Pipkin diagram

In qualitatively summarizing the flow behaviors of ER fluids, Partliasarathy [86] mapped out the frequency and strain dependence of the rheological properties of ER suspensions in the form of a Pipkin diagram [93], which is shown in Figure 40. The flow regimes are plotted as a function of the strain amplitude yo, and the dimensionless frequency,... 

Figure 40 The Pipkin diagram of the dynamic rheological behavior of ER fluids. Reproduced with permission from M. Parthasarathy and D.J. Klingenberg, J. Non-Newtonian Fluid Mech., 81 (1999) 83.

The Weissenberg number compares the elastic forces to the viscous effects. It is usually used in steady flows. One can have a flow with a small Wi number and a large De number, and vice versa. Sometimes the characteristic time of the flow in the deflnition of the Deborah number has been taken to be the reciprocal of a characteristic shear rate of the flow in these cases, the Deborah number and the Weissenberg number have the same definition. Pipkin s diagram (see Fig. 3.9 in Tanner 2000) classifies shearing flow behavior in terms of De and Wi, and provides a useful guide for the choice of constitutive equations. 

Schematic diagram showing the behavior of viscoelastic fluids in the limits of low strain rates, low amplitude deformations, and high strain rates. Adapted from Pipkin (1972).

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