Considerations on kinematic flow classification criteria

Among the presently available flow classification criteria, the ones proposed by [R.I. Tanner, R.R. Huilgol, On a classification scheme for flow fields, Rheol. Acta 14 (1975) 959-962] and [G. Astarita, Objective and generally applicable criteria for flow classification, J. Non-Newt. Fluid Mech. 6 (1979) 69-76] are of particular interest. While the former is restricted to motions with constant relative principal stretch history (MWCRPSH), the latter was shown by [R. R. Huilgol, Comments on “Objective and generally applicable criteria for flow classification”, by G. Astarita, J. Non-Newt. Fluid Mech. 7 (1980) 91-95] to fail for certain 3D kinematics. In the present work we propose a modification of Tanner-Huilgol's classification criterion to encompass motions other than MWCRPSH. We also establish both the set of flows that constitute the range of applicability of Astarita's criterion and the relationship between the two criteria. An interesting subset of flows within this range was identified, the so-called quasi-plane flows. The generalized Maxwell rheometer flow and the doubly superposed viscometric flow are analyzed from the standpoint of these two criteria and also from the standpoint of the criterion recently proposed by [R.L. Thompson, P.R. Souza Mendes, Persistence of straining and flow classification, Int. J. Eng. Sci. 43 (1-2) (2005) 79-105]. The persistence-of-straining parameter presented in this last reference is shown to perform advantageously as a flow classification parameter.