Instability Of Thin Liquid Film Research Articles

Effect of the odd viscosity on Faraday wave instability

Faraday waves arise in fluid systems with free surfaces subject to vertical oscillations of sufficient strength due to parametric resonance. The odd viscosity is a peculiar part of the viscosity stress tensor that does not result in dissipation and is allowed when parity symmetry is broken spontaneously or due to external magnetic fields or rotations. The effect of the odd viscosity on the classic Faraday instability of thin liquid films in infinite horizontal plates is investigated by utilizing both linear Floquet theory and nonlinear lubrication theory based on the weighted residual model. This work derives the nonlinear evolution equations about the flow rate and free surface height, and linear stability analysis is performed to achieve the damped Mathieu equation. The results show that the neutral stability curves derived from the Mathieu equation agree well with those obtained from the linear Floquet analysis, especially for lower viscosity ratios μ. The nonlinear numerical results simulated by the method of lines indicate interesting results where the odd viscosity gives rise to a “sliding” of the wave configuration parallel to the wall, and the interface wave then translates into a traveling wave.

Self-organization of anodic aluminum oxide layers by a flow mechanism

Anodic oxidation of aluminum in solutions that dissolve the amorphous oxide produces films with hexagonally-ordered patterns of pores. We show using linear stability analysis that an anodization model including viscous oxide flow accurately predicts the scaling relation governing pore spacing. Flow is driven by nonuniform compressive stress near the oxide-solution interface, resulting from anion adsorption on surface growth sites. The interfacial stress layer is approximated as surface stress, leading to analogous instability mechanisms as in the surface-tension driven Marangoni instability of thin liquid films.

Model for Formation of Self-Ordered Anodic Oxide Nanomaterials

Porous anodic films are self-organized porous oxides nanomaterials formed by electrochemical oxidation. Pores in porous alumina and nanotubes in TiO2nanotube layers initiate after an initial stage of barrier oxide growth. The porous film eventually evolves into a hexagonally-ordered array of parallel cylindrical pores or nanotubes of order 10-100 nm diameter with a characteristic spacing that scales directly with the cell voltage. We explore the roles of mechanical stress and oxide flow in self-ordering, through a modeling analysis of stress-driven viscous flow of oxide (1-3). The model is based on coupled viscous flow of oxide and stress- and electric field-driven migration of metal and oxygen ions (1). Stress at the film interfaces is generated by ion-transfer processes and relaxed by viscous flow, resulting in layers with elevated compressive or tensile stress within a few nm of the interfaces (2,3). Experimental evidence for these layers has been found from in situ stress measurements (2-4). We present linear stability analysis incorporating the surface stress boundary conditions in the coupled oxide flow-electrical migration model of Houser and Hebert (1). The calculations reveal self-organized pattern formation with steady-state pore spacing-voltage scaling ratios that compare favorably to those found experimentally, for both porous alumina and TiO2nanotube layers. The scaling ratios are independent of oxide viscosity or uncertainties in the values of any other model parameters. In the case of Al anodization, oxide flow resulting in pore patterns is driven by elevated stress near the oxide-solution interface, through a mechanism that has common features with the Marangoni instability in thin liquid films. Stress near the oxide surface is produced because strong electrolyte anion adsorption suppresses oxide growth on the surface. Such near-surface stress is not present in TiO2nanotube layers (5). Instead, compressive stress driving flow arises at the metal-oxide interface from the volume change upon conversion of metal to oxide. REFERENCES J. E. Houser and K. R. Hebert, Nature Mater., 8, 415 (2009).K. R. Hebert, P. Mishra, J. Electrochem. Soc., 165, E737 (2018).K. R. Hebert, P. Mishra, J. Electrochem. Soc., 165, E744 (2018).Ö. Ö. Çapraz, P. Shrotriya, P. Skeldon, G. E. Thompson, K. R. Hebert, Electrochim. Acta, 167, 404 (2015). Q. Dou, P. Shrotriya, W. F. Li, K. R. Hebert, Electrochim. Acta, 295, 418 (2019).

