Dilute Polymer Solution in Steady Shear Flow: Non-Newtonian Stress

An expression for the stress tensor of dilute polymer solution under shear has been derived via renormalization-group theory. It is valid to first order in epsilon (=4 - spatial dimensionality) and for 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.