University of Illinois Urbana-Champaign

Linear stability analysis of gravity-driven viscosity-stratified newtonian coating flow on planar incline

Figa, Jan; Lawrence, Christopher J.

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https://hdl.handle.net/2142/112488

Description

Title
Linear stability analysis of gravity-driven viscosity-stratified newtonian coating flow on planar incline
Author(s)
  • Figa, Jan
  • Lawrence, Christopher J.
Issue Date
1995-05
Keyword(s)
  • Gravity-driven Viscosity-stratified
  • Newtonian Coating Flow
  • Planar Incline
  • Linear Stability Analysis
Abstract
This theoretical investigation motivates, reviews and formulates 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 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.
Publisher
Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report Name or Number
  • TAM R 791
  • 1995-6013
ISSN
0073-5264
Type of Resource
text
Language
eng
Permalink
http://hdl.handle.net/2142/112488
Copyright and License Information
Copyright 1995 Board of Trustees of the University of Illinois

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Technical Reports - Theoretical and Applied Mechanics (TAM) PRIMARY
TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.