A theory for undercompressive shocks in tears of wine

TL;DR

This paper develops a new theoretical model for the climbing dynamics of wine tears in thin films, revealing the presence of undercompressive shocks and connecting them to observed tear patterns.

Contribution

It introduces a novel model incorporating Marangoni stress and gravity effects, and identifies undercompressive shocks as key to wine tear formation.

Findings

Identification of undercompressive shocks in wine tears

Experimental observation of both compressive and undercompressive waves

Linking reverse undercompressive shocks to wine tear emergence

Abstract

We revisit the tears of wine problem for thin films in water-ethanol mixtures and present a new model for the climbing dynamics. The new formulation includes a Marangoni stress balanced by both the normal and tangential components of gravity as well as surface tension which lead to distinctly different behavior. The prior literature did not address the wine tears but rather the behavior of the film at earlier stages and the behavior of the meniscus. In the lubrication limit we obtain an equation that is already well-known for rising films in the presence of thermal gradients. Such models can exhibit non-classical shocks that are undercompressive. We present basic theory that allows one to identify the signature of an undercompressive (UC) wave. We observe both compressive and undercompressive waves in new experiments and we argue that, in the case of a pre-coated glass, the famous "wine tears" emerge from a reverse undercompressive shock originating at the meniscus.