Inertial effects on particle dynamics

While the theory of suspension flows and particle dynamics is well understood under Stokes flow conditions when viscous forces dominate, little is known at finite Reynolds number when the inertial forces of the suspending fluid are important. In the present study, expressions are derived that allow for dynamic calculations of particle, drop, and bubble motion at finite Reynolds number. The results show a significant change in the temporal behavior of the force/velocity relationship from that derived from the unsteady Stokes equations, particularly as a body approaches its steady state. At finite Reynolds number, when the convective inertial effects are included, the hydrodynamic force on a body has much weaker history dependence on the past motion of the body and it reaches its steady state faster than what would be predicted if only the unsteady inertial effects are accounted for. When compared with numerical solutions of the Navier-Stokes equations, the analytical force expressions perform well up to a Reynolds number of 0.5. A common theme to the derivations is the use of the reciprocal theorem which provides for an efficient and elegant means for computing inertial effects in suspension mechanics. Connections with past approaches are made in light of these new applications of the reciprocal theorem