Spherical particle motion in harmonic stokes flows

An analytical study is presented on the periodic motion of a small particle in a viscous fluid. Previous analytical and numerical contributions to the understanding of particle motion in time-dependent flows are reviewed. Pre vious works in this field addressed the long-term behavior of the particle (stationary solution) as opposed to the problem treated in this study, whic h includes initial transient effects. Also presented are the relative scali ng of the virtual mass, Stokes, and history drag forces for the long-term s olution following the fractional calculus theory. The general solution of t he particle momentum equation for unsteady Stokes flows is particularized t o a harmonic background fluid velocity. The effect of a nonzero initial rel ative velocity is studied, and a discussion on the relevance of the results to the Lagrangian simulation of turbulent multiphase flows is presented. T he present theoretical results are relevant to the transient motion of smal l particles in viscous flows such as the ones found in crystal growth proce sses, fluid markers, and dilute turbulent multiphase flows in general.