University of Illinois Urbana-Champaign

Stability analysis of gravity-driven viscosity-stratified coating flows

Figa, Jan

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https://hdl.handle.net/2142/22802

Description

Title
Stability analysis of gravity-driven viscosity-stratified coating flows
Author(s)
Figa, Jan
Issue Date
1995
Doctoral Committee Chair(s)
Lawrence, Christopher J.
Department of Study
  • Applied Mechanics
  • Physics, Fluid and Plasma
Discipline
  • Applied Mechanics
  • Physics, Fluid and Plasma
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
  • Applied Mechanics
  • Physics, Fluid and Plasma
Language
eng
Abstract
This theoretical investigation presents the linear stability analysis of a gravity-driven and viscosity-stratified coating flow useful in covering a planar surface with one or more liquid layers. The challenging stability analysis of a coating flow on a curved substrate surface is discussed. The mathematical foundation on which to analyse the stability of this inherently spatial coating flow problem is provided by a Green's impulse function approach which serves as the appropriate mathematical tool to describe (arbitrary) disturbances imposed on the liquid surface. The temporal analysis showed that a two-layered Newtonian coating flow is susceptible to an instability due to viscosity stratification even without the effects of surface tension, density stratification or, surprisingly, inertia. In addition, waves with the largest growth typically occur at finite wavelengths; the properties of these waves are often of greatest practical interest. However, the temporal growth rate, for the maximally unstable mode, of order 0.0015 was small. The mathematically proper ray-speed approach, originating from a steepest descent method to determine the perturbed film thickness, removed the interpretational quandary present in the classical spatial approach and corroborated the temporal linear stability results.
Type of Resource
text
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http://hdl.handle.net/2142/22802
Copyright and License Information
Copyright 1995 Figa, Jan

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