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International audience; Hypothesis: The effective contribution of interfacial properties to the rheology of foams is a source of many open questions. Film dynamics during topological T1 changes in foams, essentially studied for low molecular weight surfactants, and scarcely for proteins, could connect interfacial properties to protein foam rheology. Experiments: We modified whey protein isolate (WPI), and its purified major protein b-lactoglobulin (b-lg) by powder pre-conditioning and dry-heating in order to obtain a broad variety of interfacial properties. We measured interfacial properties, film relaxation duration after a T1 event and bulk foam rheology. Findings: We found that, for b-lg, considered as a model protein, the higher the interfacial elastic modulus, the longer the duration of topological T1 changes and the greater the foam storage and loss moduli and the yield stress. However, in the case of the more complex WPI, these correlations were less clear. We propose that the presence in WPI of other proteins, lactose and minerals modify the impact of pre-conditioning and dry-heating on proteins and thereby, their behaviour at the interface and inside the liquid film.

A thin liquid film resting on a solid substrate that is heated or cooled from below experiences surface tension gradients, which lead to Marangoni flows. We explore the behavior of such a film on a chemically patterned substrate which drives film dewetting in order to determine how surface patterning and applied temperature gradients can be designed to influence the behavior of thin-film coatings. A nonlinear partial differential equation for the film height based on lubrication theory is solved numerically for a broad range of problem parameters. Uniform cooling of the substrate is found to significantly delay dewetting that is driven by wettability gradients. Uniform heating speeds up dewetting but can destroy the near-perfect templating imposed by the surface patterning. However, localized heating and cooling together can accelerate dewetting while maintaining templating quality. Localized heating and cooling can also be used to drive liquid onto areas that it would dewet from in the absence of heating. Overall, these results indicate that applied temperature gradients can significantly influence dewetting driven by surface patterning, and suggest strategies for the creation of spatially patterned thin-film coatings and flow control in microfluidic devices.

We consider the flow of a thin liquid film coating an inclined plane in the presence of a soluble surfactant. A two-dimensional three-equation model is derived using lubrication theory in the rapid diffusion limit and then used to investigate the stability of the fluid height and the surfactant surface and bulk concentrations. We present solutions for an insoluble surfactant system, which are then contrasted with those obtained for a system containing a soluble surfactant; both transient growth and fully nonlinear two-dimensional simulation results are discussed. Our results indicate that the characteristics of the fingering phenomena which accompany the flow are altered by the effects of solubility. In particular, we find that these effects de-stabilise the system further over an intermediate range of surfactant solubility.

A new method for bidimensional analysis of interferometric patterns of wetting liquid films obtained with the captive bubble technique is described. This method replaces one-dimensional analysis along various intensity profiles with analysis of one average intensity profile. The advantage is to concentrate the surface characteristics of the whole film image into a single intensity profile.

The impact of multiple drops on a dry substrate is studied experimentally and theoretically, as a preliminary model for relatively dense sprays. In the experiments the drop diameter, the impact velocity, the time interval between the impact of two drops, and the distance between the impacting drops were controlled. The shape of the liquid film formed on the substrate, the interface between the two drops, and the shape of the uprising sheets were observed using high-speed photography. In the theoretical model, the surface tension, wettability, viscosity, gravity, and inertia were taken into account. The agreement between the experiments and the theory is rather good considering that no adjustable parameters are used.

Thin liquid films are considered to be the basic structural elements of foam and emulsion systems. Consequently, the structure and stability of macro-dispersions are highly dependent on the dynamic structure formation and stability of a single, thin, curved film between unequal-sized bubbles and droplets as in a polydispersed foam and emulsion system. A novel experimental technique based on the differential microinterferometric method has been used to investigate the dynamic behavior of such curved foam films. The simple theoretical drainage model of Reynolds was used to calculate the drainage time for both curved and plane-parallel films, and the results were compared with the experimental observations. It was found that for thicker films (i.e., greater than 100 nm), the curved film drained twice as slowly as the plane-parallel film. However, at a film thickness less than 100 nm, the plane-parallel film has a lower rate of thinning compared to the curved film.

