Two new methods for the approximate determination of the initial coefficient of the first normal stress difference (Q1071610)

Two methods for determining the initial coefficient of the first normal stress difference are presented. They are based on the evaluation of the steady viscosity function \(\eta\) (\({\dot \gamma}\)) and the viscosity function \(\eta^+({\dot \gamma},t)\) at the start-up of a flow with a very small rate of deformation \({\dot \gamma}<{\dot \gamma}_ 0\). For the functions \(\eta\) (\({\dot \gamma}\)) and \(\eta^+({\dot \gamma}t)\), equations are given which can be used for a simple evaluation of the integral relationships obtained for \(\psi_{10}\). The values for \(\psi_{10}\) calculated by the two methods are compared with values obtained by the well-known methods via measurement of the \(\psi_ 1({\dot \gamma})\) or \(\eta\) ''(\(\omega)\)/\(\omega\) functions and extrapolation to zero). Both methods give values which are in satisfactory agreement with the experimental values.