Long-time persistence of hydrodynamic memory boosts microparticle transport

Abstract

In a viscous fluid, the past motion of an accelerating particle is retained as an imprint on the vorticity field, which decays slowly as t −3/2 . At low Reynolds number, the Basset-Boussinesq-Oseen (BBO) equation correctly describes nonuniform particle motion, capturing hydrodynamic memory effects associated with this slow algebraic decay. Using the BBO equation, we numerically simulate driven single-particle transport to show that memory effects persist indefinitely under rather general driving conditions. In particular, when driving forces do not vary smoothly, hydrodynamic memory substantially lowers the effective transport friction. Remarkably, this enables coasting over a spatially uneven potential that otherwise traps particles modeled with pure Stokes drag. Our results provide direct physical insight into role of particle-fluid coupling in nonequilibrium microparticle transport. THE BBO EQUATIONThe Basset-Boussinesq-Oseen (BBO) equation [3,6,17] is a Lagrangian description [4] of the velocity of a rigid sphere of radius R, m, and density ρ s , moving nonuniformly through an incompressible Newtonian fluid of density ρ and viscosity η. The limit of zero Reynolds and Mach number is assumed, along with no-slip boundary conditions. Expressing the velocity v of the sphere relative to the background fluid in terms of the relevant physical parameters, the BBO equation takes the following form:

Effects of Hydrodynamic Backflow on the Transmission Coefficient of a Barrier-Crossing Brownian Particle

“…It remains to be seen whether such enhancements in the rate are experimentally observable and can be traced back to backflow effects. However, their occurrence appears to be consistent with the enhancements in transport properties that have been seen in the simulations of particle motion in tilted washboard potentials alluded to in the Introduction − and with the finding that hydrodynamic memory effects can persist indefinitely under fairly general driving conditions . The physical basis for these different phenomena is not entirely clear, but a lowering of the particle’s effective friction coefficient may be one possibility …”

“…However, their occurrence appears to be consistent with the enhancements in transport properties that have been seen in the simulations of particle motion in tilted washboard potentials alluded to in the Introduction 25−28 and with the finding that hydrodynamic memory effects can persist indefinitely under fairly general driving conditions. 27 The physical basis for these different phenomena is not entirely clear, but a lowering of the particle's effective friction coefficient may be one possibility. 27 The present treatment of backflow effects on barrier crossing has been restricted to the case of Markovian friction [for which K(t) = 2δ(t) and the Stokes force F S (t) in eq 3 is just −ζv(t)], but it can be generalized to consider nonlocal friction as well, corresponding to F S (t)= −ζ ∫ 0 t dt′K(t − t′)x(t′), if it is accepted, as argued in ref 41, that hydrodynamic and frictional memory are related as…”

“…27 The physical basis for these different phenomena is not entirely clear, but a lowering of the particle's effective friction coefficient may be one possibility. 27 The present treatment of backflow effects on barrier crossing has been restricted to the case of Markovian friction [for which K(t) = 2δ(t) and the Stokes force F S (t) in eq 3 is just −ζv(t)], but it can be generalized to consider nonlocal friction as well, corresponding to F S (t)= −ζ ∫ 0 t dt′K(t − t′)x(t′), if it is accepted, as argued in ref 41, that hydrodynamic and frictional memory are related as…”

“…The potential for short-time memory to impact transition rates suggests that the barrier-crossing dynamics of actual colloidal particles (as opposed to abstract reaction coordinates) could be modified by a non-Markovian process known as hydrodynamic backflow, which results from the early time transfer of momentum back to a moving particle by the fluid molecules that it displaces in its immediate neighborhood. , The forces generated by backflow are referred to as Basset forces, their action leading to hydrodynamic (rather than frictional) memory. The existence of a colored noise spectrum of thermal fluctuations in the environment of the particle and a long t –3/2 tail in its velocity autocorrelation function are the characteristic signatures of hydrodynamic memory, − and both have been observed in experiments on the motion of single optically trapped microspheres in simple fluids. − Recent simulations have also shown that the phenomenon can strongly influence particle transport in tilted washboard potentials, causing giant enhancements as well as itinerancy in the particle’s diffusion. − However, its possible effect on barrier crossing per se does not appear to be well-studied. The goal of this paper is to see if the application of Kramers’ model of activated dynamics to the random motion of a particle experiencing Basset, frictional, and external forces can advance our understanding of the process.…”

Introducing Memory in Coarse-Grained Molecular Simulations

“…149,150 Thus, they showed that the Basset−Boussinesq equation is also applicable in the microscopic regime, with parameters that can be directly derived from the memory function. 61 Seyler and Presse 151,152 investigated the influence of this "Basset history force" on the motion of microspheres in oscillatory flow and a periodic potential. They showed that hydrodynamic memory significantly enhances the mobility of microspheres and helps them to escape potential wells in which they would otherwise remain trapped for much longer times.…”