  A key assumption of polymer physics is that the random chains polymers extend
in flow. Recent experimental evidence has shown that polymer chains compress in
Couette flow in a manner counter to expectation. Here, scaling arguments
developed previously are used to determine the relationship between the
viscosity and chain radius of gyration. Scaling arguments determine the
viscosity-radius of gyration relationship to be such that the viscosity is
proportional to the radius to the power of 9. The viscosity is shown to be a
power law function of the radius, and to decrease with decreasing radius under
conditions where the chains are ideal random walks in concentrated solution.
Furthermore, this relationship is consistent with both the widely observed
viscosity-temperature and viscosity-shear rate behavior observed in polymer
rheology. The assumption of extension is not consistent with these observations
as it would require that the chains increase in size with increasing
temperature. Shear thinning is thus a result of a decreasing radius with
increasing shear rate as the radius is proportional to the the shear rate
raised to the power law exponent divided by 9. The thermal expansion
coefficient determines the variation in the power law exponents that are
measured for different polymer systems. Typical values on n enable the measured
reduction in coils size behavior to be fitted. Furthermore, the absurd notion
that polymer chains extend to reduce the viscosity implies that an increasing
chain size results in a reduced viscosity is addressed. This assumption would
require that the viscosity increases with reducing coil radius which is simply
unphysical.
