The effect of unsteady and history forces in the gravity convection of suspensions

The effect of unsteady and history forces on the motion of a particle is studied in the case of gravitational sedimentation (rise) of a spherical particle in the harmonic velocity field of a viscous carrier phase. An algorithm is proposed to calculate the history Basset-Boussinesq force. A parameter range is found for the case when the consideration of unsteady and history forces is required to correctly describe the mesoscale motions in a settling (rising) suspension.