On integrable singularities and apparent contact angles within a classical paradigm

Far from claiming any ultimate resolution of the contact line paradoxes, we draw the reader’s attention to the fact that a somewhat controversial paradigm, originally employed by de Gennes and collaborators, actually appears both to be quite reasonable at its foundations and to lead to physically consistent final results in a wide variety of situations. Curiously enough, while containing a singularity in itself, the approach nonetheless renders the classical contact-line singularities – both hydrodynamic and thermal – integrable, in particular as far as several quantities of interest are concerned. It is also readily applicable to quite a few situations: from equilibrium shapes and moving contact lines of a non-volatile liquid, to cases with evaporation into (and even condensation from, although it is not studied here) either a pure-vapor or an inert-gas atmosphere. The paradigm actually consists in an approach involving both the (positive or negative) spreading coefficient and the disjoining pressure in the form of a positive inverse cubic law, a conceptual framework that most notably describes structures with truncated precursor films on a macroscopically bare solid surface. Whether or not the remaining integrable divergences at molecular scale can truly be considered as “benign” has to be discussed on the basis of more involved mesoscopic or microscopic approaches, quite outside the scope of the present study