Nonlinear effects of line tension in adhesion of small droplets

Three-phase line tensions may become crucial in the adhesion of micro-nanoor small droplets on solid planes. In this paper we study for the first time the nonlinear effects in adhesion spanning the full range of physically possible parameters of surface tension, line tension, and droplet size. It is shown that the nonlinear adhesion solution spaces can be characterized into four regions. Within each region the adhesion behaves essentially the same. Especially, inside the characteristic regions with violent nonlinearities, the co-existence of multiple adhesion states for given materials is disclosed. Besides, two common fixed points in the solution space are revealed. These new results are consistent with numerical analysis and experimental observations reported in the literatures.