Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-23T05:12:18.696Z Has data issue: false hasContentIssue false
  • English
  • Français

Drops of power-law fluids falling on a coated vertical fibre

Published online by Cambridge University Press:  19 June 2014

Liyan Yu Open the ORCID record for Liyan Yu [Opens in a new window]  and
John Hinch
Liyan Yu*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
John Hinch
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We study the solitary wave solutions in a thin film of a power-law fluid coating a vertical fibre. Different behaviours are observed for shear-thickening and shear-thinning fluids. For shear-thickening fluids, the solitary waves are larger and faster when the reduced Bond number is smaller. For shear-thinning fluids, two branches of solutions exist for a certain range of the Bond number, where the solitary waves are larger and faster on one and smaller and slower on the other as the Bond number decreases. We carry out an asymptotic analysis for the large and fast-travelling solitary waves to explain how their speeds and amplitudes change with the Bond number. The analysis is then extended to examine the stability of the two branches of solutions for the shear-thinning fluids.

JFM classification

Non-Newtonian Flows: Non-Newtonian Flows Waves/Free-surface Flows: Solitary waves Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 751 , 25 July 2014 , pp. 184 - 215
Copyright
© 2014 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Boulogne, F., Fardin, M. A., Lerouge, S., Pauchard, L. & Giorgiutti-Dauphiné, F. 2013 Suppression of Rayleigh–Plateau instability on a vertical fibre coated with wormlike micelle solutions. Soft Matt. 9, 7787–7796.Google Scholar
Boulogne, F., Pauchard, L. & Giorgiutti-Dauphiné, F. 2012 Instability and morphology of polymer solutions coating a fibre. J. Fluid Mech. 704, 232–250.Google Scholar
Bretherton, F. P. 1961 The motion of long bubbles in tubes. J. Fluid Mech. 10, 168–188.Google Scholar
Chang, H.-C. & Demekhin, E. A. 1999 Mechanism for drop formation on a coated vertical fibre. J. Fluid Mech. 380, 233–255.CrossRefGoogle Scholar
Chang, H.-C., Demekhin, E. & Kalaidin, E. 1995 Interaction dynamics of solitary waves on a falling film. J. Fluid Mech. 294, 123–154.Google Scholar
Hammond, P. S. 1983 Nonlinear adjustment of a thin annular film of viscous fluid surrounding a thread of another within a circular cylindrical pipe. J. Fluid Mech. 137, 363–384.CrossRefGoogle Scholar
Kalliadasis, S. & Chang, H.-C. 1994 Drop formation during coating of vertical fibres. J. Fluid Mech. 261, 135–168.Google Scholar
Quéré, D. 1999 Fluid coating on a fibre. Annu. Rev. Fluid Mech. 31, 347–384.Google Scholar
Ruyer-Quil, C. & Kalliadasis, S. 2012 Wavy regimes of flow down a fibre. Phys. Rev. E 85, 046302.Google Scholar
Yu, L. & Hinch, E. J. 2013 The velocity of ‘large’ viscous drops falling on a coated vertical fibre. J. Fluid Mech. 737, 232–248.Google Scholar