Effect of interfacial mobility on rupture of thin stagnant films on a solid surface due to random mechanical perturbations

Previous analysis of Narsimhan [G. Narsimhan, J. Colloid Interface Sci. 287 (2005) 624-633] for the evaluation of rupture of a nondraining thin film on a solid support due to imposed random mechanical perturbations modeled as a Gaussian white noise has been extended for partially mobile gas-liquid interfaces. The average rupture time of film is evaluated by first passage time analysis (as the mean time for the amplitude of perturbation to become equal to film thickness). The interfacial mobility is accounted for through surface viscosity as well as Marangoni effect. The mean rupture time for partially mobile gas-liquid interface, as characterized by two dimensionless groups, dimensionless surface viscosity and Marangoni number, lies between the two extreme limits for fully mobile and immobile films. The critical wavenumber for minimum rupture time is shown to be insensitive to interfacial mobility. However, the critical dimensionless surface viscosity and critical Marangoni number at which the behavior of thin film deviates from that of fully mobile film and the behavior approaches that of fully immobile film are smaller for higher Hamaker constants, smaller film thickness and smaller surface potentials.     

Effect of Surfactants on the Film Drainage

Drainage of a partially mobile thin liquid film between two deformed and nondeformed gas bubbles with different radii is studied. The lubrication approximation is used to obtain the influence of soluble and insoluble surfactants on the velocity of film thinning in the case of quasi-steady state approach. The material properties of the interfaces (surface viscosity, Gibbs elasticity, surface diffusivity, and/or bulk diffusivity) are taken into account. In the case of deformed bubbles the influence of the meniscus is illustrated assuming simple approximated shape for the local film thickness. Simple analytical solutions for large and small values of the interfacial viscosity, and for deformed and nondeformed bubbles, are derived. The correctness of the boundary conditions used in the literature is discussed. The numerical analysis of the governing equation shows the region of transition from partially mobile to immobile interfaces. Quantitative explanation of the following effects is proposed: (i) increase of the mobility due to increasing bulk and surface diffusivities; (ii) role of the surface viscosity, comparable to that of the Gibbs elasticity; and (iii) significant influence of the meniscus on the film drainage due to the increased hydrodynamic resistance. Copyright 1999 Academic Press.     

What is the mechanism of soap film entrainment?

Classical Frankel's law describes the formation of soap films and their evolution upon pulling, a model situation of film dynamics in foams (formation, rheology, and destabilization). With the purpose of relating film pulling to foam dynamics, we have built a new setup able to give an instantaneous measurement of film thickness, thus allowing us to determine film thickness profile during pulling. We found that only the lower part of the film is of uniform thickness and follows Frankel's law, provided the entrainment velocity is small. We show that this is due to confinement effects: there is not enough surfactant in the bulk to fully cover the newly created surfaces which results in immobile film surfaces. At large velocities, surfaces become mobile and then Frankel's law breaks down, leading to a faster drainage and thus to a nonstationary thickness at the bottom of the film. These findings should help in understanding the large dispersion of previous experimental data reported during the last 40 years and clarifying the pulling phenomenon of thin liquid films.     

Effects of interface mobility on the dynamics of colliding bubbles

At its core, the outcome of the collision between air bubbles is determined by the hydrodynamic interaction forces, which in turn are strongly dependent on the tangential mobility of the gas–liquid interfaces. A clean gas–liquid interface is tangentially mobile, whereas the presence of surfactant contaminants can immobilise the interface. Bubbles with mobile surfaces coalescence much easier because of the low hydrodynamic resistance to drainage of the thin liquid film separating the colliding bubbles. In this opinion, we highlight recent experimental and numerical simulations demonstrating that in addition to the expected faster coalescence, mobile-surface bubbles can produce a much stronger rebound from a mobile liquid interface compared to an immobile one. The stronger rebound is explained by the lower viscous dissipation during collisions involving mobile surfaces. The role of the surface mobility in controlling the stability of gas or liquid emulsion should be reassessed in the light of these new findings.     

Rupture of thin stagnant films on a solid surface due to random thermal and mechanical perturbations

A generalized formalism for the rupture of a nondraining thin film on a solid support due to imposed random thermal and mechanical perturbations, modeled as a Gaussian white noise, is presented. The evolution of amplitude of perturbation is described by a stochastic differential equation. The average film rupture time is the average time for the amplitude of perturbation to equal to the film thickness and is calculated by employing a first passage time analysis for different amplitudes of imposed perturbations, wavenumbers, film thickness, van der Waals and electrostatic interactions and surface tensions. The results indicate the existence of an optimum wavenumber at which the rupture time is minimum. A critical film thickness is identified based on the sign of the disjoining pressure gradient, below which the film is unstable in that the rupture time is very small. The calculated values of rupture time as well as the optimum wavenumber in the present analysis agree well with the results of linear stability analysis for immobile as well as completely mobile gas-liquid film interfaces. For stable films, the rupture time is found to increase dramatically with film thickness near the critical film thickness. As expected, the average rupture time was found to be higher for smaller amplitudes of imposed perturbations, larger surface potentials, larger surface tensions and smaller Hamaker constants.     

