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Title:Linear stability analysis of gravity-driven viscosity-stratified newtonian coating flow on planar incline
Author(s):Figa, Jan; Lawrence, Christopher J.
Subject(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.
Issue Date:1995-05
Publisher:Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report:TAM R 791
1995-6013
Genre:Technical Report
Type:Text
Language:English
URI:http://hdl.handle.net/2142/112488
ISSN:0073-5264
Rights Information:Copyright 1995 Board of Trustees of the University of Illinois
Date Available in IDEALS:2021-11-04


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  • Technical Reports - Theoretical and Applied Mechanics (TAM)
    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.

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