Eur. Phys. J. E (2019) 42: 122
https://doi.org/10.1140/epje/i2019-11890-y

Regular Article

Dynamics of hydrodynamically coupled Brownian harmonic oscillators in a Maxwell fluid

Indian Institute of Science Education and Research Kolkata, 741246, Mohanpur, India

^* e-mail: sp12ip006@iiserkol.ac.in

Received: 28 October 2018
Accepted: 14 August 2019
Published online: 11 September 2019

Abstract

It has been shown recently that the coupled dynamics of micro-particles in a viscous fluid has many interesting aspects including motional resonance which can be used to perform two-point micro-rheology. However, it is expected that this phenomenon 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 characteristics. 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 features.