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|Title:||Selected topics in viscous flow: Coating flow with rotation|
|Doctoral Committee Chair(s):||Lawrence, Christopher J.|
|Department / Program:||Engineering, Mechanical|
|Degree Granting Institution:||University of Illinois at Urbana-Champaign|
|Abstract:||This thesis consists of two parts concerning rotational molding and spin coating, respectively. Both parts consider coating flows which have relevance to industrial applications. The main theme of the thesis is to make appropriate simplifications to the mathematical descriptions of the flows in order to achieve meaningful analytical progress. Mathematically, the thesis involves making effective approximations so that a system of partial differential equations can be simplified into a set of more readily solvable ordinary differential equations.
Part one deals with a simple model of the rotational molding process, namely the coating flow inside a rotating horizontal cylinder. Experiments have shown a very rich collection of interesting phenomena. At low rotation rates, a single jump appears close to the bottom on the rising side of the cylinder. At moderate and high rotation rates, a gradually-varying "rimming" flow exists. Often regular or irregular waves, dripping, or fingering occur at intermediate rotation rates before or after the jump disappears. The present approach is to investigate the straight jump and the rimming flow, and then to analyze their stability with respect to small disturbances. It is found that low-Reynolds-number theory corresponds to a singular limit, and a stability analysis is pursued via singular perturbation theory. The governing equations and the jump conditions for conservation of mass and momentum are derived, and three different analytical approaches are pursued and compared. These are the integral approach, the mixed-order-equation approach, and the rigorous asymptotic approach. Experiments are described and the results compare reasonably well with theoretical predictions for the base flow. The results of the stability analysis have been somewhat inconclusive and therefore disappointing, but they have shed some light on further studies.
The second part is concerned with spin coating on a rotating disc. A three-stage model of the citing process for the transport of both momentum and diffusion has been applied and an accurate, simple approximate integral approach has been developed. The integral approach is able to predict the time evolution of the film thickness, velocity boundary-layer thickness, diffusion boundary-layer thickness, and the free-surface solute concentration. This method takes advantage of the unique asymptotic structure of the problem for large Reynolds number and large Peclet number with the thin-film approximation to simplify the system to achieve both reasonable accuracy and high efficiency. The integral approach is able to reflect the key features of the problem; the physical picture of the three stages of the coating process is very clear, the mathematical manipulation is very reasonable and thus the numerical simulation is very economical. Results for a Newtonian fluid coating on a flat disc agree well with those of Zhou and Lawrence.
|Rights Information:||Copyright 1995 Zhang, Hong-biao|
|Date Available in IDEALS:||2011-05-07|
|Identifier in Online Catalog:||AAI9543785|
This item appears in the following Collection(s)
Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois