Transport properties of concentrated polymer solutions: Hydrodynamic mean field theory of the viscosity of a sphere suspension

Abstract

The hydrodynamic mean field theory of the preceeding paper [C. Y. Mou and S. A. Adelman, J. Chem. Phys. 69,xxx(1978)] is applied to analytically calculate the concentration ρ₀ dependent viscosity η[ρ₀] for a suspension of spherical particles of radius R. One finds that η[ρ₀]=η₀[1+5/2φλ], where η₀ is the solvent viscosity, φ=4π/3 ρ₀R³ is the solute volume fraction, and where λ=2/3φ⁻¹{5/2φ−1+[(1−5/2φ)² +3φ]^1/2}. To order φ², η[ρ₀]=η₀[1+5/2φ +K (5/2φ)²] where the order φ term is the Einstein shift and where the Huggins constant K=0.70. This result for K is in good agreement with previous theoretical estimates. The full form of η[ρ₀] is compared with the experimental results of Cheng and Schachman for 2700 Å polystyrene latex spheres. Agreement between theory and experiment is fair. The discrepancy is attributed to neglect of concentration dependence in the sphere–sphere pair correlation functions and neglect of attractive intermolecular forces in the present theory.