• Open Access

Marangoni effect on small-amplitude capillary waves in viscous fluids

Li Shen, Fabian Denner, Neal Morgan, Berend van Wachem, and Daniele Dini
Phys. Rev. E 96, 053110 – Published 20 November 2017

Abstract

We derive a general integro-differential equation for the transient behavior of small-amplitude capillary waves on the planar surface of a viscous fluid in the presence of the Marangoni effect. The equation is solved for an insoluble surfactant solution in concentration below the critical micelle concentration undergoing convective-diffusive surface transport. The special case of a diffusion-driven surfactant is considered near the the critical damping wavelength. The Marangoni effect is shown to contribute to the overall damping mechanism, and a first-order term correction to the critical wavelength with respect to the surfactant concentration difference and the Schmidt number is proposed.

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  • Received 6 June 2016
  • Revised 18 July 2017

DOI:https://doi.org/10.1103/PhysRevE.96.053110

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.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

Li Shen1,*, Fabian Denner1, Neal Morgan2, Berend van Wachem1, and Daniele Dini1

  • 1Department of Mechanical Engineering, Imperial College London, London SW7 2AZ, United Kingdom
  • 2Shell Global Solutions Ltd, Brabazon House, Threapwood Road, Manchester M22 0RR, United Kingdom

  • *Corresponding author: l.shen14@imperial.ac.uk

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Issue

Vol. 96, Iss. 5 — November 2017

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