Response of active Brownian particles to shear flow

Kiryl Asheichyk, Alexandre P. Solon, Christian M. Rohwer, Matthias Krüger

Published 2018-12-20Version 1

We study the linear response of interacting active Brownian particles in an external potential to simple shear flow. Using a path integral approach, we derive the linear response of any state observable to initiating shear in terms of correlation functions evaluated in the unperturbed system. For systems and observables which are symmetric under exchange of the $x$ and $y$ coordinates, the response formula can be drastically simplified to a form containing only state variables in the corresponding correlation functions (compared to the generic formula containing also time derivatives). This simplified form is advantageous for analytical and numerical computations, as well as experimental measurements. In general, the shear couples to the particles by translational as well as rotational advection, but in the aforementioned case of $xy$ symmetry only translational advection is relevant in the linear regime. We test our response formulas analytically in solvable cases and numerically in a specific setup. In particular, we investigate the effect of a shear flow on the morphology of $N$ confined active particles in interaction, where we find that the activity increases the response.