Dynamics of two trapped Brownian particles: shear-induced cross-correlations

TL;DR

This paper analytically investigates how shear flow influences the positional correlations of two trapped Brownian particles, revealing shear-induced cross-correlations and their dependence on flow rate, trap distance, and orientation.

Contribution

It provides the first analytical calculation of shear-induced cross-correlations in a two-particle Brownian system under shear flow, including their dependence on system parameters.

Findings

Shear induces cross-correlations between orthogonal particle fluctuations.

Cross-correlations are linear in shear rate and asymmetric in time.

Correlation functions depend on the orientation of the particle connection vector.

Abstract

The dynamics of two Brownian particles trapped by two neighboring harmonic potentials in a linear shear flow is investigated. The positional correlation functions in this system are calculated analytically and analyzed as a function of the shear rate and the trap distance. Shear-induced cross-correlations between particle fluctuations along orthogonal directions in the shear plane are found. They are linear in the shear rate, asymmetric in time, and occur for one particle as well as between both particles. Moreover, the shear rate enters as a quadratic correction to the well-known correlations of random displacements along parallel spatial directions. The correlation functions depend on the orientation of the connection vector between the potential minima with respect to the flow direction. As a consequence, the inter-particle cross-correlations between orthogonal fluctuations can have zero, one or two local extrema as a function of time. Possible experiments for detecting these predicted correlations are described.