Mass flux in extended and classical hydrodynamics

Area of Science:

• Fluid Dynamics
• Statistical Mechanics
• Thermodynamics

Background:

• Classical hydrodynamics defines mass flux as the momentum field.
• Extended hydrodynamics introduces additional terms to the mass flux.
• Microstructure characterization is key to understanding fluid behavior.

Purpose of the Study:

• Introduce and investigate a novel extended hydrodynamics model.
• Prove the autonomy and compatibility of the extended hydrodynamics with fundamental principles.
• Explore reductions of the extended theory and their implications for multiscale phenomena.

Main Methods:

• Utilizing a one-particle distribution function as an extra state variable.
• Demonstrating thermodynamic compatibility (non-decreasing entropy).
• Proving mechanical compatibility (Hamiltonian evolution for entropy-preserving dynamics).

Main Results:

• The proposed extended hydrodynamics is fully autonomous.
• Reductions can yield classical hydrodynamics or multiscale hydrodynamics.
• Self-diffusion terms emerge in the mass flux within multiscale hydrodynamics, particularly with large density gradients.

Conclusions:

• Extended hydrodynamics offers a more comprehensive framework for fluid dynamics.
• The concept of multiscale hydrodynamics emerges from the reduction of extended theories.
• This work provides a mathematical formulation for multiscale hydrodynamics with self-diffusion.