Measurement of Instability of Thin Liquid Films by Synchronized Tri-wavelength Reflection Interferometry Microscope.

Film thickness measurement of unstable thin liquid films (TLFs) remains a challenge due to the difficulty in determining the order of fringes prior to the film rupture. In the present work, a synchronized tri-wavelength reflection interferometry microscope (STRIM) was developed and employed to determine the spatiotemporal thickness profiles of the TLFs between air bubbles and various hydrophobic surfaces in 10-2 M NaCl solutions. Both accuracy and precision of film thickness measurements were found to be better than 3 nm over the range of 0-1 μm. It was found that when the radii of air bubbles were in the range 0.71-0.88 mm, the critical rupture thicknesses of the wetting films formed on hydrophobic quartz surfaces having water contact angles of 95° scattered over a range of 57-335 nm with a medium rupture thickness of 122 nm. For smaller air bubbles with radii of 0.13-0.26 mm, the critical rupture thicknesses were much more narrowly distributed with a medium rupture thickness of 27 nm. The result obtained with the TLFs between two air bubbles, i.e., foam film, showed that the critical rupture thickness was increased from 25 to 40 nm, when the sizes of air bubbles were increased from 220 to 960 μm. Compared to rupture thickness of the foam film, the critical rupture thickness of the TLF between an air bubble and a dodecane droplet was smaller, indicating that the film rupture might be related to the hydrophobicity of interacting surfaces. In addition to attractive surface forces, both wave motions and gas molecules in TLF might be associated with the film rupture.

Solid structures generated by capillary instability in thin liquid films

This paper is associated with a poster winner of a 2017 APS/DFD Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available from the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2017.GFM.P0018

Erratum: “Rayleigh-Taylor instability in thin liquid films subjected to harmonic vibration” [Phys. Fluids 29, 052105 (2017)

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Rayleigh-Taylor instability in thin liquid films subjected to harmonic vibration

The dynamics of the Rayleigh-Taylor instability of a two-dimensional thin liquid film placed on the underside of a planar substrate subjected to either normal or tangential harmonic forcing is investigated here in the framework of a set of long-wave evolution equations accounting for inertial effects derived earlier by Bestehorn, Han, and Oron [“Nonlinear pattern formation in thin liquid films under external vibrations,” Phys. Rev. E 88, 023025 (2013)]. In the case of tangential vibration, the linear stability analysis of the time-periodic base state with a flat interface shows the existence of the domain of wavenumbers where the film is unstable. In the case of normal vibration, the linear stability analysis of the quiescent base state reveals that the instability threshold of the system is depicted by a combination of distinct thresholds separate for the Rayleigh-Taylor and Faraday instabilities. The nonlinear dynamics of the film interface in the case of the static substrate results in film rupture. However, in the presence of the substrate vibration in the lateral direction, the film interface saturates in certain domains in the parameter space via the mechanism of advection induced by forcing, so that the continuity of the film interface is preserved even in the domains of linear instability while undergoing the time-periodic harmonic evolution. On the other hand, sufficiently strong forcing introduces a new inertial mode of rupture. In the case of the normal vibration, the film evolution may exhibit time-periodic, harmonic or subharmonic saturated waves apart of rupture. The enhancement of the frequency or amplitude of the substrate forcing promotes the destabilization of the system and a tendency to film rupture at the nonlinear stage of its evolution. A possibility of saturation of the Rayleigh-Taylor instability by either normal or unidirectional tangential forcing in three dimensions is also demonstrated.

