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# Weissenberg number

The Weissenberg number is a dimensionless number used in the study of viscoelastic flows. It is named after Karl Weissenberg. The dimensionless number is the ratio of the relaxation time of the fluid and a specific process time. For instance, in simple steady shear, the Weissenberg number, often abbreviated as Wi or We, is defined as the shear rate times the relaxation time ($Wi = \dot{\gamma} \lambda$). 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. Therefore the exact definition of all non dimensional numbers should be given as well as the number itself.