Experiments and modeling of the drainage of the thin liquid film between two deformable spherical drops approaching each other at constant velocity in another liquid are being presented. Two numerical models based on the lubrication theory have been developed considering the cases of immobile or mobile drop interfaces. The absolute film thickness and the thinning rate have been measured using laser interferometry for a wide range of capillary numbers. In all studied cases, the model with immobile interfaces was found to give the best predictions of the experimental time evolution of the film thickness and radial expansion. These results made it possible to derive a typical time scale of the drainage process. Copyright 2000 Academic Press.

The thinning behavior of liquid films between free bubbles and silica is investigated using the interferometric technique. Stable films were obtained at higher salt concentrations compared to previous studies because of the improved cleaning procedure. In contrast to the captive bubble technique used in the past, the free bubble method employed more closely approximates such processes as flotation. The results obtained for aqueous films at low and high ionic strengths are in better agreement with theoretical predictions than those in previous studies. Copyright 2000 Academic Press.

From an analysis of tangent spherical drops in straining flow, Baldessari and Leal conclude that the drop-scale internal circulation, driven by the ambient flow, has a negligible influence on the drainage of the thin liquid film between drops under small-deformation conditions [F. Baldessari, L.G. Leal, J. Colloid Interface Sci. 289 (2005) 262]. However, their conclusion is incorrect as explained in this letter.

The effect of surfactant concentration and film area on film stability was investigated in thin liquid films of sodium dodecyl sulfate (SDS) solutions. Film stability was evaluated at various concentrations of SDS solutions and various film areas. In this study, a maximum film stability was observed for the SDS concentration of 200 mM. Interestingly, this concentration also corresponds to the maximum micelle lifetime or long relaxation time (τ2). The results also show that film stability decreases with increasing film area, and that the larger films appear to be more sensitive to the micelle stability and structuring effect in the film than films with smaller surface areas.

For two liquid films adsorbed onto two flat substrates, at distances below some threshold, sudden formation of a liquid bridge between the two substrates occurs that should be observed by various force-measurement apparatus such as the surface force apparatus and atomic force microscopy. This transition was examined by a simple mean-field model of fluid confined within a slit-type pore, and semiquantitative assessment of the condensation distance was made.

The dynamic rupture process of a thin liquid film on a cylinder is investigated numerically. First a nonlinear differential equation that describes the long-wave evolution of the interface shape is derived. After the evolution equation is solved and analyzed, the results reveal that a decrease in the cylinder radius will induce a stronger lateral capillary force and consequently will accelerate the rupture process. Moreover, the tendency of acceleration becomes more explicit in the case of large surface tension.

When two small bubbles approach each other, a dimpled thin liquid film is formed between them. A model is developed for the dynamics of the thinning film with mobile interfaces, in which the effects of surface tension gradient and surface viscosities upon the surface mobility, drainage, and rupture of a dimpled liquid film are investigated. The model predicts the coalescence time, which is the time required for the thinning and rupture of the liquid film, given only the radii of bubbles and the required physical properties of the liquid and interfaces, such as surface tension and surface viscosities, London–van der Waals constant, and surface diffusion coefficient. The predicted result is in good agreement with previous experimental results.

The absorption of air by a liquid foam was studied experimentally at various temperatures between 8 and 55°C. It causes expansion of the foam and a gradient in cell size. The rate of expansion remains approximately constant following an initial transient. A theoretical analysis of the phenomenon is presented which assumes that the permeability of the liquid films to air is inversely proportional to their thickness and exponentially dependent on temperature. It is then possible to obtain experimental values of the permeability and of the activation energy for permeation which is ∼85 kJ mol−1. This is considerably larger than the activation energy for diffusion of air in pure water.