Film drainage and interfacial instabilities in polymeric systems with diffuse interfaces

We report an experimental investigation on the effect of mutual diffusion in polymeric systems on film drainage between two captive drops. The main objective is to study the influence of diffuse interfaces on film drainage. This is done by using material combinations with different interfacial properties and interferometric visualization of the film between two interacting drops. For highly diffusive systems film drainage is observed to be, in contrast to immiscible systems, non-axisymmetric and unstable immediately after the film formation (at a few micrometers film thickness). Depending on whether the total thickness of the diffusion layers in the film is smaller or larger than the thickness of the film, Marangoni convection is found to enhance or delay film drainage. Enhanced film drainage is determined to be in order of 100 times faster than predicted by the current models, while delayed film drainage is observed after a drainage period where experimental and predicted results (assuming, a partially mobile interface) are in close agreement.     

Drainage of the air-water-quartz film: experiments and theory

Experimental results of the kinetics of drainage of the trapped water film between an approaching air bubble and a quartz plate have been analysed using recent theoretical advances in formulating and solving the flow problem in deformable films. Excellent agreement is obtained between experimental data and a model that assumes the bubble-water interface is tangentially immobile in its hydrodynamic response. The coupling between hydrodynamic pressure, disjoining pressure and film deformation is critical in determining the dynamic behaviour of the drainage process. The Reynolds parallel film model that omits the effects of film deformation predicts results that are qualitatively incorrect.     

Dewetting at soft viscoelastic interfaces

The dewetting transition of thin liquid films (approximately 100 nm) at soft viscoelastic interfaces is analyzed theoretically. It is shown that viscoelastic losses in the soft material can drastically increase the time to complete the dewetting. Thus, the influence of the thinning of the liquid film, due to the hydrodynamic drainage caused by the external applied pressure, has to be considered too. The squeezing pressure coupled with the hydrodynamic drainage may slow down the dewetting to almost zero growth rate of the dry zone; in this case a trapped rim of fluid should be observed.     

Structural analysis of organic interfacial layers by ellipsometry

Ellipsometry has ‘come of age’ as a technique for the analysis of problems related to colloid and interface science. It has advanced far beyond applications of measuring film thickness or optical constants — although these remain important uses. Studies of the structure of polymers at the solid/liquid interface have been advanced significantly by the realisation of Fourier transform ellipsometry. Another important achievement has been the calibrated measurement of the dynamic surface excess at the flowing surface of a liquid jet. The uses of ellipsometry to study critical adsorption in binary liquids and to measure the width of liquid/liquid interfaces are also noteworthy. An important development is the use of infrared — rather than visible — light, which opens up numerous possibilities for the simultaneous structural and chemical interrogation of interfaces non-invasively.     

Instabilities and pattern miniaturization in confined and free elastic-viscous bilayers

We present an analysis of the instabilities engendered by van der Waals forces in bilayer systems composed of a soft elastic film (<10 microm) and a thin (<100 nm) viscous liquid film. We consider two configurations of such systems: (a) Confined bilayers, where the bilayer is sandwiched between two rigid substrates, and (b) free bilayers, where the viscous film is sandwiched between a rigid substrate and the elastic film. Linear stability analysis shows that the time and length scales of the instabilities can be tuned over a very wide range by changing the film thickness and the material properties such as shear modulus, surface tension, and viscosity. In particular, very short wavelengths comparable to the film thickness can be obtained in bilayers, which is in contrast to the instability wavelengths in single viscous and elastic films. It is also shown that the instabilities at the interfaces of the free bilayers are initiated via an in-phase "bending" mode rather than out-of-phase "squeezing" mode. The amplitudes of deformations at both the elastic-air and elastic-viscous interfaces become more similar as the elastic film thickness decreases and its modulus increases. These findings may have potential applications in the self-organized patterning of soft materials.     

An Insoluble Surfactant Model for a Vertical Draining Free Film

A mathematical model is constructed to study the evolution of a vertically oriented thin liquid film draining under gravity when there is an insoluble surfactant with finite surface viscosity on its free surface. Lubrication theory for this free film results in three coupled nonlinear partial differential equations describing the free surface shape, the surface velocity, and the surfactant transport at leading order. We will show that in the limit of large surface viscosity, the evolution of the free surface is that obtained for the tangentially immobile case. For mobile films with small surface viscosity, transition from a mobile to an essentially immobile film is observed for large Marangoni effects. It is verified that increasing surface viscosity and the Marangoni effect retard drainage, thereby enhancing film stability. The theoretical results are compared with experiment; the purpose of both is to act as a model problem to evaluate the effectiveness of surfactants for potential use in foam-fabrication processes. Copyright 2000 Academic Press.     

