Persistence of straining and flow classification

Astarita [J. Non-Newton Fluid Mech. 6 (1979) 69-76] proposed a local and objective criterion to classify flows. His criterion is not restricted to motions with constant relative principal stretch history, and is essentially an attempt to quantify the stretch-relieving rotation experienced by the flowing material. Huilgol [Rheol. Acta 7 (1980) 91-95] analyzed Astarita's work and showed, through examples, some inconsistencies which rendered it useless as a general flow criterion. The present work revisits Huilgol's examples and discusses in detail the underlying physics that make Astarita's criterion to fail for certain flows. This analysis leads to a new criterion for flow classification based on the concept of persistence of straining. A key kinematic entity introduced in the proposed criterion is the π-plane, a plane that is normal to the relative-rate-of-rotation vector. For a more comprehensive criterion, other parameters are needed in addition to a persistence-of-straining parameter. Although emphasis is given to isochoric motions, a compressibility parameter is also introduced to encompass non-isochoric flows. The proposed kinematic criterion is local, frame-indifferent and is not restricted to particular classes of flows. Detailed analyses of some representative flows are given.