Drag measurements for axisymmetric motion of a torus at low Reynolds number

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Abstract
Measurements are presented for the drag on a torus moving along its axis of rotational symmetry at low Reynolds number. If D is the outside diameter of the torus, and d is the thickness in the axial direction, then the measurements cover the range s0 = 1 (the closed torus) to s0 = 135, where s0≡(D/d)−1. The effect of a coaxial cylindrical boundary (diameter H) is taken into account by an empirical correlation. The values of drag obtained by extrapolating to a fluid of infinite extent are in good agreement with the exact solution obtained by Majumdar and O’Neill. When πd(s0)1/2≪H, the empirical boundary correlation is consistent with the result of Brenner for a particle of arbitrary shape. Measurements with outer boundaries of square and circular cross section indicate that the relative effect of the two boundary shapes on the drag is the same for the torus as that found by Happel and Bart for a sphere. Empirical results are presented for the case in which the torus is strongly influenced by a coaxial cylindrical boundary.

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