Rate Of Film Thinning Research Articles

The effects of surface viscosity on the axisymmetric drainage of planar liquid films

AbstractThe Reynolds equation is extended to allow for the effects of shear and dilational surface viscosities on the axisymmetric drainage of planar films. It is shown that the number of immobile surfaces, n, may be expected to decrease with increasing film radius and bulk viscosity and with decreasing film thickness and surface viscosity, as observed experimentally. The predicted rate of film thinning agrees well with available experimental results.

The effect of hydrodynamic coupling on the thinning of a film between a drop and its homophase

The rate of thinning of a film trapped between a drop approaching its homophase according to a model incorporating hydrodynamic coupling is dramatically different from earlier, uncoupled models. Implications for film thinning of microflows analyzed in the preceding paper are here investigated using similar analytical methods to derive a nonautonomous, nonlinear evolution equation for the film thickness which has been solved numerically under a variety of conditions after asymptotic analytical behavior has been extracted. The applied force squeezing the film, together with the initial motion in the three phases, determines the rate of film thinning in a complicated manner through the coupling parameter R = (ρ Aμ A/ρ Bμ B) 1 2 . Experimental observations that normal drop circulation enhances thinning, whereas reversed drop circulation can cause thickening, are predicted theoretically for the first time. Films much more viscous than their surroundings are found to thin faster than the converse case, a conclusion at odds with offhand intuition but substantiated experimentally; both classes of systems behave differently, often qualitatively so, from predictions of hydrodynamically decoupled systems, and in particular film thinning rates are generally faster because of less resistance to drainage, although the limit of vanishing R does recover the special case of Reynolds' model. For short times, films are shown analytically to thin more rapidly if there is initially outward film motion and normal drop circulation, but with decreasing effectiveness as R increases, in contrast to the effect of R for intermediate and longer times; if there is initially inward film motion, thickening tendencies are enhanced by reverse drop circulation but with decreasing effectiveness as R increases. These and other detailed conclusions, most predicted theoretically for the first time, are not only in qualitative agreement with experimental observations, they are in quantitative agreement with available data.

The effect of applied force on drainage of the film between a liquid drop and horizontal surface

AbstractThe effect of applied force, drop volume, and physical properties on the rate of thinning of the draining films above and below a drop trapped between two horizontal surfaces has been examined theoretically and experimentally. The variation in film thickness with position and time has been obtained photographically and from capacitance measurements. The observed rate of film thinning may be predicted by the simple uniform film model with one immobile surface and, surprisingly, decreases when the applied force and drop volume increases.

On initial transients in Reynolds' drainage model

The time-dependent, axisymmetric drainage equations have been solved for the pseudo-steady approach of a pair of rigid disks. Use of the Laplace transformation yields two analytical forms for the solution, one having better convergence properties for shorter times, the other for longer times. Both have been used to derive from the macroscopic balances a pair of equivalent, non-linear film-thinning equations which have been solved numerically for the film thickness as a function of time. Initial transients in velocity profiles decay within t ≈ δ 2/ν under all reasonable conditions and within ≈ δ 2/2ν for an initially quiescent film. The effects of microflow transients on the rate of film thinning cannot be discerned after t ≈ r f 2/ν, where r f is the disk radius. For thin films described with reasonable accuracy by Reynolds' model, the film-thinning rate thus quickly approaches that for steady microflow unless the applied forces are abnormally weak.

The gravity approach and coalescence of fluid drops at liquid interfaces

AbstractThe rate of thinning of the liquid film trapped between a fluid drop and a liquid interface and the subsequent coalescence of the drop were investigated using an interferometric method. The rate of film thinning for small drops was in good agreement over a narrow range of film thickness with two previously proposed models. The rate was greater than predicted when the film thickness was less than 0.2 μ presumably because of movement of the interfaces. The minimum thickness in the film at rupture was usually less than 500 Å. for drop diameters up to 2500 μ. The seemingly anomalous behavior of drops previously observed in a partial coalescence series resulted from uneven film thinning with larger drops. Partial coalescence between finite drops was investigated briefly; no secondary drop was produced when the drop diameter ratio was less than about 3.5.

Some effects of interfacial diffusion on the gravity coalescence of liquid drops

The rate of thinning of the Phase 2 film separating a drop (Phase 1) from a Phase 1/ Phase 2 interface was found to increase with diffusion from, and decrease with diffusion into, the drop. The film thickness at rupture appeared to be unaffected. The results provide direct confirmation of the mechanism proposed by Groothius and Zuiderweg, based on the Marangoni effect whereby changes in the rate of film thinning arise from interfacial flow as a result of gradients in interfacial tension produced by unequal distribution of the diffusing component over the drop surface.

The approach of gas bubbles to a gas/liquid interface

The approach of nitrogen bubbles to the free surface of aqueous glycerol solutions and polyglycol oils was investigated using interference rings and interference colors to estimate the thickness of the liquid films. The rate of approach in close proximity to the liquid surface was found to decrease rapidly with decreasing separation. The intervening liquid film deformed with progressive thinning and, eventually, was thinnest around a ring at a distance c′ from the center. Analysis showed that this occurred where the upper surface started to bulge. The rate of film thinning increased with decreasing film viscosity and showed good agreement with a theoretical equation previously derived. The rupture of the intervening liquid film occurred over a range of film thicknesses in any given system, in many cases at values <900 A. The effect of an added surfactant was to decrease the rate of film thinning at comparable thicknesses, increase the mean rest-time, and lead to thinner films at rupture than in the case of the pure system.

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Analytical equations for the drainage of spherically curved uniform thin films are obtained in terms of the variation in film curvature, film contact angle, and film thickness with position and time. These enable one to predict the effects of film curvature and polydispersity of the emulsion system on the stability of the spherically curved film corresponding to the emulsion stability. The rate of film thinning for small drops was in good agreement with the model over a narrow range of film thicknesses. The rate was greater than predicted when the film thickness is very thin and film size is large due to the movement of the film interface. When a surfactant is present, the film thinning rate can be predicted with the equation developed by assuming the film surface is immobile due to tangential gradient (Marangoni-Gibbs effect) on the film surface. Good agreement with available experimental values was obtained for drops resting at a stationary interface when the surfactant was present.