Validity of Stokes Theory for Accelerating Spheres

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Abstract
Measured displacement-time relations for spheres gravitationally accelerating from rest through viscous fluids are compared with the displacement-time relations predicted by the Stokes flow solution. The Stokes flow solution, consisting of a viscous drag, an added mass effect, and a history-of-the-motion integral, agrees with experimental values over a range that is larger than expected. The total dimensionless distance for which the theoretical and measured values agree depends on the ratio of sphere density to fluid density. The instantaneous Reynolds number at the point of departure between measurements and theory depends on the Stokes theory terminal Reynolds number. For the experiments reported, the theory is valid to points for which the instantaneous Reynolds number is as high as 10,000.

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