Capillary waves with surface viscosity. (25th May 2018)

• Record Type: Journal Article
• Authors: Shen, Li; Denner, Fabian; Morgan, Neal; van Wachem, Berend; Dini, Daniele
• Is Part Of: Journal of fluid mechanics. Volume 847(2018)
• Page Start: 644
• Page End: 663
• Publication Date: 2018-05-25
• Subjects: capillary flows, -- interfacial flows (free surface), -- thin films; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2018.364
• Languages: English
• ISSNs: 0022-1120

Abstract

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 concentration, 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 to the amplitude of the capillary wave with varying degree depending on the length scale of the system. Numerically, we find that the critical damping wavelength increases for increasing surface concentration but the rate of increase remains different for both the surface viscosity and the Marangoni effect.