Stokes Flow Behavior of an Accelerating Sphere

by Allen T. Hjelmfelt, Jr.,
Lyle F. Mockros,

Serial Information: Journal of the Engineering Mechanics Division, 1967, Vol. 93, Issue 6, Pg. 87-102

Document Type: Journal Paper


The relation for the force on a sphere undergoing an arbitrary rectilinear acceleration in a viscous fluid was established by Basset in the late nineteenth century. His derivation is based on neglecting the convective acceleration in the Navier Stokes equations. Basset's integro-differential equation indicates three components to the force: the viscous drag, the force necessary to accelerate the added fluid mass, and a term describing the history of acceleration. Basset's equation is applied to a sphere accelerating due to gravity. Velocity-time and displacement-time relations are obtained, and are presented in terms of tabulated functions. The added mass and history of acceleration terms of the force relation are investigated and found to be significant for all but conditions of quite high ratios of sphere density to fluid density. Displacements and corresponding times are measured for spheres accelerating to low terminal Reynolds numbers. The measured results are found to be in satisfactory agreement with the theory.

Subject Headings: Spheres | Navier-Stokes equations | Drag (fluid dynamics) | History | Displacement (mechanics) | Arbitration | Reynolds number | Agreements and treaties

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