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Capillary waves with surface viscosity

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Title: Capillary waves with surface viscosity
Authors: Shen, L
Denner, F
Morgan, N
Van Wachem, B
Dini, D
Item Type: Journal Article
Abstract: Experiments over the last 50 years have suggested a tentative correlation between the surface (shear) viscosity and the stability of a foam or emulsion. We examine this link theoretically using small-amplitude capillary waves in the presence of a surfactant solution of dilute concentrations where the associated Marangoni and surface viscosity effects are modelled via the Boussinesq-Scriven formulation. The resulting integro-differential initial value problem is solved analytically and surface viscosity is found to contribute an overall damping effect on the amplitude of the capillary wave with varying degrees depending on the lengthscale of the system. Numerically, we find the critical damping wavelength to increase for increasing surface concentration but the rate of increase remains different for both the surface viscosity and the Marangoni effect.
Issue Date: 25-Jul-2018
Date of Acceptance: 24-Apr-2018
URI: http://hdl.handle.net/10044/1/59270
DOI: https://dx.doi.org/10.1017/jfm.2018.364
ISSN: 0022-1120
Publisher: Cambridge University Press (CUP)
Start Page: 644
End Page: 663
Journal / Book Title: Journal of Fluid Mechanics
Volume: 847
Copyright Statement: © 2018 Cambridge University Press This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/N025954/1
Keywords: Science & Technology
Technology
Physical Sciences
Mechanics
Physics, Fluids & Plasmas
Physics
capillary flows
interfacial flows (free surface)
thin films
SOLUBLE SURFACTANTS
INTERFACE
EQUATION
SHEAR
RHEOLOGY
SYSTEMS
STATE
physics.flu-dyn
01 Mathematical Sciences
09 Engineering
Fluids & Plasmas
Publication Status: Published
Online Publication Date: 2018-05-25
Appears in Collections:Mechanical Engineering
Faculty of Natural Sciences
Faculty of Engineering