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Elastohydrodynamics of contact in adherent sheets

Published online by Cambridge University Press:  22 August 2022

Stéphane Poulain Open the ORCID record for Stéphane Poulain [Opens in a new window] ,
Andreas Carlson Open the ORCID record for Andreas Carlson [Opens in a new window] ,
Shreyas Mandre Open the ORCID record for Shreyas Mandre [Opens in a new window]  and
L. Mahadevan Open the ORCID record for L. Mahadevan [Opens in a new window]
Stéphane Poulain
Affiliation:
Mechanics Division, Department of Mathematics, University of Oslo, 0316 Oslo, Norway
Andreas Carlson
Affiliation:
Mechanics Division, Department of Mathematics, University of Oslo, 0316 Oslo, Norway
Shreyas Mandre
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK
L. Mahadevan*
Affiliation:
Paulson School of Engineering and Applied Sciences, Department of Physics, Harvard University, Cambridge, MA 02138, USA Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA
*
†Email address for correspondence: lmahadev@g.harvard.edu
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Abstract

Adhesive contact between a thin elastic sheet and a substrate arises in a range of biological, physical and technological applications. By considering the dynamics of this process that naturally couples fluid flow, long-wavelength elastic deformations and microscopic adhesion, we analyse a sixth-order thin-film equation for the short-time dynamics of the onset of adhesion and the long-time dynamics of a steadily propagating adhesion front. Numerical solutions corroborate scaling laws and asymptotic analyses for the characteristic waiting time for adhesive contact and for the speed of the adhesion front. A similarity analysis of the governing partial differential equation further allows us to determine the shape of a fluid-filled blister ahead of the adhesion front. Finally, our analysis reveals a near-singular behaviour at the moving elastohydrodynamic contact line with an effective boundary condition that might be useful in other related problems.

JFM classification

Interfacial Flows (free surface): Thin films Low-Reynolds-number flows: Lubrication theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 947 , 25 September 2022 , A16
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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