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POLYFLOW - Empirical laws in rheology (Cox-Merz, Laun, Gleissle)
For some materials, there exist rules that link properties. Such laws are often empirical, and have to be handled with care. In particular, there is no theoretical proof regarding their validity. Quite often, they are applicable to polymer melts such as polyethylenes, polystyrenes, etc.
* The Cox-Merz rules:
see the document VE_guidelines_Cox_Merz.gif
* The Laun's rule (for LDPE): see the document VE_guidelines_Laun.gif
Similar laws may possibly be identified on the basis of careful experiments carried out on other melts.
* It is also interesting to mention an empirical rule stating that the log-log plot og N1 vs. tau is more or less a straight line with a slope of 2.
* Things are less easy for the second normal stress difference N2. Often, N2 is significantly lower than N1, and also more difficult to measure. Actually, from the above relationships, one relates G" to the shear viscosity and G' to N1. There is probably "nothing available" for N2. Still, there remains an empirical information stating that N2 is about -0.1*N1.
* The Gleissle mirror relationships:
see the document VE_guidelines_Gleissle.gif
* The Gleissle mirror relationships extended for elongational flows:
see the document VE_guidelines_Gleissle_ext.gif
* H.A. Barnes, J.F. Hutton and K. Walters, An introcudtion to rheology, Elsevier, 1989.
* W.P. Cox and E.H. Merz, Correlation of dynamic and steady flow properties, J. Polym. Sci. 28 (1958) 619-622.
* W. Gleissle, Two simple time-shear rate relations combining viscosity and first normal stress coefficient in the linear and non-linear flow range, in G. Astarita, G. Marrucci, L. Nicolais (eds), Rheologi, vol. II; Plenum, New York, 1980.
* H.M. Laun, Prediction of elastic strains of polymer melts in shear and elongation, J. Rheol. 30 (1986) 459-501.
* C.W. Macosko, Rheology: principles, measurements, and applications, Wiley-VCH, 1994.