Strong capillary forces between a tip in an atomic force microscope and a solid surface covered with a thin layer liquid film makes it possible to detect and study the interfacial melting phenomenon. We discuss the general characteristics of force-distance curves measured on a solid surface which undergoes interfacial melting. We estimate the thermal disturbance of interfacial melting from the laser beam reflection system which is utilized by many atomic force microscopes.

When two small drops or bubbles approach one another, a dimpled thin liquid film is formed between them. A model is developed for the dynamics of the thinning film in which both London-van der Waals and electrostatic double layer forces are recognized. The model predicts the coalescence time, which is the time required for the thinning and rupture of the liquid film, given only the radii of the drops and the required physical properties of the fluids and interfaces. In the absence of the electrostatic double layer forces, a more general expression is derived for the coalescence time. The predicted result is in good agreement with previous experimental results.

This present work aims at researching the rupture process of thin liquid film of viscous Newtonian fluid on a horizontal plane. First, we use a numerical method to solve the nonlinear evolution equation derived by Williams and Davis. The numerical results reveal that the rupture processes can be divided into two parts; one is the slow weak nonlinear process which almost dominates the whole rupture time, and the other is the rapid strong nonlinear process which just occupies a little rupture time. Second, we use the weak nonlinear theory to solve the nonlinear film equation, and modify this method to match the real process. Eventually, we can obtain the approximation analytical solutions which could predict the nonlinear film rupture time more quickly and correctly.

The monolayer properties of phospholipids have been well studied in recent years; however, the properties of glycosphingolipids, although of importance in cell recognition processes, have not been investigated as thoroughly. In this paper we report on the surface pressure-area, surface potential-area, and dipole moment-area isotherms of dipalmitoylphosphatidylcholine, DPPC, and the glycosphingolipids G M1 and G T1b . The gangliosides exhibit expanded liquid film behavior, with measurable surface pressures detectable at molecular areas of 1.5 nm 2 and 2.5 nm 2 for G M1 and G T1b , respectively. These large molecular areas are a consequence of the large headgroups of these lipids and their charged nature. In addition mixtures of the gangliosides and phospholipids have been studied. In the mixtures of DPPC and gangliosides a negative deviation of the surface pressure with area was observed, indicating a degree of association between the different lipids in the film. Although there have been some data published on these systems by other workers the data have been contradictory in nature.

The process of bubble—particle attachment has been modeled by simulating the trajectory of a small particle as it approaches a bubble. The particle trajectory has been determined using a dynamic force balance between the force pressing the particle against the bubble and the force resisting the viscous film thinning. From the simulated trajectories, the closest approach distance between the particle and the bubble has been determined. The model assumes that bubble—particle adhesion occurs when the approach distance becomes smaller than the critical thickness at which the disjoining liquid film ruptures spontaneously. The model predictions have been verified experimentally using different sizes of bubbles and particles.

This paper compares the rate of drainage of thin liquid films (TLF) containing ionic surfactants to that of TLF containing non-ionic surfactants. In essence, the theory of drainage has been developed for films containing non-ionic surfactants, while the validation of the models, based on the theory in the literature, has been performed with experiments on TLF with both, non-ionic and ionic surfactants, usually in the presence of significant background concentrations of electrolyte. Due to the complexity of problem, the dynamic effects on the electrical double layer (EDL) during the film drainage have been ignored for many years in the literature. These effects were finally treated theoretically and the problem solved numerically in a recent work. The new theoretical development however has not yet been validated. In addition, the differences in the kinetics of thinning of TLF with ionic and non-ionic surfactants have not been exposed in the literature until present. This paper is dedicated to revealing these differences. Experiments on kinetics of thinning were conducted with microscopic planar TLF, containing two non-ionic surfactants (tetraethyleneglycol mono-octylether C8E4 and n-dodecyl--d-maltoside C12G2) and two ionic surfactants (sodium dodecylsulfate SDS and tetrapentylammonium bromide TPeAB). The TLF with non-ionic surfactants drain according to the well-known theories of Scheludko or Radoev-Manev–Ivanov, which confirms their validity. On the contrary, TLFs with ionic surfactants drain in general at significantly slower rate, as compared to the TLF with non-ionic surfactants, when far from equilibrium. When they are close to the equilibrium conditions, the former drain according to the theory developed for TLF with non-ionic surfactants. An analysis of the experimental results, involving the latest achievements in the field is performed, indicating the complex behaviour of the electrical double layer under dynamic conditions.

