A fundamental problem in contact mechanics is the adhesive contact of a rigid sphere with a flat elastic substrate. For small deformation where the contact radius a is small in comparison with the radius of the sphere R, the solution was given by Johnson, Kendall and Roberts (JKR). The JKR theory has been extremely successful in describing the adhesive contact of elastic spheres; it is therefore surprising to find that the deformation of silicone gels caused by adhesion of hard spheres, in the absence of external load, deviate considerably from JKR theory. Specifically, Style et al. have reported that the power-law relation between the contact radius a (indentation depth δ) and sphere radius R changes from a ∝ R~(2/3) (δ ∝ R~(1/3) ) to a ∝ R (δ ∝ R) as the sphere reduces in size or the substrate becomes softer. This transition in scaling has been interpreted by Style et al. as a corresponding underlying transition from the JKR limit where the adhesion-driven deformation is primarily resisted by bulk elasticity, to the "liquid-like" limit where the adhesion-driven deformation is primarily resisted by the substrate-air surface tension σ.
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