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Comment on "nonlinear viscosity and Grad's method"
1Department of Chemistry and Department of Physics, McGill University, 801 Sherbrooke Street West, Montreal, Quebec, Canada H3A 2K6.
Summary
The stress tensor in nonlinear viscosity does not vanish but shows a logarithmic dependence on the Rayleigh dissipation function. Uribe and García-Colín's equations for gas flow are incomplete, contradicting experimental shear stress evidence.
Area of Science:
- Nonlinear fluid dynamics
- Thermodynamics
- Rheology
Background:
- Uribe and García-Colín proposed a nonlinear viscosity model (eta = eta(0)sinh(-1)kappa/kappa) where kappa is a Rayleigh dissipation function.
- They suggested the associated stress tensor vanishes asymptotically with increasing velocity gradient magnitude.
Discussion:
- This comment refutes the vanishing stress tensor claim, demonstrating an asymptotic logarithmic dependence on kappa.
- The authors identify missing terms in Uribe and García-Colín's evolution equations for stress tensor components.
- These omissions lead to a predicted vanishing shear stress, conflicting with experimental gas flow observations.
Key Insights:
- The stress tensor in this nonlinear viscosity model exhibits a logarithmic kappa dependence, not asymptotic vanishing.
- Corrected evolution equations must include transversal velocity gradient terms.
- Accurate modeling is crucial for predicting phenomena like gas flow in tubes.
Outlook:
- Further investigation into nonlinear rheological models is warranted.
- Experimental validation remains critical for theoretical fluid dynamics.
- Refined models can improve understanding of complex fluid behavior under varying conditions.