Resonant behavior of the spatial cross-correlation for particles embedded in viscoelastic shear flow

Abstract

Simultaneous inertial and diffusive motion of a harmonically trapped Brownian particle in a viscoelastic oscillatory shear flow is considered. A generalized Langevin equation with a power-law-type memory kernel is used to calculate the shear-induced cross-correlation functions between particle fluctuations along orthogonal directions in the shear plane. The mean angular momentum of the Brownian particles is found. The influence of the memory exponent in the dynamical regimes of the system is also investigated. It is established that in certain regions of the system parameters an interplay of the shear flow and memory effects can induce a multiresonance of the cross-correlation versus the shear frequency as well as a resonance of the angular momentum vs the shear frequency. Particularly, it is shown that the results about the behavior of cross-correlations in the system considered are significally different from some recently obtained results for models with Stokes friction.