Weissenberg number, abbreviated as \(Wi\), a dimensionless number, used in fluid mechanics to characterize the behavior of viscoelastic fluids, particularly in flows where elastic effects are significant. It represents the ratio of elastic forces to viscous forces in the fluid. It's important to note that the exact definition of the Weissenberg number can vary depending on the specific flow geometry and the way the characteristic process time is defined (using shear rate for shear flow, elongation rate for extensional flow).
Weissenberg number formula |
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\( Wi \;=\; \lambda \cdot \dot{\gamma} \) (Weissenberg Number) \( \lambda \;=\; \dfrac{ Wi }{ \dot{\gamma} }\) \( \dot{\gamma} \;=\; \dfrac{ Wi }{ \lambda }\) |
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| Symbol | English | Metric |
| \( Wi \) = Weissenberg Number | \( dimensionless \) | \( dimensionless \) |
| \( \lambda \) = Relaxation Time of the Fluid (A Measure of How Quickly the Fluid Returns to its Equilibrium State after Deformation) | \(sec\) | \(s\) |
| \( \dot{\gamma} \) = Shear Rate (The Rate at which te Fluid is Deformed) | \(sec\) | \(s\) |
In the field of polymer rheology, the Weissenberg number is used for understanding and predicting the complex flow behavior of polymer solutions and melts during processing and applications.
- Weissenberg Number emphasizes the competition between elastic and viscous stresses in a flow, often used in analyzing flow instabilities or normal stress differences.
- Deborah Number emphasizes the time scale of the material response relative to the flow, often used to describe whether a material behaves more like a fluid or a solid in a given process.
