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arXiv · 1710.10137

The Marangoni effect on small-amplitude capillary waves in viscous fluids

Li Shen·Fabian Denner·Neal Morgan·Berend van Wachem·Daniele Dini
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Abstract

We derive a general integrodifferential equation for the transient behaviour 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 (cmc) 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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Li Shen, Fabian Denner, Neal Morgan, Berend van Wachem, Daniele Dini. 2017-10-27. The Marangoni effect on small-amplitude capillary waves in viscous fluids. https://doi.org/10.1103/physreve.96.053110

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