This paper is concerned with the detachment of particles from coalescing bubble pairs. Two bubbles were generated at adjacent capillaries and coated with hydrophobic glass particles of mean diameter 66 microm. The bubbles were then positioned next to each other until the thin liquid film between them ruptured. The particles that dropped from the bubble surface during the coalescence process were collected and measured. The coalescence process was very vigorous and observations showed that particles detached from the bubble surfaces as a result of the oscillations caused by coalescence. The attached particles themselves and, to some extent the presence of the surfactant had a damping affect on the bubble oscillation, which played a decisive role on the particle detachment phenomena. The behaviour of particles on the surfaces of the bubbles during coalescence was described, and implications of results for the flotation process were discussed.

In this note, we explore the precision of the optical imaging method for measuring the free surface position of a micrometer fluid shape. For this purpose, images of a liquid film deposited on a rod were acquired and processed. The resulting contour was compared with the corresponding solution to the Young-Laplace equation. The average deviation was about 30 nm, 25 times smaller than the pixel size, reflecting the validity of optical imaging for most applications in microfluidics.

The objective of this work is to study the fundamental instability behind the crown formation in the problem of drop splashing on a pre-existing liquid film. Based on experimental and theoretical insights, we demonstrate that the most plausible instability mechanism is of the Richtmyer–Meshkov type associated with a nearly impulsive acceleration of the interface. We also discover frustration phenomena in the wave number selection of the crown spike structure and study the corresponding bifurcation picture.

Growth of a thin liquid film as a result of mass transfer from limited fluid pockets has been modelled. Approximate analytical solutions of the moving boundary problem (i.e., the film thickness and the concentration profile) have been obtained by employing Goodman's integral method. Under a typical set of physicochemical conditions, the film growth with time is found to be nearly linear.

Profiles of the Plateau border at a vertical film in a 0.02 M cetyltrimethylammonium bromide solution are measured by optical interference, in the part of the border near the film, at two heights above the bulk liquid surface. The Laplace pressure in the border, calculated from these profiles, appears to be lower than the hydrostatic equilibrium pressure at a height close to the bulk liquid meniscus (6.2 mm); at a greater altitude (11.3 mm) the pressures are equal. An upward flow in the border close to the film is observed, while a downward flow takes place in the periphery of the border. Both effects can be explained by Marangoni flows.

Theoretical studies of a drop moving under condensation from the surrounding vapor, have been provided. Two cases are considered. In the first, the rate of condensation is large that the drop "moves" because condensation has changed its dimensions. The model provided here shows that the rate of spreading is a constant, proportional to the heat flux and inversely proportional to the macroscopic contact angle. This compares well with available experimental data. The other model where the rate of condensation is small, is taken from existing results and comes close to explaining one set of experimental data. It is based on the use of viscous forces as the primary rate mechanism. Its shortcomings have been discussed.

Dewetting dynamics of a liquid film composed of two superposed ultra-thin layers of immiscible liquids resting on a solid substrate is investigated in the case when surfactants are present at the liquid-liquid interface. Two cases are considered: insoluble surfactant and surfactant soluble in the lower liquid. The dependence of Hamaker constants on the surfactant concentration is taken into account. A system of three strongly nonlinear evolution equations describing large (comparable to the layer thicknesses), long-wave perturbations of the liquid-liquid and liquid-gas interfaces, as well as the surfactant concentration, is derived for each case in the lubrication approximation. The linear stability analysis shows that in the presence of surfactants, oscillatory dewetting instability can occur. Numerical simulations of this system of nonlinear evolution equations are performed. It is found that in the case of oscillatory instabilities, the system exhibits either standing or traveling "dewetting waves." The weakly nonlinear analysis explains this phenomenon.

