SLOW VISCOUS ROTATION OF A SPHERE IN A CIRCULAR CYLINDER

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Abstract
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.