Thin-film model surface tension

Following the principles of the Petrie model, and recalling that the film thickness <5 is much smaller than the radius S/R thin-film approximation, which implies that field equations are averaged over the thickness and that there are no shear stresses and moments in the film. The film is regarded, in fact, as a thin shell in tension, which is supported by the longitudinal force Fz in the bubble and by the pressure difference between the inner and outer surfaces, AP. We further assume steady state, a clearly defined sharp freeze line above which no more deformation takes place and an axisymmetric bubble. Bubble properties can therefore be expressed in terms of a single independent spatial variable, the (upward) axial position from the die exit,2 z. The object... 

Problem 6-7. Coating Flows The Drag-Out Problem A very important model problem in coating theory is sometimes called the drag-out problem. In this problem, a flat plate is pulled through an interface separating a liquid and a gas at a prescribed velocity U. The primary question is to relate the pull velocity U to the thickness // of the thin film that is deposited on the moving plate. We consider the simplest case in which the plate is perpendicular to the horizontal interface that exists far from the plate. The density of the liquid is p, the viscosity //, and the surface tension y. 

An approach that is almost diametrically opposed to the earlier models of Khan and Armstrong, and Kraynik and Hansen, was advanced by Schwartz and Princen (108). In this model, the films are negligibly thin, so that all the continuous phase is contained in the Plateau borders, and the surfactant tiuns the film surfaces immobile as a result of surface-tension gradients. Hydrodynamic interaction between the films and the Plateau borders is considered to be crucial. This model, believed to be more realistic for common sur factant-stabilized emulsions and foams, draws on the work of Mysels et al. (109) on the dynamics of a planar, vertical soap film being pulled out of, or pushed into, a bulk solution via an intervening Plateau border. An important result of their analysis is commonly referred to as FrankeTs law, which relates the film thickness, 2h., to the pulling velocity, U, and may be written in the form ... 

An idealised model of the surface of a thin liquid film is one of a monolayer of evenly-distributed surfactant molecules. However, a more realistic model is one where the molecules are not evenly distributed therefore, the surface concentration depends on surface position. The result of this heterogeneous distribution is that gradients of surface concentration, and therefore surface tension, are present. One example of this was pointed out in Section 5.1 on the effect of Marangoni instabilities on film rupture. Regarding film drainage, a surface tension gradient exerts a surface stress that can either impede or... 

The situation is still more complex in the presence of surfactants. Recently, a self-consistent electrostatic theory has been presented to predict disjoining pressure isotherms of aqueous thin-liquid films, surface tension, and potentials of air bubbles immersed in electrolyte solutions with nonionic surfactants [53], The proposed model combines specific adsorption of hydroxide ions at the interface with image charge and dispersion forces on ions in the diffuse double layer. These two additional ion interaction free energies are incorporated into the Boltzmann equation, and a simple model for the specific adsorption of the hydroxide ions is used for achieving the description of the ion distribution. Then, by combining this distribution with the Poisson equation for the electrostatic potential, an MPB nonlinear differential equation appears. 

Monolayers of nanoparticles at liquid-fluid interfaces have attracted considerable attention over several decades [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]. Among others, the examinations focused on thin-layer preparation [10, 18, 19, 20, 21, 22, 23], emulsion stabilisation [15, 24] and particle characterisations [25, 26, 27]. The Stober silica (synthesised by controlled hydrolysis of tetraethylorthosilicate in ethanol in the presence of ammonia and water) [28] has many advantageous properties for model investigations. The nearly spherical particles show a narrow size distribution and are compact above a certain particle size (around 20 nm diameter) [29]. The particles, on the one hand, show partial wettability and, on the other hand, form a weakly cohesive two-dimensional dispersion at the water-air interface [10, 14]. All that makes them suitable to determine the total repulsive interparticle energies in a film balance by measuring the effective surface tension of the monoparticulate layer [30, 31, 32, 33, 34, 35, 36]. 

Two different, but supplementary, approaches (models) are used in the macroscopic description of a thin liquid film. The first of them, the membrane approach, treats the film as a membrane of zero thickness and one tension, y, acting tangentially to the membrane (see the right-hand side of Figure 4.16). In the detailed approach , the film is modeled as a homogeneous liquid layer of thickness h and surface tension c/. The pressure Pq in the fluid particles is larger than the pressure, P, of the liquid in the Plateau border. The difference... 

Variable temperature Scanning Force Microscopy of mixed polystyrene (2000 - 100000 g/mol) and poly (methylmethacrylate) (100000 g/mol) thin films was used to probe mechanical properties such as surface stiffness and pull-off forces. Adhesion data can be explained by the molecular properties of the constituents. The adhesion of Polystyrene samples was measured by force distance curves and using the Pulsed Force Mode. It can be shown that surface tension is not the dominant part of the tip-surface interaction, but the mechani cal properties of the material will influence the measured adhesive force. Wetting of the tip by polymer molecules at higher temperatures due to increasing mobility is one possible model. 

In nanoparticle electrocatalysis, the area that Michael entered just some time ago in Munich, he and his coworkers rationalized the sensitivity of electrocatalytic processes to the stmcture of nanoparticles and interfaces. Studies of catalytic effects of metal oxide support materials revealed intriguing electronic structure effects on thin films of Pt, metal oxides, and graphene. In the realm of nanoparticle dissolution and degradation modeling, Michael s group has developed a comprehensive theory of Pt mass balance in catalyst layers. This theory relates surface tension, surface oxidation state, and dissolution kinetics of Pt. 

FIGURE 18.4. Schematic representation of a 2D model to account for the shear modulus of a foam. The foam stmcture is modeled as a collection of thin films the Plateau borders and any other fluid between the bubbles is ignored. Furthermore, all the bubbles are taken to he uniform in size and shape. When shear is applied, the total area of the thin films increases, and the surface tension results in a restoring force, providing the shear modulus of the foam. 

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