It is well known that, in a thin liquid film, corresponding to any particular thickness there is precisely one axisymmetric equilibrium solution to the Laplace–Young capillary equation; i.e., corresponding to each film thickness there is a unique pinhole radius which has been shown to be unstable (1973, Taylor and Michael, J. Fluid Mech. 58, 625–639). We deduce an asymptotic relationship between film thickness and pinhole height in the limit of very thin films.

A process of nonlinear three-dimensional rupture of thin liquid films is numerically analyzed for the first time. With the rupture time being successfully calculated, it has been possible to develop a more complete rupture theory for thin liquid films. In contrast to the linear analysis indicating the shortest rupture time of thin liquid films to be the same for both two- and three-dimensional rupture, the nonlinear analysis reveals that the latter proceeds faster than the former. In particular, among all three-dimensional disturbance modes, the symmetric one makes the thin liquid films rupture fastest. It is concluded that the rupture process develops at a point rather than along a line on thin liquid films.

The nonlinear evolution equations derived by the integral method are used to study the inertial effect on rupture process of a thin liquid film. The nonlinear numerical results show that inertial effect accelerates the rupture process, and this phenomenon is explicit in the situation of weak effect of van der Waals potential. Finally, we use the perturbation method to obtain the nonlinear solutions which could predict the rupture time approximately.

A liquid foam can be regarded as a single fluid with a characteristic "surface tension". This property is calculated for two- and three-dimensional ordered and disordered foams using a broken bond approach. The contact angle of a foam with a solid or a liquid substrate is also calculated from the energies of the bubbles in contact with the substrate. Experiments were carried out in which the contact angles of foams were measured, with reasonable agreement with the predictions. Copyright 2001 Academic Press.

Effects of electromagnetic retardation on the rupture process of a very thin liquid film coated on a flat plate are studied. The analysis results indicate that the electromagnetic retardation effect (D) for the case A0 (attraction) is a stabilization factor, which prolongs the rupture time. The wavenumber of the most unstable mode is decreasing as D increases. It is also found that the linear solution of rupture time T(LM) is larger than the nonlinear rupture time T(NM), but the gradient of T(LM) to D is comparable to that of T(NM). Copyright 1999 Academic Press.

Coating processes are of technological interest. We focus here on the extraction of a vertical plate out of a wetting liquid. We first summarize the Landau-Levich-Derjaguin theory, including the gravity corrections which have been proposed in particular by White and Tallmadge. We propose a new numerical solution to the problem. Then, we discuss further developments: for liquids of low viscosity, it is shown that above a threshold in capillary number, the film is thickened because of inertia. A simple scaling argument is proposed for predicting the location of the threshold. Copyright 1998 Academic Press.

The generalized gradient theory for structural forces in liquid film, proposed by Mitlin and Sharma (1), is commented on. It is shown that this theory is not complete. The existence of very long range forces between hydrophobic surfaces is unlikely to be explainable on the basis of gradient theory.

Surfactant spreading phenomena on thin films is a fundamental problem in a number of fields including biomedical and chemical engineering. Coating processes, film drainage, and paint technology are all examples of technological applications. Research in this area has experienced a recent surge of activity, partly due to the biomedical applications of surfactant replacement therapy in prematurely born infants. A brief review of the surfactant spreading literature is given in this letter.

When a surfactant solution emerges from a slot to form a falling liquid film, an adsorption process occurs which generates a gradient in surface concentration. This concentration gradient gives rise to a gradient in the surface tension which retards the development of the velocity profile. Experimental measurements of the surface velocity, theoretical analysis of the adsorption process, and visual observation of the entrance region all indicate the existence of a double-vortex recirculation zone at the head of the entrance region. The surfactant adsorption process is largely controlled by the flow field in the recirculation zone as the downstream vortex provides a mechanism of convective transport from the bulk to the surface phase.

