmetry in the system. The symmetrization time is found to depend on the membrane thickness, surface tension, and viscosity.
We present a novel experimental setup to investigate two-dimensional thermal convection in a freestanding thin liquid film. We develop a setup for the reproducible generation of freestanding thin liquid films. Such films can be produced in a controlled way on the scale of 5 to 1000 nanometers. Our primary goal is to investigate the statistics of reversals in Rayleigh-Bénard convection with varying aspect ratio; here numerical works are quite expensive and 3D experiments prohibitively complicated and costly. However, as well questions regarding the physics of liquid films under controlled condi…
Soap bubbles are by essence fragile and ephemeral. Depending on their composition and environment, bubble bursting can be triggered by gravity-induced drainage and/or the evaporation of the liquid and/or the presence of nuclei. They can also shrink due to the diffusion of the inner gas in the outside atmosphere induced by Laplace overpressure. In this paper, we design bubbles made of a composite liquid film able to neutralize all these effects and keep their integrity for more than one year in a standard atmosphere. The unique properties of this composite film are rationalized with a nonlinear…
Numerical simulations of spontaneous dewetting of non-slipping, variable viscosity unstable thin liquid films on homogeneous substrates reveal the existence of sub-spinodal lengthscales through formation of satellite holes, a marker of nucleated dewetting and/or heterogeneous substrates, in the late stages of dewetting if the liquid viscosity decreases continually with decreasing film thickness. These films also show established signatures of slipping films such as faster rupture and flatter morphologies in the early stages even without invoking any slippage.
The effect of rigid surfaces on the dynamics of thin liquid films which are amenable to the lubrication approximation is considered. It is shown that the Helfrich energy of the layer gives rise to additional terms in the time-evolution equations of the liquid film. The dynamics is found to depend on the absolute value of the spontaneous curvature, irrespective of its sign. Due to the additional terms, a novel finite wavelength instability of flat rigid interfaces can be observed. Furthermore, the dependence of the shape of a droplet on the bending rigidity as well as on the spontaneous curvatu…
It is well known that electro-hydrodynamical effects in freely suspended liquid films can flow the liquid. Here we report a purely electrically driven rotation in water and some other liquid suspended films with full control on the velocity and the chirality of the rotating vortices. The device, which is called ``film motor'', consists of a quasi two-dimensional electrolysis cell in an external in-plane electric field, crossing the mean electrolysis current density. If either the external field or the electrolysis voltage exceeds some threshold (while the other one is not zero), the liquid fil…
It is demonstrated that the dynamic structure is very important for the rate of drainage of a thin liquid film and it can be effectively taken into account by a dynamic fractal dimension. It is shown that the latter is a powerful tool for description of the film drainage and classifies all the known results from the literature. The obtained general expression for the thinning rate is a heuristic one and predicts variety of drainage models, which are even difficult to simulate in practice. It is a typical example of a scaling law, which explains the origin of the complicate dependence of the th…
Our recent quasi-two-dimensional thermodynamic description of thin-liquid films stabilized by colloidal particles is generalized to describe nonuniform equilibrium states of films in external potentials and nonequilibrium transport processes produced in the film by gradients of thermodynamic forces. Using a Monte--Carlo simulation method, we have determined equilibrium equations of state for a film stabilized by a suspension of hard spheres. Employing a multipolar-expansion method combined with a flow-reflection technique, we have also evaluated the short-time film-viscosity coefficients and c…
We consider the feasibility of large-scale free-standing thin liquid film experiment in the space environment as a new realization to study two-dimensional hydrodynamics. We identify material and environmental criteria necessary to avoid freezing, evaporation, chemical degradation, and spontaneous collapse of the film. These criteria pose no obstacles to achieving films of kilometer scale and lifetime of many months, with attainable Reynolds number up to 10^7. However, impacts from meteoroids pose a serious threat to the film, and require substantial shielding or unproven self-healing properti…
We investigate the motion through a wet tube of transverse soap films, or lamellae, of high surface dilatationnal modulus. Combining local thickness and velocity measurements in the wetting film, we reveal a zone of several centimeters in length, the dynamic wetting film, which is significantly influenced by a moving lamella. The dependence of this influence length on lamella velocity and wetting film thickness provides a discrimination among several possible surfactant minimal models. A spectacular jumpy mode of unsteady motion of a lamella is also evidenced.
