The dispersive effects of Basset history forces on particle motion in a turbulent flow

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Abstract
A calculation of the asymptotic particle diffusion coefficient in an unbounded stationary homogeneous turbulent flow is performed for a particle subjected to both added mass and Basset history forces, as well as the normal Stokes drag. The original value obtained by Tchen is shown to be in error by an additional term which for a sphere of diameter d is given by (d2/2πνf)σ, νf being the kinematic viscosity, and σ the covariance of the incipient relative velocity between particle and local fluid. Noticeably this term does not depend upon the particle density. This extra term is consistent with values obtained for the particle diffusion coefficient from a numerical simulation.