Resonant behavior of trapped Brownian particles in an oscillatory shear flow

Abstract

The response of harmonically trapped Brownian particles to an externally imposed oscillatory shear flow is explored by theory and computer simulation. The special case of a single trapped particle is solved analytically. We present explicit results for the time-dependent density and the velocity distribution. The response of the many-body problem is studied by computer simulations. In particular, we investigate the influence of oscillatory shear flow on the internal modes of the cluster. As a function of the shear oscillation frequency, we find resonant behavior for certain (antisymmetric) normal modes, implying that they can be efficiently excited by oscillatory shear. Our results are verifiable in experiments on dusty plasmas and trapped colloidal dispersions.

Brownian systems perturbed by mild shear: Comparing response relations

“…The response of a single underdamped particle can be evaluated analytically [36][37][38][39]. This appendix complements the results of Refs.…”

“…3(a). This quantity characterizes the morphology of the system: When shear is applied, the spatial distribution of the particles changes from circular to ellipsoidal (where principal axes of the ellipse are rotated with respect to the coordinate system), such that A becomes positive on average [35][36][37][38][39]. For overdamped particles, there is a simple monotonic relaxation towards the steady state, as was observed in Ref.…”

“…For N = 1, i.e., a single particle, we provide the analytical solution in Appendix D, complementing the results of Refs. [36][37][38][39] with the transient response.…”

“…6(b) and Refs. [37,39]). However, the transient response can be positive for a many-particle system, whereas it is always below or equals zero for a single particle [compare Figs.…”

“…One more fact is that underdamped Brownian particles have been investigated much less frequently than overdamped ones, because the latter model is more simple yet widely applicable in many practical cases. Even if the particle inertia is formally considered [19,26,32,[35][36][37][38][39], typically, little attention is paid to its effect on the system response. On the other hand, it was proven that inertial effects play an important role at short time scales [40][41][42][43][44][45].…”