Hydrodynamic interaction of particles with grafted polymer brushes and applications to rheology of colloidal dispersions

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Abstract
We calculate the lubrication force that acts in the normal direction between spherical surfaces bearing grafted polymer brushes and immersed in a viscous fluid. Brinkman’s equation is employed to describe the flow in the brushes. For noncompressed brushes we include a slip approximation that applies to poorly permeable brushes of arbitrary density profile. For the step-function profile we present an analytical representation of the force valid for any separation. For compressed brushes we assume the density to increase homogeneously through the gap depending only on the local separation and derive an integral representation for the force along with analytical approximations valid up to rather strong compression. Our results generalize earlier estimates, providing convenient representations for analyses of hydrodynamic interaction between polymerically stabilized colloidal particles. As the simplest application we calculate the viscosity of a non-Brownian suspension of such particles for comparison with the measured high-shear viscosity for polymerically stabilized lattices.

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