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Drops on soft solids: free energy and double transition of contact angles

Published online by Cambridge University Press:  10 April 2014

L. A. Lubbers ,
J. H. Weijs ,
L. Botto ,
S. Das ,
B. Andreotti  and
J. H. Snoeijer
L. A. Lubbers
Affiliation:
Physics of Fluids Group, Faculty of Science and Technology, Mesa+ Institute, University of Twente, 7500 AE Enschede, The Netherlands
J. H. Weijs*
Affiliation:
Physics of Fluids Group, Faculty of Science and Technology, Mesa+ Institute, University of Twente, 7500 AE Enschede, The Netherlands
L. Botto
Affiliation:
School of Engineering and Materials Science, Queen Mary University of London, London E1 4NS, UK
S. Das
Affiliation:
Department of Mechanical Engineering, University of Maryland, College Park, MD 20742, USA
B. Andreotti
Affiliation:
Physique et Mécanique des Milieux Hétérogènes, UMR 7636 ESPCI-CNRS, Univ. Paris-Diderot, 10 rue Vauquelin, 75005, Paris, France
J. H. Snoeijer
Affiliation:
Physics of Fluids Group, Faculty of Science and Technology, Mesa+ Institute, University of Twente, 7500 AE Enschede, The Netherlands Department of Applied Physics, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
*
†Email address for correspondence: [email protected]
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Abstract

The equilibrium shape of liquid drops on elastic substrates is determined by minimizing elastic and capillary free energies, focusing on thick incompressible substrates. The problem is governed by three length scales: the size of the drop $R$, the molecular size $a$ and the ratio of surface tension to elastic modulus $\gamma /E$. We show that the contact angles undergo two transitions upon changing the substrate from rigid to soft. The microscopic wetting angles deviate from Young’s law when $\gamma /(Ea)\gg 1$, while the apparent macroscopic angle only changes in the very soft limit $\gamma /(ER)\gg 1$. The elastic deformations are worked out for the simplifying case where the solid surface energy is assumed to be constant. The total free energy turns out to be lower on softer substrates, consistent with recent experiments.

JFM classification

Interfacial Flows (free surface): Capillary flows Interfacial Flows (free surface): Contact lines Drops and Bubbles: Drops
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 747 , 25 May 2014 , R1
Copyright
© 2014 Cambridge University Press 

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