In this paper, we derive a lubrication model to describe the non-stationary free liquid film that is created when a vertical frame is pulled out of a liquid reservoir at a given velocity. We here focus on the case of a pure liquid, corresponding to a stress-free boundary condition at the liquid/air interfaces of the film, and thus employ an essentially extensional description of the flow. Taking into account van der Waals interactions between the interfaces, we observe that film rupture is well-defined in time as well as in space, which allows us to compute the critical thickness and the film …
The stability of thin liquid coatings is of fundamental interest in every- day life. Homogeneous and non-volatile liquid coatings may dewet either by heterogeneous nucleation, thermal nucleation, or spinodal dewetting. Wetting and dewetting is explained on a fundamental level, including a discussion of relevant interactions. The article will also address the various dewetting scenarios and explain how the effective interface potential governs the behavior obtained for various stratified substrates and film thicknesses.
We consider a carpet of self-propelled particles at the liquid-gas interface of a liquid film on a solid substrate. The particles excert an excess pressure on the interface and also move along the interface while the swimming direction performs rotational diffusion. We study the intricate influence of these self-propelled insoluble surfactants on the stability of the film surface and show that depending on the strength of in-surface rotational diffusion and the absolute value of the in-surface swimming velocity several characteristic instability modes can occur. In particular, rotational diffu…
Phase equilibria between regions of different thickness in thin liquid films stabilized by colloidal particles are investigated using a quasi-two-dimensional thermodynamic formalism. Appropriate equilibrium conditions for the film tension, normal pressure, and chemical potential of the particles in the film are formulated, and it is shown that the relaxation of these parameters occurs consecutively on three distinct time scales. Film stratification is described quantitatively for a hard-sphere suspension using a Monte-Carlo method to evaluate thermodynamic equations of state. Coexisting phases…
Coalescence of droplets is an ubiquitous phenomenon in chemical, physical and biolog-ical systems. The process of merging of liquid objects has been studied during the pastyears experimentally and theoretically in different geometries. We introduce a uniquesystem that allows a quasi two-dimensional description of the coalescence process,micrometer-sized flat droplets in freely suspended smectic liquid-crystal films. We findthat the bridge connecting the droplets grows linearly in time during the initial stage ofcoalescence, both with respect to its height and lateral width. We also verify self…
A surface instability is reported in thin nematic films of 5CB and 8CB, occurring near the nematic--isotropic phase transition. Although this instability leads to patterns reminiscent of spinodal dewetting, we show that it is actually based on a nucleation mechanism. Its characteristic wavelength does not depend markedly on film thickness, but strongly on the heating rate.
A scattering polarizer is created by subjecting a polymer dispersed liquid crystal (PDLC) film to tensile strain. The optomechanical properties of the film are investigated by simultaneously measuring the stress-strain and polarization dependent optical transmission characteristics. The correlation between transmittances of two orthogonal polarizations and the stress-strain curve reveals that the polymer orientation as well as the droplet shape anisotropy influences the liquid crystal alignment within the droplets. A Monte-Carlo simulation based on the Lebwohl-Lasher model is used to explain t…
Theoretical calculations, computer simulations and experiments indicate the possible existence of a ferromagnetic liquid state, although definitive experimental evidence is lacking. Should such a state exist, demagnetization effects would force a nontrivial magnetization texture. Since liquid droplets are deformable, the droplet shape is coupled with the magnetization texture. In a thin-film geometry in zero applied field, the droplet has a circular shape and a rotating magnetization texture with a point vortex at the center. We calculate the elongation and magnetization texture of such ferrom…
A transient surface instability is reported in thin nematic films of 5CB and 8CB, occurring near the nematic-isotropic phase transition. Although this instability leads to patterns reminiscent of spinodal dewetting, we show that it is actually based on a nucleation mechanism. Its characteristic wavelength does not depend markedly on film thickness, but strongly on the heating rate.
