Brownian motion and correlation functions in a viscoelastic fluid

A model for a solid sphere undergoing Brownian motion in a viscoelastic (Maxwell) fluid is described in terms of a non-Markovian Langevin equation. By solving this equation exactly, the particle's density-density and current-current time correlation functions are calculated. From the former, the time-dependent self-diffusion coefficient, D(t), is evaluated for an ensemble of Brownian particles. Then a numerical estimation of D(t) is performed for typical values of the sphere's parameters and for two viscoelastic fluids describable by Maxwell's model. A comparison of this result with the corresponding expressions for D(t) for a Newtonian fluid in the Stokes and Boussinesq-Basset approximations for the drag, shows that for the Maxwell fluid the behaviour of D(t) is analytic and similar to that of the Newtonian fluid in the Stokes regime. The authors find that elasticity has a minor influence on D(t) and that persistent correlations (long-time tails) in diffusion do not occur for this model. They also compare their results with other related works.