Dimensional considerations for visco-elastic fluids

It has been a common practice to describe visco-elastic fluid behaviour in steady shear in terms of a shear stress Ty and the first normal stress difference (N ) both of which are functions of shear rate. Generally, a fluid relaxation or characteristic time, Xf, (or a spectrum) is defined to quantify the viscoelastic behaviour. There are several ways of defiiung a characteristic time by combining shear stress and the first normal stress difference, e.g. the so-called Maxwellian relaxation time is given by  

in the limit of yy 0, both (= Ni/Vyx ) and jx = Xy / j/yx) approach constant values, 7/ also approaches a constant value. Though equation (1.31) defines a fluid characteristic time as a fimction of shear rate, its practical utility is severely limited by the fact that in most applications, the kinematics (or shear rate) is not known a priori. Many authors [Leider and Bird, 1972 Grimm, 

1978] have obviated this difficulty by introducing the following alternative definition of A,/  

This definition is based on the assumption that both Ni and Xya, can be approximated as power-law functions of shear rate in the range of conditions of 

By re-defining A/ in this manner, it is not necessary to extend the rheological measurements to the zero-shear region. Note that in the limit of Yyx 0, p 1, n and thus equation (1.32) coincides with equation (1.31). 

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