Response to contact line perturbations and chemo-capillary instability of a sessile drop

Equilibrium and motion of a contact line, described in the lubrication approximation, are viewed as analogs of phase equilibrium and motion of an interphase boundary. This approach allows one to directly relate such equilibrium characteristics as the contact angle and line tension with the functional form of the disjoining pressure, and carry out stability analysis, which points out the tendency to minimization of the length of the contact line at equilibrium. The concept of line tension has to be used, however, with caution, in view of a qualitatively different relaxation response of the contact line, compared to a two-dimensional curve. Both the analogy and qualitative distinction extend to a non-equilibrium situation arising due to coupling with reversible substrate modification. Under these conditions, the contact line may suffer a variety of chemo-capillary instabilities (fingering, traveling and oscillatory), similar to those of dissipative structures in nonlinear non-equilibrium systems. The preference order of the various instabilities changes, however, significantly due to a different way the interfacial curvature is relaxed.