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LW Schwartz

Publications and source records attributed to LW Schwartz.

5 recordsLinked to original sources
PubMed2000

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.

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PubMed1999

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.

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PubMed1997

Simulation of Coating Layer Evolution and Drop Formation on Horizontal Cylinders

The lubrication form of the equations governing the flow of a thin liquid film on a horizontal right circular cylinder is derived. The equations are discretized and solved numerically using an alternating-direction implicit algorithm. Simulations demonstrate that the transition from a uniform coating to a final configuration of distinct drops follows a similar evolution for a wide range of cylinder radii. Initially gravity-driven drainage from the top and sides of the cylinder dampens the formation of any axial disturbances; only when this drainage slows do longitudinal waves begin to develop along the bottom of the cylinder. These waves grow rapidly and a series of alternating primary and satellite drops form during the transition from a linear to a nonlinear wave growth regime. This is followed by a slow drainage between adjacent drops as the drop pattern approaches an equilibrium state where surface tension forces exactly balance gravitational forces in each discrete drop. For large cylinder radii, these drops are localized on the bottom of the cylinder, while, for sufficiently small cylinder radii, these drops may wrap around the entire circumference of the cylinder. Integral measures of the evolving coating profile, such as the total energy and viscous dissipation rate, clearly show these growth phases. The equilibrium shape of large-amplitude pendant drops and the maximum sustainable drop volume for various cylinders are also considered.

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