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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

REFERENCES

Alexander, J.C., Bernoff, A.J., Mann, E.K., Mann, J.A. Jr. & Wintersmith, J. 2007 Domain relaxation in Langmuir films. J.Fluid Mech. 571, 191–219.CrossRefGoogle Scholar
Alexander, J.C., Bernoff, A.J., Mann, E.K., Mann, J.A. Jr. & Zou, L. 2006 Hole dynamics in polymer Langmuir films. Phys. Fluids 18, 062103.CrossRefGoogle Scholar
Barentin, C., Ybert, C., di Meglio, J.-M. & Joanny, J.-F. 1999 Surface shear viscosity of Gibbs and Langmuir monolayers. J.Fluid Mech. 397, 331–349.CrossRefGoogle Scholar
Drescher, K., Leptos, K.C., Tuval, I., Ishikawa, T., Pedley, T.J. & Goldstein, R.E. 2009 Dancing Volvox: hydrodynamic bound states of swimming algae. Phys. Rev. Lett. 102, 168101.CrossRefGoogle ScholarPubMed
Gradshteyn, I.S. & Ryzhik, I.M. 2007 Table of Integrals, Series, and Products. Elsevier.Google Scholar
Jarvis, N.L. 1966 Surface viscosity of polydimethylsiloxane monolayers. J.Phys. Chem. 70, 3027–3033.CrossRefGoogle Scholar
Jia, L.L., Irvine, W.T.M. & Shelley, M.J. 2022 Incompressible active phases at an interface. I. Formulation and axisymmetric odd flows. in revision; arXiv:2202.13962.Google Scholar
Joly, M. 1964 Surface viscosity. In Recent Progress in Surface Science (ed. J.F. Danielli, K.G.A. Pankhurst & A.C. Riddiford), Recent Progress in Surface Science, vol. 1, chap. 1, pp. 1–50. Elsevier.CrossRefGoogle Scholar
Khattari, Z., Hatta, E., Heinig, P., Steffen, P., Fischer, T.M. & Bruinsma, R. 2002 Cavitation of Langmuir monolayers. Phys. Rev. E 65, 041603.CrossRefGoogle ScholarPubMed
de Koker, R. & McConnell, H.M. 1993 Circle to dogbone: shapes and shape transitions of lipid monolayer domains. J.Phys. Chem. 97 (50), 13419–13424.CrossRefGoogle Scholar
Mann, E.K., Hénon, S. & Langevin, D. 1992 Molecular layers of a polymer at the free water surface: microscopy at the Brewster angle. J.Phys. II 2, 1683–1704.Google Scholar
Mann, E.K., Hénon, S., Langevin, D., Meunier, J. & Léger, L. 1995 Hydrodynamics of domain relaxation in a polymer monolayer. Phys. Rev. E 51, 5708.CrossRefGoogle Scholar
Mann, E.K. & Langevin, D. 1991 Poly(dimethylsiloxane) molecular layers at the surface of water and of aqueous surfactant solutions. Langmuir 7 (6), 1112–1117.CrossRefGoogle Scholar
Petroff, A.P., Wu, X.-L. & Libchaber, A. 2015 Fast-moving bacteria self-organize into active two-dimensional crystals of rotating cells. Phys. Rev. Lett. 114, 158102.CrossRefGoogle ScholarPubMed
Piessens, R. 2000 The Hankel transform. In The Transforms and Applications Handbook, 2nd edn (ed. A.D. Poularikas), chap. 9. CRC Press, LLC.CrossRefGoogle Scholar
Saffman, P.G. & Delbrück, M. 1975 Brownian motion in biological membranes. Proc. Natl Acad. Sci. USA 72 (8), 3111–3113.CrossRefGoogle ScholarPubMed
Stone, H.A. & McConnell, H.M. 1995 Hydrodynamics of quantized shape transitions of lipid domains. Proc. R. Soc. Lond. A 448, 97–111.Google Scholar
Watson, G.N. 1922 A Treatise on the Theory of Bessel Functions. Cambridge University Press.Google Scholar
Zou, L., Bernoff, A.J., Mann, J.A. Jr, Alexander, J.C. & Mann, E.K. 2010 Gaseous hole closing in a polymer Langmuir monolayer. Langmuir 26 (5), 3232–3236.CrossRefGoogle Scholar