Stability of viscous film flow coating the interior of a vertical tube with a porous wall

Rong Liu, Zijing Ding

Research output: Contribution to journalArticle (Academic Journal)peer-review

10 Citations (Scopus)
308 Downloads (Pure)

Abstract

The stability of the gravity-driven flow of a viscous film coating the inside of a tube with a porous wall is studied theoretically. We used Darcy's law to describe the motion of fluids in a porous medium. The Beaver-Joseph condition is used to describe the discontinuity of velocity at the porous-fluid interface. We derived an evolution equation for the film thickness using a long-wave approximation. The effect of velocity slip at the porous wall is identified by a parameter β. We examine the effect of β on the temporal stability, the absolute-convective instability (AI-CI), and the nonlinear evolution of the interface deformation. The results of the temporal stability reveal that the effect of velocity slip at the porous wall is destabilizing. The parameter β plays an important role in determining the AI-CI behavior and the nonlinear evolution of the interface. The presence of the porous wall promotes the absolute instability and the formation of the plug in the tube.
Original languageEnglish
Article number053101
Number of pages10
JournalPhysical Review E
Volume95
Issue number5
Early online date1 May 2017
DOIs
Publication statusPublished - May 2017

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