Effects of History and Lift Forces on Particle Trajectories in Oscillatory Rotating Fluids

The effect of the Basset history force on particle trajectories within various flows is ex- amined theoretically and computationally. A set of model problems that describe rectilinear particle motion in a viscous fluid under the influence of the history force are first examined. Several numerical schemes for integrating the equations are compared and benchmarked against the exact analytical results, including some new ones, obtained by using Laplace transforms. Numerical methods are then applied to simulate particle tra- jectories in steady rotational flows in order to analyze the role of the Basset history force in the motion of particles. Simulations are also performed for the trajectories of non-neutrally-buoyant particles in a viscous fluid undergoing oscillatory rotational motion, in cases where the container undergoes oscillatory rigid-body rotation. In the absence of the history force, an oscillatory counter-centrifugation phenomenon is predicted in which heavy (light) particles may migrate toward (away from) the rotation axis at high enough frequencies, in contrast with ordinary centrifugation. By carrying out detailed parametric studies of the role of the history force, it is found that oscillatory counter- centrifugation persists even when the history term is taken into account. Besides the history force, the so-called lift force, which is also significant in the oscillatory rotational motion, is incorporated into the analysis of the particle dynamics and is shown to extend the parameter regime for which oscillatory counter-centrifugation might be observed. Finally, particle trajectories in flows that combine both steady and oscillatory rotating components are considered and their fascinating behaviors catalogued.