Residual stability of sessile droplets with negative line tension.

We study the local stability of a sessile droplet with nonvanishing line tension along the contact line, where three phases are in equilibrium. We confirm Widom's results [J. Phys. Chem. 99, 2803 (1995)] on the local stability of a droplet with positive line tension in a larger class of perturbations. When the line tension is negative, we prove that the restricted class of perturbations employed by Widom fails to capture the instability of equilibria. A notion of residual stability is introduced, which makes quantitative the condition under which equilibrium of droplets with negative line tension are likely to be observed.