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Interfacial instabilities in plane Poiseuille flow of two stratified viscoelastic fluids with heat transfer. Part 1. Evolution equation and stability analysis

Published online by Cambridge University Press:  26 April 2006

Sang W. Joo
Sang W. Joo
Affiliation:
Department of Mechanical Engineering, Wayne State University, Detroit, MI 48282, USA
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Abstract

An evolution equation is derived that describes the nonlinear development of the interface between two viscoelastic fluids flowing, under the action of imposed pressure gradient and gravity, in a vertical channel. The channel walls are kept at different temperatures, resulting in heat transfer across the layers. The equation, based on the lubrication approximation, models the effects of stratifications in density, viscosity, elasticity, shear thinning, and thermal conductivity. It also describes the capillary and thermocapillary effects, as well as the sensitivity of viscosities to temperature. Linear-stability analysis is performed based on the evolution equation to understand the competing effects of viscous, elastic, and Marangoni instabilities. Particular attention is paid to the active control of the interfacial instabilities through the thermocapillarity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 299 , 25 September 1995 , pp. 241 - 265
Copyright
© 1995 Cambridge University Press

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