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The role of monolayer viscosity in Langmuir film hole closure dynamics

Published online by Cambridge University Press:  02 September 2022

Leroy L. Jia Open the ORCID record for Leroy L. Jia [Opens in a new window]  and
Michael J. Shelley
Leroy L. Jia*
Affiliation:
Center for Computational Biology, Flatiron Institute, New York, NY 10010, USA
Michael J. Shelley
Affiliation:
Center for Computational Biology, Flatiron Institute, New York, NY 10010, USA Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
*
†Email address for correspondence: ljia@flatironinstitute.org
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Abstract

We re-examine the model proposed by Alexander et al. (Phys. Fluids, vol. 18, 2006, 062103) for the closing of a circular hole in a molecularly thin incompressible Langmuir film situated on a Stokesian subfluid. For simplicity their model assumes that the surface phase is inviscid which leads to the result that the cavity area decreases at a constant rate determined by the ratio of edge tension to subfluid viscosity. We reformulate the problem, allowing for a regularising monolayer viscosity. The viscosity-dependent corrections to the hole dynamics are analysed and found to be non-trivial, even when the monolayer viscosity is small; these corrections may explain the departure of experimental data from the theoretical prediction when the hole radius becomes comparable to the Saffman–Delbrück length. Through fitting, under these relaxed assumptions, we find the edge tension could be as much as six times larger ($\sim$4.0 pN) than reported previously.

JFM classification

Low-Reynolds-number flows: Stokesian dynamics Interfacial Flows (free surface): Thin films
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 948 , 10 October 2022 , A1
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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