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

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[ρ ₀] 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 ρ ₀R³ 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.