Demonstration of the famed “tears of wine” problem at the 2019 SIAM Conference on Analysis of Partial Differential Equations, held in La Quinta, Calif., this past December. Photo courtesy of Claudia Falcon.
During the
2019 SIAM Conference on Analysis of Partial Differential Equations (PD19), which took place this past December in La Quinta, Calif., Andrea Bertozzi and postdoctoral researcher Claudia Falcon—both of the University of California, Los Angeles (UCLA)—performed a demonstration of “tears of wine.” The tears of wine problem is a curious phenomenon that wine drinkers have observed for centuries. In the right setting, one may notice a thin layer of water-ethanol mixture that travels up inclined surfaces—such as wine glasses—against gravity and falls down in the form of “tears.”
Bertozzi and Falcon presented a live experiment with a pre-swirled glass, wherein the famous wine tears emerged. They described this particular behavior using a mathematical model that involves a conservation law with a nonconvex flux and higher-order diffusion, due to the bulk surface tension. Such equations have nonclassical “undercompressive” shock solutions, which were the main drivers of the destabilizing front in the demonstration at PD19. Bertozzi and Falcon’s work—conducted with UCLA student Yonatan Dukler and postdoctoral researcher Hangjie Ji—will appear in Physical Review Fluids and is currently available online.
Prior mathematical modeling of this problem addressed the behavior of the meniscus and the film at earlier stages, rather than the wine tears.
Claudia Falcon, a postdoctoral researcher at the University of California, Los Angeles, addresses the “tears of wine” problem at the 2019 SIAM Conference on Analysis of Partial Differential Equations, which took place this past December in La Quinta, Calif. Photo courtesy of Andrea Bertozzi.
— Andrea Bertozzi and Claudia Falcon