Trapping and Transport of Inertial Particles in a Taylor-Green Vortex: Effects of Added Mass and History Force

Abstract

We investigate the dynamics of small inertial particles in a two-dimensional, steady Taylor-Green vortex flow. A classic study by Taylor (2022) showed that heavy inertial point particles (having density parameter R = 1) are trapped by the flow separatrices when the particle Stokes number St, which measures the particle's inertia, is less than 1/4. Here, we consider finitely dense particles, incorporating the previously neglected effects of added mass and the Boussinesq-Basset history force. Using linear stability analysis near stagnation points, we determine the critical parametric conditions in the St-R plane that leads to particle trapping within vortex cells. We identify additional stagnation points perceived by inertial particles, beyond the traditional ones at vortex cell corners, when the added mass effect is included, and we analyze their stability. Numerical analysis of the full nonlinear system confirms the existence of distinct particle behaviours--trapped, diffusive, and ballistic--depending on initial conditions, consistent with Nath et al. (2024), with modifications due to added mass effect. We delineate the regions in the St-R plane where these behaviours dominate based on the prominent particle dynamics. However, when both the history force and added mass effect are included, all particles exhibit ballistic motion regardless of St and R.