Considerations on Flow Classification Criteria

Flow classification is still an open problem in continuum mechanics. Among the presently available flow criteria, there are two that have an outstanding importance, namely, Tanner and Huilgol (1975) and Astrarita (1979). While the former is restricted to MWCSH, the latter was shown by Huilgol (1980) to fail for certain 3-D kinematics. In the present work we suggest a generalization of Tanner-Huilgol’s classification to encompass motions other then MWCSH. We also establish both the range of applicability of Astarita’s criterion and the relationship between the two criteria. The application to the Doubly Superposed Viscometric Flow of these two criteria and also of the one recently proposed by Thompson and Souza Mendes (2004), shows that it is advantageous to adopt the persistence-of-straining parameter proposed by Thompson and Souza Mendes (2004).