An investigation of the spin coating process and a model for three-dimensional regular foams
Zhou, Weiqun
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Permalink
https://hdl.handle.net/2142/19450
Description
Title
An investigation of the spin coating process and a model for three-dimensional regular foams
Author(s)
Zhou, Weiqun
Issue Date
1993
Doctoral Committee Chair(s)
Lawrence, Christopher J.
Department of Study
Mechanical Science and Engineering
Discipline
Theoretical and Applied Mechanics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Applied Mechanics
Language
eng
Abstract
The thesis consists of two independent parts. The first part is entitled: An investigation of the spin-coating process; the second part is entitled: A model for three-dimensional regular foams.
For spin-coating, a detailed numerical investigation of the spin-coating process has been performed. Our numerical approach takes advantage of the known asymptotic structure of the solution to the governing equations, and uses an adaptive scheme with multiple grids to achieve substantial improvements in accuracy and efficiency over previous approaches. As a result, the final coating thickness may be predicted, with good accuracy and efficiency, in terms of the spin speed and various material properties.
For foam rheology, a model for the 3-D regular foam is developed. The 3-D model is considerably more realistic than the 2-D model used by previous researchers. The static shape of a foam cell is governed by the Young-Laplace equation, with one free boundary. The general problem was solved numerically, while asymptotic approximations were pursued for the limit of the gas volume fraction approaching unity. To study the rheology, we need to determine the geometry of the tessellating cells under deformation. To this end, a formalism is developed, which takes advantage of the affine movement of particular points of the tessellating cells (face centers, centroid of cell). Finally, as an example, the stretch of our 3-D model is examined in detail. Significant differences between the 3-D and 2-D models are observed. Most notably, the elastic modulus predicted by the 3-D model is lower and decreases faster with stretch than that predicted by the 2-D model, which suggests that the 3-D model might give closer agreement with experiments than the 2-D model.
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