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The inertial response of a particle to turbulent flows is a problem ofrelevance to a wide range of environmental and engineering problems. Theequation most often used to describe the force balance is the Maxey-Rileyequation, which includes in addition to buoyancy and steady drag forces, anunsteady Basset drag force related to past particle acceleration. Here weprovide a historical review of how the Maxey-Riley equation was developed andhow it is only suited for studies where the Reynolds number is less than unity.Revisiting the innovative mathematical methods employed by Basset (1888), weintroduce an alternative formulation for the unsteady drag for application to abroader range of particle motions. While the Basset unsteady drag is negligibleat higher Reynolds numbers, the revised unsteady drag is not.

On the Maxey-Riley equation of motion and its extension to high Reynolds numbers