Hydrodynamic memory and driven microparticle transport: hedging against fluctuating sources of energy

In a viscous fluid, the motion of an accelerating particle is retained as an imprint on the vorticity field, giving rise to the famous t^-3/2 decay of the velocity autocorrelation. For nonuniform particle motion at low Reynolds number, this hydrodynamic memory effect is captured by the Basset-Boussinesq-Oseen (BBO) equation, which can be derived from various physical perspectives, including (fluctuating) hydrodynamics and kinetic theory. Moreover, finite-temperature dynamics can be modeled by using fluctuation-dissipation to reincorporate (correlated) thermal noise, turning BBO into a generalized Langevin equation. In this work, we numerically solve the BBO equation to simulate driven microparticles and show that hydrodynamic memory generally reduces transport friction, particularly when driving forces do not vary smoothly. Remarkably, this enables coasting over uneven potentials that otherwise trap particles modeled by pure Stokes drag. Our results are germane to questions surrounding intracellular transport efficiency and, more generally, provide direct physical insight into the role of particle-fluid coupling in microparticle transport.