Geometric mixing

Mixing fluids often involves a periodic action, like stirring one’s tea. But reciprocating motions in fluids at low Reynolds number, in Stokes flows where inertia is negligible, lead to periodic cycles of mixing and unmixing, because the physics, molecular diffusion excepted, is time reversible. So...

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Bibliographic Details
Published in:Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences physical, and engineering sciences, 2020-09, Vol.378 (2179), p.20200168-20200168
Main Authors: Arrieta, Jorge, Cartwright, Julyan H. E., Gouillart, Emmanuelle, Piro, Nicolas, Piro, Oreste, Tuval, Idan
Format: Article
Language:English
Subjects:
Review
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Summary:Mixing fluids often involves a periodic action, like stirring one’s tea. But reciprocating motions in fluids at low Reynolds number, in Stokes flows where inertia is negligible, lead to periodic cycles of mixing and unmixing, because the physics, molecular diffusion excepted, is time reversible. So how can fluid be mixed in such circumstances? The answer involves a geometric phase. Geometric phases are found everywhere in physics as anholonomies, where after a closed circuit in the parameters, some system variables do not return to their original values. We discuss the geometric phase in fluid mixing: geometric mixing. This article is part of the theme issue ‘Stokes at 200 (part 2)’.
ISSN:1364-503X
1471-2962
DOI:10.1098/rsta.2020.0168