A quantitative analysis of the emergence of memory in the viscously coupled dynamics of colloids

TL;DR

This paper investigates how hydrodynamic interactions induce memory effects in the Brownian motion of colloidal particles, revealing that these effects depend on particle separation and trap stiffness, and can be modeled as a viscoelastic medium.

Contribution

It provides a quantitative framework linking hydrodynamic interactions to emergent memory effects, modeling particle pairs as a single viscoelastic medium.

Findings

Memory effects decrease with particle separation.

Memory effects increase with trap stiffness imbalance.

The system can be modeled as a single viscoelastic medium.

Abstract

We provide a quantitative description of the evolution of memory from the apparently random Markovian dynamics of a pair of optically trapped colloidal microparticles in water. The particles are trapped in very close proximity of each other so that the resultant hydrodynamic interactions lead to non-Markovian signatures manifested by the double exponential auto-correlation function for the Brownian motion of each particle. In connection with the emergence of memory in this system, we quantify the storage of energy and demonstrate that a pair of Markovian particles - confined in individual optical traps in a viscous fluid - can be described in the framework of a single Brownian particle in a viscoelastic medium. We define and quantify the equivalent storage and loss moduli of the two-particle system, and show experimentally that the memory effects reduce with increasing particle separation and increase with a skewed stiffness ratio between the traps.