Intrinsic instability of thin liquid films on nanostructured surfaces

The instability of a thin liquid film on nanostructures is not well understood but is important in liquid-vapor two-phase heat transfer (e.g., thin film evaporation and boiling), lubrication, and nanomanufacturing. In thin film evaporation, the comparison between the non-evaporating film thickness and the critical film breakup thickness determines the stability of the film: the film becomes unstable when the critical film breakup thickness is larger than the non-evaporating film thickness. In this study, a closed-form model is developed to predict the critical breakup thickness of a thin liquid film on 2D periodic nanostructures based on the minimization of system free energy in the limit of a liquid monolayer. Molecular dynamics simulations are performed for water thin films on square nanostructures of varying depth and wettability, and the simulations agree with the model predictions. The results show that the critical film breakup thickness increases with the nanostructure depth and the surface wettability. The model developed here enables the prediction of the minimum film thickness for a stable thin film evaporation on a given nanostructure.

Dry-spot nucleation in thin liquid films on chemically patterned surfaces

We systematically study the influence of chemical patterning on the instability of thin liquid films induced by chemical heterogeneities on a flat, horizontal, and partially wetting substrate. We consider common geometric shapes like wedges, circles, and stripes and determine the time required for nucleation of a dry-spot as a function of film thickness, contact angle, pattern dimensions, and geometry. Moreover, we characterized the resulting liquid distribution and identified conditions that avoid the formation of residual droplets on the less wettable regions, which is usually undesirable in technological applications.

Labyrinthine instability in thin liquid films

When a thin liquid film on a solid surface has a thickness corresponding to a particularpart the spinodal region of the disjoining pressure versus thickness isotherm, the filmbreaks down. One of the patterns that emerges on the breakdown has been referred to aswavy instability. It is compared here to the labyrinthine instability seen in magnetic films.The system is modeled following the procedure used in magnetic systems, and the patternof wavy instability is broken down into a curved thick–thin film in equilibrium with a flatthin–thin film of constant thickness. Minimization of free energy leads to expressions forvarious length scales that characterize the system. Comparisons with publishedexperimental results on nematic liquid crystals for a number of very different features aresatisfactory. They include film thicknesses in the bulk at equilibrium where thecapillary pressure is not zero, and is determined as a part of the solution, as wellas film thicknesses in the ledge where the capillary pressure is zero. Stabilityanalysis shows that the system is unstable in both directions with some qualifiers. Amodel is proposed in the form of a tiled structure to explain the labyrinthineform.

Suppression of the Rayleigh-Taylor instability of thin liquid films by the Marangoni effect

Stabilization of the Rayleigh-Taylor instability of a thin liquid film by the Marangoni effect arising from heating of the liquid at the gas-liquid interface in a bilayer setting is investigated. Solution of time-dependent Navier-Stokes and long-wave evolution equations in both two and three dimensions shows the emergence of nontrivial nonruptured steady states in the system when the applied temperature gradient exceeds a certain critical value.

Acoustical observation of bubble oscillations induced by bubble popping

Acoustic measurements of aqueous foams show three distinct radiation mechanisms that contribute to the sound pressure field: oscillations of a bubble surface that precede popping due to the instability of thin liquid film, impulsive radiation due to bursts of bubbles, and oscillations from neighboring bubbles excited by a burst bubble. The movies captured by a fast camera confirm that the bubbles adjacent to a breaking bubble oscillate under the influence of the pressure generated by the burst bubble. The spectra of resulting transient sounds fall in the range of 2-8 kHz and those from bubble oscillations correlate well with the bubble size.

Nonlinear rupture of thin liquid films on solid surfaces

In this letter we investigate the rupture instability of thin liquid films by means of a bifurcation analysis in the vicinity of the short-scale instability threshold. The rupture time estimate obtained in closed form as a function of the relevant dimensionless groups is in striking agreement with the results of the numerical simulations of the original nonlinear evolution equations. This suggests that the weakly nonlinear theory adequately captures the underlying physics of the instability. When antagonistic (attractive/repulsive) molecular forces are considered, nonlinear saturation of the instability becomes possible. We show that the stability boundaries are determined by the van der Waals potential alone.

