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Theory for undercompressive shocks in tears of wine

Yonatan Dukler1,*, Hangjie Ji1,†, Claudia Falcon1,‡, and Andrea L. Bertozzi1,2,§

  • 1Department of Mathematics, University of California, Los Angeles, Los Angeles, California 90095, USA
  • 2Department of Mechanical and Aerospace Engineering Department, University of California, Los Angeles, Los Angeles, California 90095, USA

  • *ydukler@math.ucla.edu
  • †hangjie@math.ucla.edu
  • ‡cfalcon@math.ucla.edu
  • §bertozzi@math.ucla.edu
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Phys. Rev. Fluids 5, 034002 – Published 17 March, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.034002

Abstract

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.

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Physics Subject Headings (PhySH)

Synopsis

Why My Wine Glass Cries

Published 17 March, 2020

An unstable shock wave causes the famous “tears” that form on a wine glass, according to a new model.

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Article Text

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Phys. Rev. Fluids 5, 034002– Published 17 March, 2020
  • Received 17 September 2019
  • Accepted 11 February 2020
Article part of CHORUS
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