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Updated: Jul 7, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
Asymptotic analysis of tracer diffusivity in nonadsorbing polymer solutions
Tai-Hsi Fan1, Bin Xie, Remco Tuinier
1Department of Mechanical Engineering, University of Connecticut, Storrs, Connecticut 06269-3139, USA.
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.
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