Weissenberg number
Encyclopedia
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
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.
While Wi 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.
Karl Weissenberg
Karl Weissenberg was an Austrian physicist, notable for his contributions to rheology and crystallography.The Weissenberg effect was named after him, as was the Weissenberg number...
. 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
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.
While Wi similar to the Deborah number
Deborah number
The Deborah number is a dimensionless number, often used in rheology to characterize the fluidity of materials under specific flow conditions. It was originally proposed by Markus Reiner, a professor at Technion in Israel, inspired by a verse in the Bible, stating "The mountains flowed before the...
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.