Normal stress coefficient limiting primary

At low values of 7, the coefficients 1 and 2 approach the zero-shear-rate limits of j,o and 2,0 respectively. All the single-integral equations mentioned above predict for the limiting primary normal stress coefficient ... 

The relationship tells us that, in the limit of low shear rates, we still have only two parameters which are independent. The primary normal stress coefficient does not represent an independent property, but is deducable from the two parameters controlling the linear response, and r/o-... 

The third curve in the figure, denoted 7e, gives the amount of shear strain recovery subsequent to a removal of the external torque. There is an interesting observation. The linear increase of 7e with 7 at low shear rates is exactly determined by the zero shear rate values of the viscosity and the primary normal stress coefficient, 770 and This is revealed by the coincidence of the limiting curve 70(7 —0) with the dotted line representing the linear function... 

It should be noted that as t becomes large the lowest order term in the coefficient of the K-term is just 60, that is one half the zero-shear-rate value of the primary normal stress function. A similar result was obtained by Bird and Marsh (7) and by Carreau (14) from the slowly varying flow expansions of two continuum models. Hence the time-dependent behavior of the shear stress is related to the steady-state primary normal stress difference in the limit of vanishingly small shear rate. 

The 3.4 power dependence has been observed experimentally and predicted theoretically. Furthermore, the primary normal stress difference coefficient in the limit as y goes to zero, 4 1,0, is observed to be proportional to M raised to the 7.0 power that is. 

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