Adhesion maps of spheres corrected for strength limit.

Present understanding of adhesion is mostly due to the well-known contact theories for spheres, including JKR (Johnson-Kendall-Roberts), DMT (Derjaguin-Muller-Toporov) and MD (Maugis-Dugdale). Since most of the models exhibit their optimal applicability only in a specific regime, an adhesion map has been developed [K.L. Johnson, J.A. Greenwood, J. Colloid Interface Sci. (1997)] to guide the selection among different models. In the JG (Johnson-Greenwood) map, however, an important physical fact has been neglected that the adhesion strength must not exceed the theoretical strength; thereby the applicability of the classical adhesion models is overestimated and misguidance may arise from the JG map. To avoid this limitation, in this paper we introduce the strength limit into the adhesion map and find that the selection of adhesion models depends not only on the Tabor number but also on the ratio of the theoretical strength to the stiffness. Given this ratio, there exists a critical Tabor number or the size of the sphere, below which adhesion is dominated by the limiting strength and the classical adhesion models are no longer appropriate for spheres. These results eventually lead to a corrected adhesion map for spheres.