Theory for undercompressive shocks in tears of wine

Tears of wine, in which a thin layer of a water-ethanol mixture travel up an inclined surface against gravity and then fall down in the form of tears, have been observed in wine glasses for centuries. It has been modeled with a conservation law with a nonconvex flux and higher order diffusion due to the bulk surface tension. The resulting nonclassical ``undercompressive'' shock solutions are the main driver of the destabilizing front forming the ``wine tears''. Prior modeling did not address the wine tears but rather the behavior of the film at earlier stages and the behavior of the meniscus.