NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2016, 7 (2), P. 324–331
Steady Stokes flow between confocal semi-ellipses
I.V. Makeev – ITMO University, Kronverkskiy, 49, St. Petersburg, 197101, Russia
I.Yu. Popov – ITMO University, Kronverkskiy, 49, St. Petersburg, 197101, Russia; popov1955@gmail.com
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.
Keywords: Stokes flow, biharmonic equation.
PACS 68.90.+g, 05.60.k, 62.10.+s
DOI 10.17586/2220-8054-2016-7-2-324-331
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