When a macroscopic droplet spreads, a thin precursor film of liquid moves ahead of the advancing liquid-solid-vapor contact line. Whereas this phenomenon has been explored extensively for planar solid substrates, its presence in nanostructured geometries has barely been studied so far, despite its importance for many natural and technological fluid transport processes. Here we use porous photonic crystals in silicon to resolve by light interferometry capillarity-driven spreading of liquid fronts in pores of few nanometers in radius. Upon spatiotemporal rescaling the fluid profiles collapse on …
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.
We report on a new experimental procedure for forming and studying polar smectic liquid crystal films. A free standing smectic film is put in contact with a liquid drop, so that the film has one liquid crystal/liquid interface and one liquid crystal/air interface. This polar environment results in changes in the textures observed in the film, including a boojum texture and a previously unobserved spiral texture in which the winding direction of the spiral reverses at a finite radius from its center. Some aspects of these textures are explained by the presence of a Ksb term in the bulk elastic …
This study reveals the influence of the surface energy and solid/liquid boundary condition on the breakup mechanism of dewetting ultra-thin polymer films. Using silane self-assembled monolayers, SiO$_2$ substrates are rendered hydrophobic and provide a strong slip rather than a no-slip solid/liquid boundary condition. On undergoing these changes, the thin-film breakup morphology changes dramatically -- from a spinodal mechanism to a breakup which is governed by nucleation and growth. The experiments reveal a dependence of the hole density on film thickness and temperature. The combination of l…
We show that the electric field driven surface instability of visco-elastic films has two distinct regimes: (1) The visco-elastic films behaving like a liquid display long wavelengths governed by applied voltage and surface tension, independent of its elastic storage and viscous loss moduli, and (2) the films behaving like a solid require a threshold voltage for the instability whose wavelength always scales as ~ 4 x film thickness, independent of its surface tension, applied voltage, loss and storage moduli. Wavelength in a narrow transition zone between these regimes depends on the storage m…
The stability of nonvolatile thin liquid films and of sessile droplets is strongly affected by finite size effects. We analyze their stability within the framework of density functional theory using the sharp kink approximation, i.e., on the basis of an effective interface Hamiltonian. We show that finite size effects suppress spinodal dewetting of films because it is driven by a long-wavelength instability. Therefore nonvolatile films are stable if the substrate area is too small. Similarly, nonvolatile droplets connected to a wetting film become unstable if the substrate area is too large. T…
We investigate energetically favorable configurations of point disclinations in nematic films having a bump geometry. Gradual expansion in the bump width Δ gives rise to a sudden shift in the stable position of the disclinations from the top to the skirt of the bump. The positional shift observed across a threshold Δth obeys a power law function of |Δ-Δth|, indicating a new class of continuous phase transition that governs the defect configuration in curved nematic films.
We analyze theoretically the influence of backward propagating waves on the primary threshold when a linearly polarized light impinges at normal incidence on a planarly aligned nematic liquid crystal films. We show, that the primary threshold, as a function of the phase delay induced by the nematic layer, exhibits oscillations. The amplitude of oscillations depends strongly on the drop of the refractivity indices of the nematic and outer media at the boundaries.
The room temperature liquid metal related electronics has been found important in a wide variety of emerging areas over the past few years. However, its failure features under high electrical current densities are not clear until now. Here we show that a liquid metal thin film would break-up as the applied current increases to a critical magnitude. The break-up phenomenon is attributed to be caused by the so-called electromigration effect. This problem could be one of the major hurdles that must be tackled with caution in the research and application of future liquid metal film electronics.
