Molecular hydrodynamic theory of the velocity autocorrelation function

Area of Science:

• Fluid dynamics
• Statistical mechanics
• Computational physics

Background:

• The velocity autocorrelation function (VACF) contains vital information on fluid molecular structure and hydrodynamics.
• A key question is the extent to which hydrodynamic theories can capture these molecular features.

Purpose of the Study:

• To formulate a hydrodynamic theory for the tagged-particle VACF in simple fluids.
• To investigate how well a purely hydrodynamic description can recover molecular fluid properties.

Main Methods:

• Modeling collective hydrodynamic modes and tagged-particle self-motion using linear hydrodynamic equations.
• Identifying the fluid's spatial velocity power spectrum as a crucial initial condition for momentum current correlation.
• Interpreting the VACF as a weighted superposition of quasinormal hydrodynamic modes.

Main Results:

• The theory quantitatively matches existing methods for liquid noble gases and alkali metals.
• A novel hydrodynamic form of the self-intermediate scattering function was derived and validated for low-density fluids.
• Excellent agreement was achieved with molecular dynamics calculations for dense supercritical fluids.

Conclusions:

• The developed hydrodynamic theory provides a robust framework for understanding fluid dynamics.
• The spatial velocity power spectrum acts as a bridge between continuum hydrodynamics and discrete-particle kinetics.
• The theory accurately describes fluid properties across different densities and states, including supercritical conditions.