Effect of mass transfer on the film drainage between colliding drops

The influence of mass transfer on the drainage behaviour of the thin liquid film between two drops immersed in another liquid colliding at constant approach velocity has been studied experimentally. The liquid-liquid system used is glycerol in silicone oil. The transferred solute is acetone and the volume concentration difference across the interface ranges from 1 to 5%. The film thickness evolution has been measured using a laser interferometry technique. The direction of mass transfer (from the drops towards the film phase and inversely) has been investigated and the results compared to the case with no mass transfer. When the solute transfers from the drops towards the continuous phase, the drainage rate is significantly higher than in the case with no mass transfer. This result is interpreted as a consequence of the mass transfer induced surface mobility in the film region (the so-called Marangoni effect) due to localized surface tension differences. This effect has been demonstrated by the visualization of the flow patterns in the drops and in the film phase (using a particle tracer technique). In this case, the slope of the film height as a function of time seems to be independent of the approach velocity condition imposed on the drop and appears to be controlled by the interfacial tension gradient. In the opposite case, when the solute transfers from the continuous phase towards the drops, the film drainage rate is lowered with respect to the case of no mass transfer, goes to zero or even changes its sign depending on the mass transfer intensity. The results also show that in the range of solute concentration studied, the effect of mass transfer on the film drainage process takes place at large distances compared to the scales at which lubrication theory is valid.     

The Life of a Surface Bubble

Surface bubbles are present in many industrial processes and in nature, as well as in carbonated beverages. They have motivated many theoretical, numerical and experimental works. This paper presents the current knowledge on the physics of surface bubbles lifetime and shows the diversity of mechanisms at play that depend on the properties of the bath, the interfaces and the ambient air. In particular, we explore the role of drainage and evaporation on film thinning. We highlight the existence of two different scenarios depending on whether the cap film ruptures at large or small thickness compared to the thickness at which van der Waals interaction come in to play.     

Dynamics of interactions involving deformable drops: hydrodynamic dimpling under attractive and repulsive electrical double layer interactions

A model developed previously to analyze force measurements between two deformable droplets in the atomic force microscope [Langmuir 2005, 21, 2912-2922] is used to model the drainage of an aqueous film between a mica plate and a deformable mercury drop for both repulsive and attractive electrical double-layer interactions between the mica and the mercury. The predictions of the model are compared with previously published data [Faraday Discuss. 2003, 123, 193-206] on the evolution of the aqueous film whose thickness has been measured with subnanometer precision. Excellent agreement is found between theoretical results and experimental data. This supports the assumptions made in the model which include no-slip boundary conditions at both interfaces. Furthermore, the successful fit attests to the utility of the model as a tool to explore details of the drainage mechanisms of nanometer-thick films in which fluid flow, surface deformations, and colloidal forces are all involved. One interesting result is that the model can predict the time at which the aqueous film collapses when attractive mica-mercury forces are present without the need to invoke capillary waves or other local instabilities of the mercury/electrolyte interface.     

Droplet size effects on film drainage between droplet and substrate

When a droplet approaches a solid surface, the thin liquid film between the droplet and the surface drains until an instability forms and then ruptures. In this study, we utilize microfluidics to investigate the effects of film thickness on the time to film rupture for water droplets in a flowing continuous phase of silicone oil deposited on solid poly(dimethylsiloxane) (PDMS) surfaces. The water droplets ranged in size from millimeters to micrometers, resulting in estimated values of the film thickness at rupture ranging from 600 nm down to 6 nm. The Stefan-Reynolds equation is used to model film drainage beneath both millimeter- and micrometer-scale droplets. For millimeter-scale droplets, the experimental and analytical film rupture times agree well, whereas large differences are observed for micrometer-scale droplets. We speculate that the differences in the micrometer-scale data result from the increases in the local thin film viscosity due to confinement-induced molecular structure changes in the silicone oil. A modified Stefan-Reynolds equation is used to account for the increased thin film viscosity of the micrometer-scale droplet drainage case.     

Thermodynamic studies on thin liquid films. I. General formulation

From the viewpoint that thermodynamic study is essential to elucidate the structure and properties of thin liquid films, thermodynamic equations based on a new convention and employing pressure as a thermodynamic variable are developed for adsorption at film interfaces of a plane-parallel film. The equations together with quasi-thermodynamic ones correlate the dependence of film tension on concentration, temperature, pressure, and disjoining pressure to film density, entropy and volume changes associated with adsorption, and thermodynamic film thickness, respectively. Based on the formulation adopting pressure as a variable, equations are also derived for the differences in thermodynamic quantity between the film and the bulk interfaces coexisting at equilibrium.This revised version was published online in October 2004.Due to an unfortunate error Figure 1 has been omitted in the first version of the article which was published online first on April 23, 2004.     

