Nonlinear viscosity and velocity distribution function in a simple longitudinal flow

Area of Science:

• Fluid Dynamics
• Statistical Mechanics
• Non-equilibrium Thermodynamics

Background:

• Compressible flow phenomena are crucial in various scientific and engineering applications.
• Understanding non-Newtonian fluid behavior is essential for accurate modeling.
• Kinetic theory provides a microscopic approach to macroscopic fluid properties.

Purpose of the Study:

• To analyze a specific compressible flow velocity field using kinetic models.
• To investigate the influence of the longitudinal deformation rate on gas expansion and condensation.
• To characterize the non-Newtonian behavior and velocity distribution functions.

Main Methods:

• Analysis of the Boltzmann equation and the Bhatnagar-Gross-Krook (BGK) kinetic model.
• Investigation of a compressible flow with velocity field u(x)(x, t)=ax/(1+at).
• Application of Chapman-Enskog expansion to analyze dimensionless nonlinear viscosity.

Main Results:

• The sign of the longitudinal deformation rate (a) determines expansion (a>0) or condensation (a<0).
• Temperature decreases with time during expansion and increases during condensation.
• A dimensionless nonlinear viscosity eta(*) depends on the dimensionless rate a(*), with asymptotic Chapman-Enskog expansion.
• The velocity distribution function exhibits an algebraic high-velocity tail, causing moment divergence.

Conclusions:

• The study provides insights into the non-Newtonian behavior of gases under compressible flow conditions.
• The divergence of velocity moments is linked to the high-velocity tail of the distribution function.
• The findings are relevant for understanding complex fluid dynamics from a kinetic perspective.