Faxén's theorem for nonsteady motion of a sphere through a compressible linear viscoelastic fluid in arbitrary flow

A generalization of the Faxén’s theorem to the nonsteady motion of a sphere through a compressible linear viscoelastic fluid in arbitrary flow is presented. From this result, expressions for the velocity autocorrelation function (VAF) and the time-dependent diffusion coefficient of the particle can be obtained. We analyze the behavior of the VAF and the time-dependent diffusion coefficient for different physical regimes of the suspending fluid. The relevance of the theorem to microrheology is discussed
Support of the Spanish Government under Project No. FIS2007-65869-C03-03 is appreciated. A.V.-Q. thanks the projects MODELICO-CM-52009/ESP-1691 from Comunidad de Madrid and “Programa propio de la Investigación de la Universidad Nacional de Educación a Distancia, 2010” for financial support. M.E. financial support provided by the Deutsche Forschungsgemeinschaft (DFG) via the Grant No. EL503/1-2 is also gratefully acknowledged. Support from BIFI is also appreciated