Enhancement of mobility in an interacting colloidal system under feedback control

TL;DR

This paper proposes a feedback control scheme to significantly enhance the collective mobility of interacting colloidal particles in a tilted washboard potential, demonstrating robustness and inducing oscillations under certain conditions.

Contribution

It introduces a novel feedback control method that boosts colloidal transport efficiency and analyzes its effects using Smoluchowski and DDFT models, revealing large mobility enhancements.

Findings

Mobility can be increased by several orders of magnitude.

Optimal effects occur at intermediate trap stiffness and large particle numbers.

Feedback control induces velocity oscillations and is robust to small delays.

Abstract

Feedback control schemes are a promising way to manipulate transport properties of driven colloidal suspensions. In the present article we suggest a feedback scheme to enhance the collective transport of colloidal particles with repulsive interactions through a one-dimensional tilted washboard potential. The control is modelled by a harmonic confining potential, mimicking an optical "trap", with the center of this trap moving with the (instantaneous) mean particle position. Our theoretical analysis is based on the Smoluchowski equation combined with Dynamical Density Functional Theory (DDFT) for systems with hard-core or ultra-soft (Gaussian) interactions. For either type of interaction we find that the feedback control can lead to an enhancement of the mobility by several orders of magnitude relative to the uncontrolled case. The largest effects occur for intermediate stiffness of the trap and large particle numbers. Moreover, in some regions of the parameter space the feedback control induces oscillations of the mean velocity. Finally, we show that the enhancement of mobility is robust against a small time delay in implementing the feedback control.