Dilute polymer solution in steady shear flow: Non-Newtonian stress

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Abstract
An expression for the stress tensor of a dilute polymer solution under shear has been derived via renormalization-group theory. It is valid to first order in ε(=4-d, where d is the spatial dimensionality) to arbitrary flow rates. The polymeric contribution to the viscosity exhibits shear thinning for intermediate values of the shear. This thinning depends sensitively on the solvent quality (amount of excluded volume): for good solvents, the thinning is greatly enhanced, as is observed experimentally. The first and second normal stresses are also calculated. The ratio of the second to first normal stress for low shear is found to be a small negative quantity, approximately -0.03, nearly independent of solvent quality. This is in reasonable agreement with the sparse experimental results. A discussion of the Fokker-Planck operator and steady-state correlation functions for the Rouse theory is provided.