COMMENT ON INVARIANCE-PRINCIPLE FOR EXTENSION OF HYDRODYNAMICS - NONLINEAR VISCOSITY

Recently, Karlin, Dukek, and Nonnenmacher [Phys. Rev. E 55, 1573 (1997 )] obtained an ordinary differential equation of first order for the v iscosity factor, which was not solved by them. Here we solve their equ ation using two methods; Adams' method and the backward differentiatio n formula as implemented by the Numerical Algorithm Group library. Whe n the reduced longitudinal rate is greater than zero, the numerical so lutions (for different models) are within 4% with respect to the solut ion for the Maxwell model. However, if the longitudinal rate is negati ve, our results indicate that the equation may not provide a unique so lution for the viscosity factor.