The stability of gravity driven viscoelastic film-flow at low to moderate Reynolds number
type: Item
instance of: scholarly article
title: The stability of gravity driven viscoelastic film-flow at low to moderate Reynolds number
zbMATH Open document ID: 0659.76015
DOI: 10.1016/0377-0257(89)80015-1
author: Eric S. G. Shaqfeh
author: Ronald G. Larson
author: Glenn H. Fredrickson
published in: Journal of Non-Newtonian Fluid Mechanics
publication date: 1989-01-01T00:00:00Z
review text: The hydrodynamic stability of a film of viscoelastic fluid falling under its own weight down an inclined surface is considered. As a first step, the stability to infinitesimal disturbances (linear stability) is studied. The equations governing the growth of small, two dimensional disturbances in the parallel base state are derived and solved numerically for the Oldroyd-B fluid model as well as the multiple-mode Rouse model over a wide range of the relevant viscoelastic parameter - the Deborah number. Our results demonstrate that for small Reynolds number, although viscoelastic effects are destabilizing as predicted by other authors, the growth rate of the resulting purely elastic waves remains very small and, therefore, these waves are presumably of little consequence in practical situations. On the other hand, at moderate Reynolds numbers, viscoelastic effects are primarily stabilizing. Both results suggest that the perturbation analyses employed by previous authors are simply too limited in their scope to describe the complex nature of the instability in this viscoelastic, free-surface flow.
Mathematics Subject Classification ID: 76A10
Mathematics Subject Classification ID: 76E99
Mathematics Subject Classification ID: 76M99
zbMATH DE Number: 4078985
zbMATH Keywords: hydrodynamic stability
zbMATH Keywords: film of viscoelastic fluid
zbMATH Keywords: Oldroyd-B fluid
zbMATH Keywords: multiple-mode Rouse model
zbMATH Keywords: viscoelastic, free-surface flow
MaRDI profile type: Publication
full work available at URL: 0377-0257(89)80015-1
OpenAlex ID: W2095517963
Wikidata QID: Q126645144
description: scientific article; zbMATH DE number 4078985