najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2016-7-2-324-331najo-831Research ArticleCONTRIBUTED TALKSCONTRIBUTED TALKSSteady Stokes flow between confocal semi-ellipsesSteady Stokes flow between confocal semi-ellipsesMakeevI. V.MakeevI. V.

Kronverkskiy, 49, St. Petersburg, 197101

Kronverkskiy, 49, St. Petersburg, 197101

PopovI. Yu.PopovI. Yu.

Kronverkskiy, 49, St. Petersburg, 197101

Kronverkskiy, 49, St. Petersburg, 197101

popov1955@gmail.comITMO UniversityITMO University20161308202572Special Issue324331Copyright © Makeev I.V., Popov I.Y., 20252025Makeev I.V., Popov I.Y.Makeev I.V., Popov I.Y.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/831

Analytical solutions for the Stokes equations in a cavity bounded by two confocal semi-ellipses and two line segments are derived here. The exact solution for the stream function, in the form of a Fourier series, is obtained. Eddy structure is described for different boundary conditions.

Analytical solutions for the Stokes equations in a cavity bounded by two confocal semi-ellipses and two line segments are derived here. The exact solution for the stream function, in the form of a Fourier series, is obtained. Eddy structure is described for different boundary conditions.

Stokes flowbiharmonic equationStokes flowbiharmonic equationThis work was partially financially supported by the Government of the Russian Fed- eration (grant 074-U01), by Ministry of Science and Education of the Russian Federation (GOSZADANIE 2014/190, Projects No 14.Z50.31.0031 and No. 1.754.2014/K), by grant MK-5001.2015.1 of the President of the Russian Federation, by grant 16-11-10330 of Russian Science Foundation.This work was partially financially supported by the Government of the Russian Fed- eration (grant 074-U01), by Ministry of Science and Education of the Russian Federation (GOSZADANIE 2014/190, Projects No 14.Z50.31.0031 and No. 1.754.2014/K), by grant MK-5001.2015.1 of the President of the Russian Federation, by grant 16-11-10330 of Russian Science Foundation.ReferencesLi D. Encyclopedia of Microfluidics and Nanofluidics, 2008 Springer, New York.Li D. Encyclopedia of Microfluidics and Nanofluidics, 2008 Springer, New York.Rivera J. L. and Starr F. 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The authors declare that there are no conflicts of interest present.