Dispersion of Inertial Particles in Cellular Flows: Influence of Added Mass and History Force

This study explores the transport and dispersion of heavy inertial particles in Taylor-Green (TG) vortex flows, accounting for added mass and the Boussinesq-Basset history force—effects often neglected in prior analyses. We examine particles with varying density ratios (R) and Stokes numbers (St), identifying critical parametric conditions that lead to particle trapping within vortex cells. Notably, the added mass effects generate additional stagnation points beyond conventional vortex corners, influencing transport behaviour. By analyzing the stability of these stagnation points, we classify transport dynamics into open and trapped trajectories. Our numerical results, excluding the history force, identify fractal boundaries in the St–R space that distinguish distinct transport behaviours such as diffusion, ballistic, and trapped dynamics using mean-squared displacement (MSD) metrics. Crucially, when the history force is included, all particles transition to ballistic motion, irrespective of their initial conditions, with only transient delays for low R and St values. This highlights the dominant role of memory effects in long-time particle dynamics. Our findings provide new insights into inertial particle transport in cellular flows, which are relevant to soft matter systems and environmental transport phenomena.