Active Brownian motion with memory delay induced by a viscoelastic medium

TL;DR

This paper develops an analytical model for active Brownian particles in viscoelastic media, incorporating memory effects via a generalized Langevin equation, and predicts measurable delays in particle dynamics.

Contribution

It introduces a novel analytical framework for active Brownian motion with memory delay in viscoelastic environments, extending traditional models to include time-dependent friction kernels.

Findings

Derived analytical expressions for correlation functions and mean-square displacement.

Identified a memory-induced delay between propulsion force and particle orientation.

Predicted measurable effects in active colloids within viscoelastic fluids.

Abstract

By now active Brownian motion is a well-established model to describe the motion of mesoscopic self-propelled particles in a Newtonian fluid. On the basis of the generalized Langevin equation, we present an analytic framework for active Brownian motion with memory delay assuming time-dependent friction kernels for both translational and orientational degrees of freedom to account for the time-delayed response of a viscoelastic medium. Analytical results are obtained for the orientational correlation function, mean displacement and mean-square displacement which we evaluate in particular for a Maxwell fluid characterized by a kernel which decays exponentially in time. Further, we identify a memory induced delay between the effective self-propulsion force and the particle orientation which we quantify in terms of a special dynamical correlation function. In principle our predictions can be verified for an active colloidal particle in various viscoelastic environments such as a polymer solution.