History effects on the viscous motion of acoustically forced particles

摘要

We examine memory viscous effects on the motion of a particle in the vicinity of nodal points. The Basset history force has a fractional derivative dependence of order 3/2 on the particle displacement, and its contribution to the dynamics of acoustically forced particles is demonstrated for typical conditions occurring in acoustic separation devices. The inclusion of the Basset history force in the formulation has the net effect of changing the eigenfunctions of the problem from exponential to Mittag-Leffler functions, thus affecting the overall balance of forces considered.