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Brownian motion in viscoelastic flow Einarsson, Jonas


We consider the Brownian motion of a small spherical particle in viscoelastic flow. Even in absence of external flow or forcing the particle resistance is frequency-dependent which establishes a link between observed Brownian displacements and the linear rheology of the fluid [Mason, T.G., Weitz, D.A., 1995. PRL. 74, 1250.] Under external flow or forcing the frequency-dependent particle resistance may become anisotropic and non-symmetric due to fluid elasticity. We derive the Brownian mean-square displacements as function of time under the usual assumptions of statistical stationarity and equipartition. We also derive explicit results for the particle resistance via perturbation theory of the time-dependent Oldroyd-B model. We discuss potential applications of our results to Taylor dispersion and microrheology.

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