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 language | English |
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Article number | 053101 |
Number of pages | 10 |
Journal | Physical Review E |
Volume | 95 |
Issue number | 5 |
Early online date | 1 May 2017 |
DOIs | |
Publication status | Published - May 2017 |