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Center for Nonlinear Studies |
We revisit the tears of wine problem for thin films in water-ethanol mixtures and present a model for the climbing dynamics. The 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 nonclassical shocks that are undercompressive. We present basic theory that allows one to identify the signature of an undercompressive wave. We observe both compressive and undercompressive waves in new experiments, and we argue that, in the case of a preswirled glass, the famous “wine tears” emerge from a reverse undercompressive shock originating at the meniscus.
Bio: Andrea Bertozzi is a leading applied mathematician renowned for foundational contributions to nonlinear PDEs, fluid dynamics, and data-driven modeling, with applications spanning image processing, social dynamics, and swarming systems. A Princeton-trained mathematician, she is Professor of Mathematics (and Mechanical and Aerospace Engineering) at UCLA, where she served for two decades as Director of Applied Mathematics and holds the Betsy Wood Knapp Chair for Innovation and Creativity. A member of the U.S. National Academy of Sciences, Bertozzi is a highly cited researcher and recipient of numerous major honors, including the PECASE, SIAM Kovalevsky and Kleinman Prizes, and a Simons Math+X Investigator Award—among many others.
Host: Chris Fryer