Dynamics of hydrodynamically coupled Brownian harmonic oscillators in a Maxwell fluid
Indian Institute of Science Education and Research Kolkata, 741246, Mohanpur, India
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Accepted: 14 August 2019
Published online: 11 September 2019
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.
Key words: Flowing Matter: Liquids and Complex Fluids
© EDP Sciences / Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2019