Weissenberg number

For instance, in simple steady shear, the Weissenberg number, often abbreviated as Wi or We, is defined as the shear rate

Since this number is obtained from scaling the evolution of the stress, it contains choices for the shear or elongation rate, and the length-scale.

While Wi is similar to the Deborah number and is often confused with it in technical literature, they have different physical interpretations.

The Weissenberg number indicates the degree of anisotropy or orientation generated by the deformation, and is appropriate to describe flows with a constant stretch history, such as simple shear.

In contrast, the Deborah number should be used to describe flows with a non-constant stretch history, and physically represents the rate at which elastic energy is stored or released.