title: Asymptotic analysis of tracer diffusivity in nonadsorbing polymer solutions.
abstract: We present an asymptotic and scaling analysis of the long-time self-diffusivity of a Brownian spherical particle in dilute polymer solutions with nonadsorbing chains. The polymer depletion zone near the particle surface is described by a continuous polymer density profile. Hydrodynamics formulated by the modified Stokes equation with nonuniform viscosity is solved by a regular perturbation approximation using the Green function method. The asymptotes predict how polymer depletion alters the friction a spherical particle experiences during translational and rotational motion within a quiescent fluid. The analysis agrees very well with full numerical computation, which enables us to investigate the scaling law for the polymer-mediated retardation effect using a stretched exponential form that is commonly applied by experimentalists. The scaling exponents revealed are consistent with the nominal values from collected experiment observations.
authors.affiliation: Department of Mechanical Engineering, University of Connecticut, Storrs, Connecticut 06269-3139, USA.
authors.forename: Tai-Hsi
authors.initials: TH
authors.lastname: Fan
authors.forename: Bin
authors.initials: B
authors.lastname: Xie
authors.forename: Remco
authors.initials: R
authors.lastname: Tuinier