Fractional Particle Dynamics in Harmonic Flows at Finite Reynolds Numbers

The stationary behavior of freely moving spherical particles under harmonic flow forcing from a Newtonian fluid ranging from low to high particle Reynolds (Re-p) numbers and from low to high Strouhal (Sl) numbers is studied numerically. This study extends the classical studies on harmonic Stokes flows by exploring particle dynamics in regimes where the convective contributions can no longer be neglected. High-order finite-element numerical simulations determine the order of the derivative that satisfies the long term (stationary) solution for the particle velocities. We propose a new history drag expression that correlates well (R-2 > 0.995) with the numerical results for (radius-based) particle Reynolds numbers up to 10, and for dimensionless frequency (S = SlRe(p)) values up to 10. Copyright (C) 2024 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)