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The Quarterly Journal of Mechanics and Applied Mathematics 1964 17(1):55-63; doi:10.1093/qjmam/17.1.55
© 1964 by Oxford University Press
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SLOW VISCOUS ROTATION OF A SPHERE IN A CIRCULAR CYLINDER

H. BRENNER and R. M. SONSHINE

( Department of Chemical Engineering, New York University )

Calculations are presented for the torque required to maintain the steady, symmetric rotation of a sphere in a viscous fluid bounded externally by an infinitely long circular cylinder. The solution is limited to situations in which the inertial terms in the equations of motion are negligible. Exact numerical values are provided for sphere-cylinder diameter ratios from 0 to 0.999. An approximate theory developed for the case where the ratio is very near nity is shown to agree well with the exact results.


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