Equation of motion for a small rigid sphere in a nonuniform flow
1983/04/01 by Martin R. Maxey, Martin Maxey, James J. Riley · 3,384 citations
Engineering · #Classical mechanics #Equations of motion #Flow (mathematics) #Fluid Dynamics and Turbulent Flows #Granular flow and fluidized beds #Mechanics #Motion (physics) #Particle Dynamics in Fluid Flows #Physics #Potential flow #Stokes flow
paper · doi:10.1063/1.864230
published in The Physics of Fluids 26(4), 883-889 (AIP Publishing)
openalex publication_date 1983/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Abstract
The forces on a small rigid sphere in a nonuniform flow are considered from first prinicples in order to resolve the errors in Tchen’s equation and the subsequent modified versions that have since appeared. Forces from the undisturbed flow and the disturbance flow created by the presence of the sphere are treated separately. Proper account is taken of the effect of spatial variations of the undisturbed flow on both forces. In particular the appropriate Faxen correction for unsteady Stokes flow is derived and included as part of the consistent approximation for the equation of motion.
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