Fluctuations in the structure of three-phase lines

We study the fluctuations in the density and composition of the contact line at which three phases meet. The equilibrium structure of the contact line is obtained by minimizing a model free-energy functional and then the fluctuations about that structure are analyzed via the spectrum of the free energy’s second functional derivative. Three zero eigenvalues correspond to three fluctuation modes in which the positions of the contact line and interfaces change with no change in their internal structure. These eigenvalues are at the bottom of a continuum in which most of the corresponding fluctuation modes involve perturbations in the structure of the interfaces, extending far from the three-phase contact line. We identify one mode that is localized at the contact line and discuss its physical significance.