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Calculating the Motion of a Viscous Fluid that Partially Fills a Cylindrical Cavity

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Abstract

The plane-parallel steady motion of a viscous incompressible fluid that partially fills a cylindrical rotating cavity is under consideration. The region occupied by the fluid is simply connected, with two points of a sliding three-phase contact, and the contact angles at which the fluid approaches the walls are specified at these points. The free boundary of the fluid is curvilinear. There is a slip condition at the interface between the fluid and solid wall, which corresponds to proportionality of tangential stresses of a velocity difference of the solid and fluid particles. The flow region is conformally mapped onto a rectangle. The vortex and current function with a given slip coefficient and different rotation velocities of the cylinder are calculated.

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Authors and Affiliations

  1. Lavrent’ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia

    Yu. V. Pivovarov

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  1. Yu. V. Pivovarov
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Correspondence to Yu. V. Pivovarov.

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Original Russian Text © Yu.V. Pivovarov.

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 60, No. 3, pp. 106–119, May–June, 2019.

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Pivovarov, Y.V. Calculating the Motion of a Viscous Fluid that Partially Fills a Cylindrical Cavity. J Appl Mech Tech Phy 60, 491–502 (2019). https://doi.org/10.1134/S0021894419030118

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  • DOI: https://doi.org/10.1134/S0021894419030118

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