From adhesion to wetting of a soft particle

Using a thermodynamical approach, we calculate the deformation of a spherical elastic particle placed on a rigid substrate, under zero external load, and including an ingredient of importance in soft matter: the interfacial tension of the cap. In a first part, we limit the study to small deformation. In contrast with previous works, we obtain an expression for the energy that precisely contains the JKR and Young-Dupre ́ asymptotic regimes, and which establishes a continuous bridge between them. In a second part, we consider the large deformation case, which is relevant for future comparison with numerical simulations and experiments on very soft materials. Using a fruitful analogy with fracture mechanics, we derive the exact energy of the problem and thus obtain the equilibrium state for any given choice of physical parameters. Since the seminal works of Hertz [1, 2], Johnson, Kendall and Roberts (JKR) [3], and Derjaguin, Muller and Toporov (DMT) [4], the contact of adhesive elastic solids has been widely studied [5, 6, 7]. This area of research is of tremendous impor-tance: the range of application now spreads from biology to en-gineering, as shown by the recent developments on latex parti-cles [8], biological cells [9, 10], or micro-patterned substrates [11] for instance. Extensions of JKR theory to large deformation hav