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oai:www.ideals.illinois.edu:2142/22802 2023-07-10 col_2142_5131 com_2142_5130

Lawrence, Christopher J. Figa, Jan 2011-05-07T13:51:57Z 2011-05-07T13:51:57Z 10000-01-01 1995 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. Made available in DSpace on 2011-05-07T13:51:57Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9543583.pdf: 9435746 bytes, checksum: d5cebae7d80eaf6243d24b7141357a77 (MD5) Previous issue date: 1995 Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T15:00:06Z Item is restricted indefinitely. Restriction data tranferred 2014-07-01T11:28:24-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission ETDs are only available to UIUC Users without author permission U of I Only AAI9543583 (UMI)AAI9543583 http://hdl.handle.net/2142/22802 eng Copyright 1995 Figa, Jan Applied Mechanics Physics, Fluid and Plasma Stability analysis of gravity-driven viscosity-stratified coating flows text Applied Mechanics Physics, Fluid and Plasma Applied Mechanics Physics, Fluid and Plasma University of Illinois at Urbana-Champaign Dissertation Ph.D.