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Axisymmetric spreading of surfactant from a point source

Published online by Cambridge University Press:  30 October 2017

Shreyas Mandre Open the ORCID record for Shreyas Mandre [Opens in a new window]
Shreyas Mandre*
Affiliation:
School of Engineering, Brown University, Providence, RI 02912, USA
*
†Email address for correspondence: shreyas_mandre@brown.edu
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Abstract

Guided by computation, we theoretically calculate the steady flow driven by the Marangoni stress due to a surfactant introduced on a fluid interface at a constant rate. Two separate extreme cases, where the surfactant dynamics is dominated by the adsorbed phase or the dissolved phase, are considered. We focus on the case where the size of the surfactant source is much smaller than the size of the fluid domain, and the resulting Marangoni stress overwhelms the viscous forces so that the flow is strongest in a boundary layer close to the interface. We derive the resulting flow in a region much larger than the surfactant source but smaller than the domain size by approximating it with a self-similar profile. The radially outward component of fluid velocity decays with the radial distance $r$ as $r^{-3/5}$ when the surfactant spreads in an adsorbed phase, and as $r^{-1}$ when it spreads in a dissolved phase. Universal flow profiles that are independent of the system parameters emerge in both the cases. Three hydrodynamic signatures are identified to distinguish between the two cases and verify the applicability of our analysis with successive stringent tests.

JFM classification

Convection: Convection Convection: Marangoni convection
Type
Papers
Information
Journal of Fluid Mechanics , Volume 832 , 10 December 2017 , pp. 777 - 792
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Copyright
© 2017 Cambridge University Press 

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