TY - JOUR
T1 - Asymmetric three-dimensional Stokes flows about two fused equal spheres
AU - Zabarankin, Michael
PY - 2007/9/8
Y1 - 2007/9/8
N2 - Exact solutions to three-dimensional Stokes flow problems for asymmetric translation and rotation of two fused rigid spheres of equal size have been obtained in toroidal coordinates. The problems have been reduced to three-contour equations for meromorphic functions from a certain class, and then the latter have been reduced to Fredholm integral equations of the second kind by the Mehler-Fock transform of order 1. For the specified class of functions, the equivalence of the corresponding three-contour and Fredholm equations has been established in the framework of Riemann boundary-value problems for analytic functions. As an illustration for the obtained solutions, the pressure has been calculated at the surface of the body for both problems, and resisting force and torque, experienced by the body in asymmetric translation and rotation, have been computed as functions of a geometrical parameter of the body.
AB - Exact solutions to three-dimensional Stokes flow problems for asymmetric translation and rotation of two fused rigid spheres of equal size have been obtained in toroidal coordinates. The problems have been reduced to three-contour equations for meromorphic functions from a certain class, and then the latter have been reduced to Fredholm integral equations of the second kind by the Mehler-Fock transform of order 1. For the specified class of functions, the equivalence of the corresponding three-contour and Fredholm equations has been established in the framework of Riemann boundary-value problems for analytic functions. As an illustration for the obtained solutions, the pressure has been calculated at the surface of the body for both problems, and resisting force and torque, experienced by the body in asymmetric translation and rotation, have been computed as functions of a geometrical parameter of the body.
KW - Asymmetric Stokes flow
KW - Exact solution
KW - Fredholm integral equation
KW - Fused spheres
KW - Mehler-Fock transform of general order
KW - Three-contour equation
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U2 - 10.1098/rspa.2007.1872
DO - 10.1098/rspa.2007.1872
M3 - Article
AN - SCOPUS:36349010306
SN - 1364-5021
VL - 463
SP - 2329
EP - 2350
JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
IS - 2085
ER -