Stability of draining plane-parallel films containing surfactants

The stability of partially mobile draining thin liquid films with respect to axisymmetric fluctuations was studied. The material properties of the interfaces (Gibbs elasticity, surface and bulk diffusions) were taken into account. When studying the long wave stability of films, the coupling between the drainage and perturbation flows was considered and the lubrication approximation was applied. Two types of wave modes were examined: radially-bounded and unbounded waves. The difference between the thickness of loss of stability, h(st), the transitional thickness, h(tr), at which the critical wave causing rupture becomes unstable, and the critical thickness, h(cr), when the film ruptures, is demonstrated. Both the linear and the non-linear theories give h(st) > h(tr) > h(cr). The numerical results show that the interfacial mobility does not significantly influence the thickness of the draining film rupture. The interfacial tension and the disjoining pressure are the major factors controlling the critical thickness. The available experimental data for critical thicknesses of foam and emulsion films show excellent agreement with the theoretical predictions. The important role of the electromagnetic retardation term in the van der Waals interaction is demonstrated. Other published theories of the film stability are discussed.     

Control of wettability of molecularly thin liquid films by nanostructures

The patterning of liquid thin films on solid surfaces is very important in various fields of science and engineering related to surfaces and interfaces. A method of nanometer-scale patterning of a molecularly thin liquid film on a silicon substrate using the lyophobicity of the oxide nanostructures has recently been reported (Fukuzawa, K.; Deguchi, T.; Kawamura, J.; Mitsuya, Y.; Muramatsu, T.; Zhang, H. Appl. Phys. Lett. 2005, 87, 203108). However, the origin of the lyophobicity of the nanostructure with a height of around 1 nm, which was fabricated by probe oxidation, has not yet been clarified. In the present study, the change in thickness of the liquid film on mesa-shaped nanostructures and the wettability for the various combinations of the thickness of the liquid films and the height of ridge-shaped nanostructures were investigated. These revealed that lyophobicity is caused by a lowering of the intermolecular interaction between the liquid and silicon surfaces by the nanostructure and enables the patterning of a liquid film along it. The tendency of the wettability for a given liquid film and nanostructure size can be predicted by estimating the contributions of the intermolecular interaction and capillary pressure. In this method, the height of the nanostructure can control the wettability. These results can provide a novel method of nanoscale patterning of liquid thin films, which will be very useful in creating new functional surfaces.     

Stability of thin stagnant film on a solid surface with a viscoelastic air-liquid interface

Linear stability analysis for a film on a solid surface with a viscoelastic air-liquid interface is presented. The interfacial dilatational and shear viscoelastic properties were described by Maxwell models. Dilatational and shear interfacial elasticity and viscosity were shown to improve film stability. When the interfacial rheological properties are extremely large or small, the maximum perturbation growth coefficient is shown to reduce to those for immobile and mobile interfaces respectively. Calculated values of maximum growth coefficient for thin film stabilized by 0.5% beta-lactoglobulin approached those of mobile films for thick (>2000 nm) and those for immobile films for thin (<100 nm) films respectively with the values lying between the two limits for intermediate film thicknesses.     

Effect of Insoluble Surfactants on Drainage and Rupture of a Film between Drops Interacting under a Constant Force

The deformation, drainage, and rupture of an axisymmetrical film between colliding drops in the presence of insoluble surfactants under the influence of van der Waals forces is studied numerically at small capillary and Reynolds numbers and small surfactant concentrations. Constant-force collisions of Newtonian drops in another Newtonian fluid are considered. The mathematical model is based on the lubrication equations in the gap between drops and the creeping flow approximation of Navier–Stokes equations in the drops, coupled with velocity and stress boundary conditions at the interfaces. A nonuniform surfactant concentration on the interfaces, governed by a convection–diffusion equation, leads to a gradient of the interfacial tension which in turn leads to additional tangential stress on the interfaces (Marangoni effects). The mathematical problem is solved by a finite-difference method on a nonuniform mesh at the interfaces and a boundary-integral method in the drops. The whole range of the dispersed to continuous-phase viscosity ratios is investigated for a range of values of the dimensionless surfactant concentration, Peclét number, and dimensionless Hamaker constant (covering both “nose” and “rim” rupture). In the limit of the large Peclét number and the small dimensionless Hamaker constant (characteristic of drops in the millimeter size range) a fair approximation to the results is provided by a simple expression for the critical surfactant concentration, drainage being virtually uninfluenced by the surfactant for concentrations below the critical surfactant concentration and corresponding to that for immobile interfaces for concentrations above it.