The microscopic origin of droplet line tension

Abstract

The size dependence of the equilibrium droplet contact angle is governed by line tension. In this work, we identify a contribution to line tension arising from gravitational effects and pressure-induced changes in volume-fraction-dependent interfacial tensions within an adsorption layer. This mechanism addresses a multiscale problem of line tension in droplets ranging from nanometric to millimetric sizes that change sign and span several orders of magnitude, in agreement with experimental and simulation results. The sign of the apparent line tension is controlled by surface wettability, the initial volume fraction in the adsorption layer, and the droplet size, which also strongly influences its magnitude. Our results provide a unified physical interpretation of the experimentally observed variability in both the sign and magnitude of line tensions.