2018/05/16 by S. Paul, Paul, Shuvojit
Economics, Econometrics and Finance · Engineering · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Applied Physics (physics.app-ph) #Complex Systems and Time Series Analysis #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Soft Condensed Matter (cond-mat.soft)
paper · pdf · doi:10.48550/arxiv.1805.06147
openalex publication_date 2018/05/16 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
Recently, many interesting features of the hydrodynamically coupled motions\nof the Brownian particles in a viscous fluid have been reported which are\nimpossible for the uncoupled motions of the similar particles. However, it is\nexpected that those physics in a viscoelastic fluid is much more interesting\ndue to the presence of the additional frequency dependent elasticity of the\nmedium. Thus, a theory describing the equilibrium dynamics of two\nhydrodynamically coupled Brownian harmonic oscillators in a viscoelastic\nMaxwell fluid has been derived which appears with new and impressive aspects.\nInitially, the response functions have been calculated and then the\nfluctuation-dissipation theorem has been used to calculate the correlation\nfunctions between the coloured noises present on the concerned particles placed\nin a Maxwell fluid due to the thermal motions of the fluid molecules. These\ncorrelation functions appear to be in a linear relationship with the\ndelta-correlated noises in a viscous fluid. Consequently, this reduces the\nstatistical description of a simple viscoelastic fluid to the statistical\nrepresentation for an extended dynamical system subjected to delta-correlated\nrandom forces. Thereupon, the auto and cross-correlation functions in the time\ndomain and frequency domain and the mean-square displacement functions of the\nparticles have been calculated which are perfectly consistent with their\ncorresponding established forms in a viscous fluid and emerge with exceptional\ncharacteristics.\n