Relationships between Steady and Transient Flow Functions for Viscoelastic Polymer Liquids : Experimental and Theoretical Examination of the Gleissle Mirror Relations
Vol. 52, No. 3, pp. 172-184,
Jun. 2015
10.12772/TSE.2015.52.172
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Abstract
The objective of this study is to systematically investigate the relationships between steady flow functions and transient flow functions for viscoelastic polymer liquids. Using a strain-controlled rheometer (Advanced Rheometric Expansion System (ARES)), the steady shear flow properties and the transient shear flow properties of concentrated poly(ethylene oxide) (PEO) solutions have been measured over a wide range of shear rates and times. The validity of the three forms of the Gleissle mirror relations was examined by comparing them with the experimentally obtained results. In addition, the effect of nonlinearity on the applicability of these Gleissle mirror relations was discussed from a theoretical view-point by introducing the concept of a nonlinear strain measure. The main findings obtained from this study can be summarized as follows: (1) A nonlinear strain measure is decreased with an increase in strain magnitude, after reaching the maximum value at small strain range. This behavior is quite different from the theoretical prediction to satisfy the conditions of the Gleissle mirror relations. (2) The first mirror relation describing the equivalence between steady shear flow viscosity and shear stress growth coefficient is valid over a wide range of shear rates and is hardly affected by the nonlinearity of polymer solutions. (3) The second mirror relation expressing the equivalence between first normal stress coefficient and first normal stress growth coefficient is also applicable over a wide range of shear rates. This relation is, however, significantly influenced by the degree of nonlinearity (i.e., shape of a nonlinear strain measure) of polymer solutions. (4) The third mirror relation can be regarded as a very useful empirical model to predict the first normal stress coefficient from steady shear flow viscosity data, provided that an appropriate value of a shift factor is given.
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