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 | \( dimensionless \) | \( dimensionless \) |
| \( \lambda \) = The Relaxation Time of the Fluid (A Measure of How Quickly the Fluid Returns to its Equilibrium State after Deformation) | \(sec\) | \(s\) |
| \( \dot{\gamma} \) = The shear rate (The Rate at which te Fluid is Deformed) | \(sec\) | \(s\) |
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).
- Low Weissenberg Number () - The relaxation time of the fluid is much shorter than the characteristic flow time. This means the fluid has enough time to relax during the deformation, and its behavior is dominated by viscous forces. The fluid will exhibit more Newtonian-like behavio
- Intermediate Stokes Number () - The relaxation time and the flow time are comparable. Elastic and viscous effects become equally important, and the fluid's viscoelastic nature is significant.
- High Weissenberg Number () - The relaxation time is much longer than the characteristic flow time. The fluid does not have enough time to relax during the deformation. Elastic forces dominate, leading to phenomena like high normal stresses, recoil, and other elastic effects. The fluid exhibits significant non-Newtonian behavior.
Weissenberg Number vs Deborah Number Differences
- 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.
