On viscous film flows coating the interior of a tube: Thin-film and long-wave models

Roberto Camassa, H. Reed Ogrosky

Research output: Contribution to journalArticle

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Abstract

A theoretical and numerical investigation of two classes of models for pressure-driven core-annular flow is presented. Both classes, referred to as 'long-wave' and 'thin-film' models, may be derived from a unified perspective using long-wave asymptotics, but are distinct from one another in the role played by the curved tube geometry with respect to the planar (limiting) case. Analytical and numerical techniques are used to show and quantify the significant differences between the behaviour of solutions to both model types. Temporal linear stability analysis of the constant solution is carried out first to pinpoint with closed-form mathematical expressions the different dynamical regimes associated with absolute or convective instabilities. Numerical simulations for the models are then performed and qualitative differences in the evolution of the free surface are explored. Mathematically, different levels of asymptotic accuracy are found to result in different regularizing properties affecting the long-time behaviour of generic numerical solutions. Travelling wave solutions are also studied, and qualitative differences in the topology of streamline patterns describing the flow of the film in a moving reference frame are discussed. These topological differences allow for further classification of the models. In particular, a transition from a regime in which waves trap a fluid core to one where waves travel faster than any parcel of the underlying fluid is documented for a variant of the primary model. In the corresponding thin-film model, no such transition is found to occur. The source of these differences is examined, and a comparison of the results with those of related models in the literature is given. A brief discussion of the merits of each class of models concludes this study.

LanguageEnglish (US)
Pages569-599
Number of pages31
JournalJournal of Fluid Mechanics
Volume772
DOIs
StatePublished - Jun 1 2015

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planetary waves
tubes
coatings
Thin films
Coatings
thin films
annular flow
Linear stability analysis
Fluids
fluids
traveling waves
travel
topology
Topology
traps
Geometry
Computer simulation
geometry

Keywords

  • core-annular flow
  • instability
  • thin films

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Condensed Matter Physics

Cite this

On viscous film flows coating the interior of a tube : Thin-film and long-wave models. / Camassa, Roberto; Ogrosky, H. Reed.

In: Journal of Fluid Mechanics, Vol. 772, 01.06.2015, p. 569-599.

Research output: Contribution to journalArticle

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