Dewetting: Nucleation and growth of dry regions

A Mathematical Model for Crater Defect Formation in a Drying Paint Layer

Certain deep indentations observed in dry coatings are referred to as "craters". They are believed to arise from gradients in the coating surface tension. A mathematical model of surface-tension-gradient-driven flow, using the lubrication approximation for thin layers, is developed to study the formation of craters. The paint is modeled as consisting of an evaporating "solvent" part and a nonvolatile "resin" part. Surface tension gradients on the coating surface arise due to a nonuniform distribution of surfactant. Axisymmetric numerical simulations using the model are performed to explore two candidate crater production mechanisms: an initial release of concentrated surfactant and a steady surfactant source. The effects of changes in various properties, such as the paint drying rate, the surfactant diffusivity, and the viscosity increase during drying, are examined. The model produces craters with large diameters, pronounced rims, and central peaks, similar to those seen in practice. Drying rate has a large influence on crater diameter and depth, by limiting flow due to surface tension gradients within a given time. Reduction of the paint viscosity increase during drying causes increased flow rates, leading to larger craters. A preexisting layer of surfactant on the paint surface sharply reduces the extent of cratering. Surfactant diffusion also tends to reduce the severity of cratering by alleviating surface tension gradients. In some cases, a simplified form of the drying model may be used to quickly approximate the results of the full model. The model provides useful insights into the craters seen in industrial coating applications. Copyright 2000 Academic Press.

Wetting Film Dynamics

The spreading of a tiny macroscopic drop of a nonvolatile, completely wetting liquid over a flat solid is considered, assuming no gravitation. A liquid, in creeping, is subjected to capillary forces and van der Waals forces. This nonstationary and nonlinear problem in the dynamics of the wetting film from a droplet is studied using numerical modeling. The precursor wetting film motion is described by an evolution equation with conditions at the moving boundaries. The wetting line is regarded as an unknown boundary to be determined in the course of solution. A simplified equation for the wetting line dynamics is analyzed. The difference between the wetting line radius and a fixed (nonzero) radius is described by a diffusion time law. Results of numerical experiments show the simplified law of wetting to be valid over a wide range of spreading times (or a wide range of radii of the wetting line). Copyright 2000 Academic Press.

Wetting Line Dynamics in the Process of Drop Spreading

Spreading of a tiny macroscopic droplet of a nonvolatile, completely wetting liquid over a flat solid is considered. A liquid in creeping is subjected to capillary forces and long-range molecular forces. The droplet may be surrounded with a precursor wetting film. This paper deals with the problem of determining of the microscopic parameter that influences the interface shape near the apparent line of wetting; this is regarded as the inverse problem in the hydrodynamics of wetting. If the system includes a precursor film, the microscopic parameter coincides with the maximum thickness of the film. A series of inverse equations for the microparameter is obtained, which relate it to, first, the current geometric parameters of the macroscopic drop part and, second, the spreading time. A method for determining how the microparameter depends on the wetting line speed is proposed. The theory expands the opportunity to perform macroscopic measurements and reveals additional parameters. The inverse relations may be used to experimentally study the growth of the maximum thickness of a precursor film during drop spreading. Copyright 2000 Academic Press.

Modeling Draining Flow in Mobile and Immobile Soap Films

A mathematical model is constructed to describe the two-dimensional flow in a vertical soap film that is draining under gravity. An asymptotic analysis is employed that uses the long-wave or "lubrication" approximation. The modeling results in three coupled partial differential equations that include a number of dimensionless input parameters. The equations are solved numerically. The three functions calculated, as they vary in space and time, are the film thickness, the surface concentration of an assumed insoluble surfactant, and the slip or surface velocity. The film is assumed to be supported by "wire frame" elements at both the top and the bottom; thus the liquid area and the total surfactant are conserved in the simulation. A two-term "disjoining" pressure is included in the model that allows the development of thin, stable, i.e., "black," films. While the model uses a simplified picture of the relevant physics, it appears to capture observed soap film shape evolution over a large range of surfactant concentrations. The model predicts that, depending on the amount of surfactant that is present, the film profile will pass through several distinct phases. These are (i) rapid initial draining with surfactant transport, (ii) slower draining with an almost immobile interface due to the surface tension gradient effect, and (iii) eventual formation of black spots at various locations on the film. This work is relevant to basic questions concerning surfactant efficacy, as well as to specific questions concerning film and foam draining due to gravity. Prospects for extension to three-dimensional soap film flows are also considered. Copyright 1999 Academic Press.

Dewetting of a Heated Surface by an Evaporating Liquid Film under Conjoining/Disjoining Pressures

In the present work we consider a model for the evolution of a thin nonpolar liquid film on a coated solid surface under the action of attractive and repulsive molecular forces governed by a 3-4 power-law potential, rather than the Lennard-Jones 3-9 potential employed for an ideal plane interface (molecularly clean and smooth). The model is used for both volatile and nonvolatile isothermal liquid films. It is shown that in the nonvolatile case the evolution results in the emergence of static steady states consisting of liquid ridges separated by very thin films. A supercritical bifurcation from the trivial state is shown to be possible in the presence of repulsive forces, while in the presence of only attractive forces the bifurcation is subcritical. In the evaporative case the long-time evolution of the film is shown to lead to its flattening and then to its apparent vanishing. Several scenarios for the film disappearance are found. A relationship between the rate of expansion of the dry spot and the apparent contact angle is examined. The effect of thermocapillarity on the film evolution is also considered. Copyright 1999 Academic Press.

Surfactant-spreading and surface-compression disturbance on a thin viscous film

Spreading of a new surfactant in the presence of a pre-existing surfactant distribution is investigated both experimentally and theoretically for a thin viscous substrate. The experiments are designed to provide a better understanding of the fundamental interfacial and fluid dynamics for spreading of surfactants instilled into the lung. Quantitative measurements of spreading rates were conducted using a fluorescent new surfactant that was excited by argon laser light as it spread on an air-glycerin interface in a petri dish. It is found that pre-existing surfactant impedes surfactant spreading. However, fluorescent microspheres used as surface markers show that pre-existing surfactant facilitates the propagation of a surface-compression disturbance, which travels faster than the leading edge of the new surfactant. The experimental results compare well with the theory developed using lubrication approximations. An effective diffusivity of the thin film system is found to be Deff = (E*gamma)/(mu/H), which indicates that the surface-compression disturbance propagates faster for larger background surfactant concentration, gamma, larger constant slope of the sigma*-gamma* relation, -E*, and smaller viscous resistance, mu/H. Note that sigma* and gamma* are the dimensional surface tension and concentration, respectively, mu is fluid viscosity, and H is the unperturbed film thickness.

Dewetting of Thin Block Copolymer Films

The dewetting of thin films of low molecular weight diblock and triblock copolymers of poly(oxyethylene)/poly(oxybutylene) on silicon has been studied using video microscopy and X-ray reflectivity. Dewetted films were observed to comprise polygonal domains of polymer droplets, with a domain size of several millimeters. The dewetted films were studied using X-ray reflectivity, which showed that a film of polymer <50 Å thick remains on the substrate at the same time as the macroscopic droplets. This suggests that autophobic dewetting occurred in this system; i.e., a microscopically thin film was in equilibrium with macroscopic droplets. The growth velocity of holes in the polymer film was found to be constant at a fixed temperature in the stage of hole growth that could be studied using optical microscopy. The velocity was found to be an exponential function of temperature. Copyright 1999 Academic Press.