In this paper we try to work out in detail the implications of a microscopic theory for capillary waves under the assumption that the density is given along lines normal to the interface. Our study provides interface Hamiltonians for adsorbed films in a variety of systems, and shows that the corrections to the classical capillary wave spectrum are of the same order as the surface tension. This implies that it is possible, at least in principle, to measure them in x-ray surface scattering experiments. Interestingly, our study also sheds some light on the nature of the liquid-vapor interface in …
We study the structure of very thin liquid crystal films frustrated by antagonistic anchorings in the smectic phase. In a cylindrical geometry, the structure is dominated by the defects for film thicknesses smaller than 150 nm and the detailed topology of the defects cores can be revealed by x-ray diffraction. They appear to be split in half tube-shaped Rotating Grain Boundaries (RGB). We determine the RGB spatial extension and evaluate its energy per unit line. Both are significantly larger than the ones usually proposed in the literature
We study spinodal phase separation in unstable thin liquid films on chemically disordered substrates via simulations of the thin-film equation. The disorder is characterized by immobile patches of varying size and Hamaker constant. The effect of disorder is pronounced in the early stages (amplification of fluctuations), remains during the intermediate stages and vanishes in the late stages (domain growth). These findings are in contrast to the well-known effects of quenched disorder in usual phase-separation processes, viz., the early stages remain undisturbed and domain growth is slowed down …
We study universality in the kinetics of spinodal phase separation in unstable thin liquid films, via simulations of the thin film equation. It is shown that in addition to morphology and free energy,the number density of local maxima in the film profile can also be used to identify the early, intermediate and late stages of spinodal phase separation. A universal curve between the number density of local maxima and rescaled time describes the kinetics of early stage in d = 2, 3. The Lifshitz-Slyozov exponent of -1/3 describes the kinetics of the late stage in d = 2 even in the absence of coexi…
We study the static and dynamic interaction between a horizontal cylindrical nano-probe and a thin liquid film. The effects of the physical and geometrical parameters, with a special focus on the film thickness, the probe speed, and the distance between the probe and the free surface are analyzed. Deformation profiles have been computed numerically from a Reynolds lubrication equation, coupled to a modified Young-Laplace equation, which takes into account the probe/liquid and the liquid/substrate non-retarded van der Waals interactions. We have found that the film thickness and the probe speed…
Small-amplitude dynamic atomic force microscopy (dynamic-AFM) in a simple nonpolar liquid was studied through molecular dynamics simulations. We find that within linear dynamics regime, the contact stiffness and damping of the confined film exhibit the similar solvation force oscillations, and they are generally out-of-phase. For the solidified film with integer monolayer thickness, further compression of the film before layering transition leads to higher stiffness and lower damping. We find that molecular diffusion in the solidified film was nevertheless enhanced due to the mechanical excita…
Slip-boundary effects on the polar liquid film motor (PLFM) -- a novel micro-fluidic device with important implications for advancing knowledge on liquid micro-film's structure, dynamics, modeling and technology -- are studied. We develop a mathematical model, under slip boundary conditions, describing electro-hydro-dynamical rotations in the PLFMs induced either by direct current (DC) or alternating current (AC) fields. Our main results are: (i) rotation characteristics depend on the ratio $k=l_{s}/D$ ($l_{s}$ denotes the slip length, resulting from the interface's impact on the structure of …
Slippage of Newtonian liquids in the presence of a solid substrate is a newly found phenomenon the origin of which is still under debate. In this paper, we present a new analysis method to extract the slip length. Enhancing the slip of liquids is an important issue for microfluidic devices that demand for high throughput at low pumping power. We study the velocity of short-chained liquid polystyrene (PS) films dewetting from non-wettable solid substrates. We show how the dynamics of dewetting is influenced by slippage and we compare the results of two types of substrates that give rise to diff…