Erratum: Instability of Thin Liquid Films by Density Variations: A New Mechanism that Mimics Spinodal Dewetting [Phys. Rev. Lett.PRLTAO0031-900789, 186101 (2002)

Erratum: Instability of Thin Liquid Films by Density Variations: A New Mechanism that Mimics Spinodal Dewetting [Phys. Rev. Lett.PRLTAO0031-9007<b>89</b>, 186101 (2002)

Instability of thin liquid films by density variations: a new mechanism that mimics spinodal dewetting.

Based on the linear stability analysis and nonlinear simulations, conditions are established under which instability and dewetting of a thin liquid film can be engendered solely by the density variations (for example, due to confinement, layering, defects, and restructuring) related to changes in the local film thickness. An increase in the density with the increasing film thickness can stabilize a thermodynamically unstable film, and, equally interesting, a decrease in the density with increasing film thickness can render a thermodynamically stable film unstable. Morphological characteristics of this novel density variation induced instability closely resemble the well-known spinodal dewetting.

Enhanced instability in thin liquid films by improved compatibility

We investigated experimentally the morphological evolution of thin polydimethylsiloxane films sandwiched between a silicon wafer and different bounding liquids with interfacial tensions varying by 2 orders of magnitude. It is shown that increasing the compatibility between film and bounding liquid by adding a few surfactant molecules results in a faster instability of shorter characteristic wavelength. Inversely, based on the characteristic parameters describing the instability we determined extremely small interfacial tensions with a remarkable accuracy.

Nonlinear dynamics of three-dimensional long-wave Marangoni instability in thin liquid films

The three-dimensional evolution of the long-wave Marangoni instability of thin liquid films is studied. According to earlier theoretical predictions no continuous steady states exist and the film ruptures. As in two dimensions, the mechanism of fingering is found to be a main route to rupture. A four-fold rotational symmetry of the film interface is retained, when a square periodic domain and the harmonic initial disturbance are used. A use of initial random disturbances in general eliminates the square symmetry of the solution. An increase of the domain size results in a growing complexity of the emerging patterns. In contrast with the dynamics in two dimensions the evolution of the interface in three dimensions and in particular the pattern emerging at rupture may strongly depend on the choice of the initial condition. The two-dimensional evolution of the film is found to be unstable to small three-dimensional random disturbances.

Dynamical Instability of Thin Liquid Films Between Conducting Media

It is shown that thin dielectric liquid films between electrically conducting media are dynamically unstable if the electronic work functions of the conductors are different. As a consequence, they are expected to dewet by a spinodal dewetting scenario, i.e., via amplification of surface waves with mode selection. The wave number of the fastest growing mode is discussed as a function of the strength of the electric and dispersive forces. In contrast to what seems to be widely believed, it turns out that electric forces dominate over dispersive forces in most experimental situations of the rather general type studied here.

Capillary instability of thin liquid film on a cylinder

The capillary instability of a thin liquid layer on a cylinder is studied. Using an integral approach and lubrication approximation, transport equations governing the spatiotemporal evolution of a film thickness and the temperature along the film are obtained. Evolution of the system under both isothermal and nonisothermal conditions is studied numerically. It is shown that nonlinear interaction of the linearly unstable modes begets an additional mode with a wavelength equal to that of the fastest growing wave. This, in turn, causes the formation of satellite drops along with the main ones. Application of these results in a possible continuous technology of high-temperature superconductor wire fabrication is discussed.

The mechanism for the long-wave instability in thin liquid films

A physical mechanism for the long-wave instability of thin liquid films is presented. We show that the many diverse systems that exhibit this instability can be classified into two large groups. Each group is studied using the model of a thin liquid film with a deformable top surface flowing down a rigid inclined plane. In the first group, the top surface has an imposed stress, while in the other, an imposed velocity. The proposed mechanism shows how the details of the energy transfer from the basic state to the disturbance are handled differently in each of these cases, and how a common growth mechanism produces the unstable motion of the disturbance.