Geodesic
Steady motion of a~ball in a~Stokes--Poiseuille flow
Sibirskij žurnal industrialʹnoj matematiki, Tome 18 (2015) no. 3, pp. 76-85

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The existence of steady solutions to the problem of the motion of a rigid ball in a cylindrical pipe filled with a viscous incompressible fluid is proved. The cross section of the pipe has an arbitrary form and the fluid flow is governed by the Stokes equations. At the infinity, the velocity profile tends to that of the Poiseuille flow. It is established that a steady solution exists for any position of the ball in the pipe. The ball performs a straight motion along the generatrices of the pipe and its linear and angular velocities depend on the position of the ball's center in the cross section of the cylinder.
Mots-clés : viscous incompressible fluid
Keywords: rigid body, cylindrical pipe, steady motion. 
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     author = {V. N. Starovoitov},
     title = {Steady motion of a~ball in {a~Stokes--Poiseuille} flow},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {76--85},
     publisher = {mathdoc},
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     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2015_18_3_a7/}
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V. N. Starovoitov. Steady motion of a~ball in a~Stokes--Poiseuille flow. Sibirskij žurnal industrialʹnoj matematiki, Tome 18 (2015) no. 3, pp. 76-85. http://geodesic.mathdoc.fr/item/SJIM_2015_18_3_a7/