Curved textures of ferroelectric smectic C* liquid crystals produce space charge when they involve divergence of the spontaneous polarization field. Impurity ions can partially screen this space charge, reducing long range interactions to local ones. Through studies of the textures of islands on very thin free-standing smectic films, we see evidence of this effect, in which materials with a large spontaneous polarization have static structures described by a large effective bend elastic constant. To address this issue, we calculated the electrostatic free energy of a free standing film of ferr…
Micron-sized objects confined in thin liquid films interact through forces mediated by the deformed liquid-air interface. This capillary interactions provide a powerful driving mechanism for the self-assembly of ordered structures such as photonic materials or protein crystals. Direct probing of capillary interactions requires a controlled force field to independently manipulate small objects while avoiding any physical contact with the interface. We demonstrate how optical micro-manipulation allows the direct measurement of capillary interactions between two micron sized spheres in a free sta…
Probing the fluid dynamics of thin films is an excellent tool to study the solid/liquid boundary condition. There is no need for external stimulation or pumping of the liquid due to the fact that the dewetting process, an internal mechanism, acts as a driving force for liquid flow. Viscous dissipation within the liquid and slippage balance interfacial forces. Thereby, friction at the solid/liquid interface plays a key role towards the flow dynamics of the liquid. Probing the temporal and spatial evolution of growing holes or retracting straight fronts gives, in combination with theoretical mod…
Using dissipative particle dynamics simulations, we study the effects of an embedding bulk fluid on the phase separation dynamics in a thin planar liquid film. The domain growth exponent is altered from 2D to 3D behavior upon the addition of a bulk fluid, even though the phase separation occurs in 2D geometry. Correlated diffusion measurements in the film show that the presence of bulk fluid changes the nature of the longitudinal coupling diffusion coefficient from logarithmic to algebraic dependence of 1/s, where s is the distance between the two particles. This result, along with the scaling…
The structure of the soluble protonated (pH=2) octadecanoic acid film adsorbed on the saturated hydrocarbon (n-hexane) - water and aromatic hydrocarbon (toluene)-water interfaces is studied by X-ray reflectometry using synchrotron radiation. The experimental data demonstrate that a solid phase of a Gibbs monolayer (26 +/- 1) Angstrom thick, in which aliphatic tails are perpendicular to the surface and the area per molecule is A=(18 +/- 2) Angstrom^2, forms in the film at the n-hexane - water interface. The solid monolayer on the toluene - water interface in the adsorbed film melts when tempera…
Thin liquid films on surfaces are part of our everyday life, they serve e.g. as coatings or lubricants. The stability of a thin layer is governed by interfacial forces, described by the effective interface potential, and has been subject of many studies in the last decades. In recent years, the dynamics of thin liquid films came into focus since results on the reduction of the glass transition temperature raised new questions on the behavior of especially polymeric liquids in confined geometries. The new focus was fired by theoretical models that proposed significant implication of the boundar…
DNA molecules spin-coated on amorphous quartz substrates are shown to form stable films. Electron density profiles (EDPs) along the film depth show that film prepared from aqueous solution of DNA exhibits layering of the molecules in three stacks parallel to the substrate whereas film prepared from counterion added solution does not have layering but have smaller thickness and enhanced surface roughness, although both films have 'liquid-like' height-height correlations. We explain these results by a model of film of a 'liquid' comprising of rod-like molecules where the counterion concentration…
Our understanding of both structure and dynamics of adsorbed liquids heavily relies on the capillary wave Hamiltonian, but a thorough test of this model is still lacking. Here we study the capillary wave fluctuations of a liquid film with short range forces adsorbed on a solid exhibiting van der Waals interactions. We show for the first time that the measured capillary wave spectrum right above the first order wetting transition provides an interface potential consistent with independent calculations from thermodynamic integration. However, the surface tension exhibits an oscillatory film thic…
We develop the theory for stick-slip motion in ultra-thin liquid films confined between two moving atomically-flat surfaces. Our model is based on hydrodynamic equation for the flow coupled to the dynamic order parameter field describing the ``shear melting and freezing'' of the confined fluid. This model successfully accounts for observed phenomenology of friction in ultra-thin films, including periodic and chaotic sequences of slips, transitions from stick-slip motion to steady sliding.
