We investigate the dynamics of small inertial particles in a two-dimensional, steady Taylor-Green vortex flow. A classic study by Taylor (1940) showed that infinitely heavy inertial point particles (having density parameter $R=1$) are trapped by the flow separatrices when the particle Stokes number $\text{St}$, which measures the particle's inertia, is less than $1/4$. Here, we consider finitely heavy particles, incorporating the previously neglected effects of added mass and the Boussinesq-Basset history force. Using linear stability analysis near fixed points, we determine the critical parametric conditions in the $\text{St}\text{−}R$ plane that lead to particle trapping within vortex cells. Including the added mass effect identifies additional fixed points beyond the traditional ones located at the vortex cell corners, and we analyze their stability. Numerical analysis of the full nonlinear system confirms the existence of distinct particle behaviors—trapped, diffusive, and ballistic—depending on initial conditions, consistent with Nath et al. [Phys. Rev. Fluids 9, 014302 (2024)], with modifications due to added mass effect. We delineate the regions in the $\text{St}\text{−}R$ plane where these behaviors 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 $\text{St}$ and $R$.

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• Particle-laden flows
• Viscosity
• Lagrangian particle tracking
• Stokes equations