The elasticity of a contact line

We calculate the work required to deform a three-phase contact line between two fluid phases and one solid phase using an interface displacement model. This includes the effects of both surface and line tensions. The leading-order dependence on the wavenumber q of the distortion has been described by Joanny and de Gennes (J. Chem. Phys. 81(1984)552). We examine the next-to-leading term, which contrary to expectation is not the line tension but a quantity of similar magnitude. Cases of divergent line tension are also examined, which demonstrate a regularization exhibiting scaling on a length scale set by q. Negative line tension does not lead to instability of the contact line to small amplitude deformations at any wavenumber.