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Viscoplasticity can stabilize liquid collar motion on vertical cylinders

James D. Shemilt1,2,*, Alice B. Thompson1, Alex Horsley3, Carl A. Whitfield1,3, and Oliver E. Jensen1

  • *Contact author: jds74@cam.ac.uk
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Phys. Rev. Fluids 10, 103301 – Published 22 October, 2025

DOI: https://doi.org/10.1103/dqm7-p5vp

Abstract

Liquid films coating vertical cylinders can form annular liquid collars which translate downwards under gravity. We investigate the dynamics of a thin viscoplastic liquid film coating the interior or exterior of a vertical cylindrical tube, quantifying how the yield stress modifies both the Rayleigh-Plateau instability leading to collar formation and the translation of collars down the tube. We use thin-film theory to derive an evolution equation for the layer thickness, which we solve numerically to examine the nonlinear dynamics. Instability and collar formation occur when gravity is sufficiently strong to make the fluid yield initially. We use matched asymptotics to derive a model describing the quasisteady translation of a slender liquid collar when the Bond number is small. The structure of the asymptotic solution for a viscoplastic collar shares some features with the Newtonian version, but there are several novel asymptotic regions that emerge at the two ends of the collar. The global force balance, which determines the collar's speed, is modified by a leading-order contribution from viscous drag in the collar when the liquid is viscoplastic. We use the asymptotic model to describe slow changes in collar volume when the film thicknesses ahead of, and behind, the collar are unequal. When the film thickness ahead of the collar is less than a critical value that we determine, viscoplastic collars adjust their volume and reach a steadily translating state. This contrasts with the Newtonian problem, where the only state in which steady translation occurs is unstable to small changes in the film thickness.

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Model of Fluid Draining in Lung Airways

Published 22 October, 2025

A theory for the motion of a fluid “bump” inside a cylinder may lead to improved drugs for lung diseases.

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Phys. Rev. Fluids 10, 103301– Published 22 October, 2025
  • Received 25 February 2025
  • Accepted 26 August 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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