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

Abstract

This is the final published version of the article (version of record). It first appeared online via APS Physics at https://doi.org/10.1103/PhysRevE.95.053101 . Please refer to any applicable terms of use of the publisher. University of Bristol -Explore Bristol Research General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/about/ebr-terms PHYSICAL REVIEW E 95, 053101 (2017) 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. Stability of viscous film flow coating the interior of a vertical tube with a porous wall

Falling liquid films in narrow tubes: occlusion scenarios

“…Using the low-dimensional model introduced in Dietze & Ruyer-Quil (2015), which had been applied only to gravity-free films, we have performed spatio-temporal computations of spatially-evolving falling films and computed travelling-wave solutions through numerical continuation. Our model extends upon the earlier works of Trifonov (1992), Camassa et al (2014Camassa et al ( , 2017, Zhou et al (2016), Liu & Ding (2017), and Ding et al…”

“…The model employed in our current study extends upon the earlier works of Trifonov (1992), Camassa et al (2014Camassa et al ( , 2017, Zhou et al (2016), Liu & Ding (2017), and Ding et al (2019) by accounting for axial viscous diffusion and inertia. This has allowed us to investigate four real liquids, for which we determine the lower and upper occlusion bounds…”

“…These terms appear when the underlying long-wave expansion is performed up to second order. This was not done in the previous modelling works of Trifonov (1992), Camassa et al (2014Camassa et al ( , 2017, Zhou et al (2016), Liu & Ding (2017) and Ding et al (2019). So, the question is whether retaining these terms is worth the effort.…”

A long-wave model for film flow inside a tube with slip

“…Halpern & Wei (2017) determined that for films coating a fibre, slip at the wall resulted in larger drops; their results suggested a possible explanation for slight discrepancies between no-slip models and the experiments of Quéré (1990). For a falling film inside a tube, Liu & Ding (2017) extended the long-wave model of Camassa et al (2014) to account for slip due to a porous wall. Their numerical simulations and classification of instabilities as absolute or convective demonstrated that slip promotes plug formation.…”

Fingering Instability of a Gravity-Driven Thin Film Flowing Down a Vertical Tube with Wall Slippage

“…As a common situation in interstifial flow, thin liquid film flowing on porous medium exhibits interesting dynamical phenomena. Ding and Liu [26,27] discovered that the film flowing on a porous vertical cylinder was more unstable and the increasing permeability of the porous medium significantly enhanced the destabilizing effect. The slippery effect often has a connection with wettability and porosity of the materials [28][29][30].…”