Three regimes of a steady-state rimming flow of the liquid polymers

Sergei Fomin, Toshiyuki Hashida

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Rimming flow on the inner surface of a horizontal rotating cylinder is investigated. Simple lubrication theory is applied since the Reynolds number is small and liquid film thin. Since the Deborah number is very small the flow is viscometric. A general constitutive law for this kind of flow requires only a single function relating shear stress and shear rate that corresponds to a generalized Newtonian liquid. For this case the run-off condition for rimming flow is derived. Provided the run-off condition is satisfied, the existence of a steady-state solution is proved. In the bounds implied by this condition film thickness admits a continuous solution, which corresponds to subcriticai and critical flow regimes. In the supercritical case when the mass of liquid polymer exceeds a certain value or the speed of rotation is less than an indicated limit, a discontinuous solution is possible and a hydraulic jump may occur. As an example, the location and height of the hydraulic jump is determined numerically for Ellis model.

Original languageEnglish
Title of host publicationSlow Dynamics in Complex Systems
Subtitle of host publication3rd International Symposium on Slow Dynamics in Complex Systems
EditorsMichio Tokuyama, Irwin Oppenheim
PublisherAmerican Institute of Physics Inc.
Pages275-276
Number of pages2
ISBN (Electronic)0735401837
DOIs
Publication statusPublished - 2004 Apr 30
Event3rd International Symposium on Slow Dynamics in Complex Systems - Sendai, Japan
Duration: 2003 Nov 32003 Nov 8

Publication series

NameAIP Conference Proceedings
Volume708
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Other

Other3rd International Symposium on Slow Dynamics in Complex Systems
CountryJapan
CitySendai
Period03/11/303/11/8

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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