title: Indentation of a rigid sphere into an elastic substrate with surface tension and adhesion.
abstract: The surface tension of compliant materials such as gels provides resistance to deformation in addition to and sometimes surpassing that owing to elasticity. This paper studies how surface tension changes the contact mechanics of a small hard sphere indenting a soft elastic substrate. Previous studies have examined the special case where the external load is zero, so contact is driven by adhesion alone. Here, we tackle the much more complicated problem where, in addition to adhesion, deformation is driven by an indentation force. We present an exact solution based on small strain theory. The relation between indentation force (displacement) and contact radius is found to depend on a single dimensionless parameter:ω=σ(μR)-2/3((9π/4)Wad)-1/3, whereσandμare the surface tension and shear modulus of the substrate,Ris the sphere radius andWadis the interfacial work of adhesion. Our theory reduces to the Johnson-Kendall-Roberts (JKR) theory and Young-Dupre equation in the limits of small and largeω, respectively, and compares well with existing experimental data. Our results show that, although surface tension can significantly affect the indentation force, the magnitude of the pull-off load in the partial wetting liquid-like limit is reduced only by one-third compared with the JKR limit and the pull-off behaviour is completely determined byω.
authors: Field of Theoretical and Applied Mechanics, Department of Mechanical and Aerospace Engineering , Cornell University , Ithaca, NY 14850, USA.
authors: Chung-Yuen
authors: CY
authors: Hui
authors: Field of Theoretical and Applied Mechanics, Department of Mechanical and Aerospace Engineering , Cornell University , Ithaca, NY 14850, USA.
authors: Tianshu
authors: T
authors: Liu
authors: School of Engineering and Applied Sciences , Harvard University , Cambridge, MA 02138, USA.
authors: Thomas
authors: T
authors: Salez
authors: PCT Laboratory, UMR CNRS 7083 Gulliver, ESPCI ParisTech , PSL Research University, 10 rue Vauquelin , 75005, Paris, France.
authors: Elie
authors: E
authors: Raphael
authors: Department of Chemical and Biomolecular Engineering , Lehigh University , Bethlehem, PA 18015, USA.
authors: Anand
authors: A
authors: Jagota
keywords: adhesion; contact mechanics; indentation; surface tension