The coagulation of aqueous ZnO dispersions is investigated at various shear rates, in a shear field generated by stirring in a cylindrical vessel, and at different ~" potential values. Laser Doppler anemometry measurements permitted the construction of a model of the shear field by which average shear rates could be calculated. At low shear rates (~ -32 mV). At larger shear rates, the capture efficiencies rise with increasing -~, if the absolute value of the ~-potential is ~

A model of the “liquid-like” layer between ice and a substrate is used to predict the dynamics of particle rejection at a phase change interface. Predictions of the effects of particle radius, temperature gradient, and force applied to the particle on the engulfment velocity compare favorably with measurements. In the model used the driving force for water flow into the space between the particle and the ice, that is the force which produces the particle rejection, is a spreading pressure in the liquid film near the particle.

A macroscopic liquid film supported on a solid surface rupture due to hole formation when its thickness is reduced to a certain critical thickness. A theory is presented for obtaining the dependence of the critical thickness on the solid and liquid interfacial tensions and the equilibrium angle of contact between solid and liquid. The theory is based on the thermodynamic argument that when the free energy of the film-solid system becomes equal to or greater than the free energy after the formation of a hole in the liquid film, the film breakup becomes possible. The critical thickness increases with the contact angle in a nonlinear fashion and is directly proportional to the hole radius. The predicted variation of the critical thickness with the contact angle is in qualitative and quantitative agreement with the available data on the rupture of thin, macroscopic (several hundred micrometers thick) liquid films. The present theory provides a criterion for the design of surfaces that remain wettable by liquid films of given thicknesses.

A study has been made of the influence of gravitational forces on the thinning of the liquid film which forms as a solid sphere comes to rest on a liquid/fluid interface. It is found that rates of drainage can be dramatically affected by the ratio of gravity to surface tension forces within the film. At long times a secondary film can possibly be formed which spreads out radially from the apex of the sphere.

Stable unsymmetrical liquid films in the mercury-aqueous dodecyltriethylammonium perchlorate (DTEAClO4) solutions-air system were formed. Under similar experimental conditions, in the case of DTEACl, the films ruptured within 20 sec. Electrochemical studies of the mercury electrode in DTEAClO4 and DTEACl solutions suggest that strong lateral interactions between adsorbed ions occur for DTEAClO4.

In this paper an experimental technique, using capillary wave generation, for measuring the dynamic surface tension in an asymmetric free-falling liquid film is described. The method is checked for symmetrical films by comparing data with results obtained with the Mach angle technique. Furthermore it is shown that the experimental data, giving a value which is the arithmetic mean of the surface tensions of front- and backsides, are in good agreement with the theoretical adsorption-kinetic description.

The effect of hexanoic and heptanoic acid on the surface velocity profile in the entrance region of a thin falling liquid film has been studied experimentally and theoretically. Hexanoic acid solutions produce a negligible effect whereas heptanoic acid is capable of significantly retarding the establishment of uniform flow. The deviation of the surface velocity profile from that obtained with a “clean” surface is essentially independent of the diffusivity of heptanoic acid, illustrates a mild dependence on the adsorption kinetics and the equilibrium relation, and is strongly dependent on the compositional surface elasticity.

Migration of mineral particles in ice subjected to a temperature gradient was attributed to osmotic phenomena in an unfrozen liquid film surrounding these particles. Two models were formulated to simulate the observations with spherical glass beads, one based on electric double-layer effects and viscous flow of water, the other based on a brine pocket enclosing the particle and diffusion phenomena. Diffusion appeared to be the prevalent migratory mechanism. Computed film thicknesses close to the 0°C isotherm for the fast moving particles were of the order of magnitude of several hundred angstroms.

A method has been developed to calculate the hydrodynamic pressure distribution in a liquid film for a drop at a liquid-liquid interface. This method uses the relative thickness data obtained from light interference measurements made on the liquid film. Once the hydrodynamic pressure distribution is known, the three-dimensional or absolute drop and bulk surface shapes can be calculated.