Abstract
We consider the situation in which a colloidal particle modifies locally the solvent leading to a spatially dependent viscosity. This situation is typical for colloidal particles in crowded environment, for example DNA-grafted particles in a polymer solution, or a hot particle which implies a temperature gradient to a viscous liquid. By means of suitable approximations we calculate the dependence of the friction force on the profile of the local viscosity. Our results show that in the case of axially symmetric viscosity profile the friction force is sensitive to the anisotropy of the viscous profile whereas it is not sensitive to for-ahead asymmetries. Our results are crucial for active microrheology measurements where tracer particles are pulled through complex fluids.
Highlights
Particles in the nanometer size range coated with polymers are of growing importance for rather diverse applications [1]
Hydrodynamics was formulated by the modified Stokes equation with non-uniform spherically symmetric viscosity, which was solved by a regular perturbation approximation using the Green function method. We extend this analysis to account for anisotropic viscosity profile around a spherical particle, which may result from anisotropically grafted nanoparticles in a nonadsorbing polymer solution
In the following we focus on the dependence of the local velocity field on the local viscosity for anisotropic viscosity profiles
Summary
Particles in the nanometer size range coated with polymers are of growing importance for rather diverse applications [1]. Diffusion of isolated spherical nanoparticle in the simple molecular liquids is well-described by the Fick’s law, which says that the mean-square displacement changes linearly in time The rate of this change, the translational diffusion coefficient Dt, is related to the macroscopic viscosity of the solvent ηm (as measured rheometer) via Stokes-Sutherland-Einstein (SSE) relation [6, 8]; Dt = kBT/ζm where ζm is the hydrodynamic drag coefficient given by the Stokes equation ζm = 6π ηmR. For translational motion a scalar stream function, which transforms vectorial equations to the scalar ones is well-established We demonstrate that these properties hold for the modified Stokes equations with axisymmetric viscosity profile and provide a formalism to calculate the drag force experienced by a translating particle.
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