Dynamics of hydrodynamically coupled Brownian harmonic oscillators in a Maxwell fluid

TL;DR

This paper develops a theoretical framework for the equilibrium dynamics of two hydrodynamically coupled Brownian harmonic oscillators in a Maxwell viscoelastic fluid, revealing unique correlation behaviors influenced by the fluid's elasticity.

Contribution

It introduces a new theory describing coupled Brownian oscillators in a Maxwell fluid, extending previous viscous fluid models to include viscoelastic effects and their impact on correlation functions.

Findings

Correlation functions are linearly related to delta-correlated noises in viscous fluids.

Auto and cross-correlation functions exhibit unique characteristics in Maxwell fluids.

Mean-square displacement functions align with established viscous fluid forms, with notable differences.

Abstract

Recently, many interesting features of the hydrodynamically coupled motions of the Brownian particles in a viscous fluid have been reported which are impossible for the uncoupled motions of the similar particles. However, it is expected that those physics in a viscoelastic fluid is much more interesting due to the presence of the additional frequency dependent elasticity of the medium. Thus, a theory describing the equilibrium dynamics of two hydrodynamically coupled Brownian harmonic oscillators in a viscoelastic Maxwell fluid has been derived which appears with new and impressive aspects. Initially, the response functions have been calculated and then the fluctuation-dissipation theorem has been used to calculate the correlation functions between the coloured noises present on the concerned particles placed in a Maxwell fluid due to the thermal motions of the fluid molecules. These correlation functions appear to be in a linear relationship with the delta-correlated noises in a viscous fluid. Consequently, this reduces the statistical description of a simple viscoelastic fluid to the statistical representation for an extended dynamical system subjected to delta-correlated random forces. Thereupon, the auto and cross-correlation functions in the time domain and frequency domain and the mean-square displacement functions of the particles have been calculated which are perfectly consistent with their corresponding established forms in a viscous fluid and emerge with exceptional characteristics.