Time correlation functions of hard sphere and soft sphere fluids

Area of Science:

• Statistical Mechanics
• Computational Physics
• Fluid Dynamics

Background:

• Transport coefficients in fluids are determined by time correlation functions.
• The Green-Kubo formulas relate these coefficients to integrals of time correlation functions.
• Understanding the transition from soft repulsive potentials to hard spheres is crucial for fluid modeling.

Purpose of the Study:

• To analyze the analytic forms of time correlation functions for r(-n) potentials.
• To extend Dufty's framework for the shear stress correlation function to bulk viscosity and thermal conductivity.
• To characterize the transition to the hard sphere limit for transport properties.

Main Methods:

• Analysis of analytic forms of time correlation functions for r(-n) potentials.
• Extension of Dufty's theoretical framework to bulk viscosity and thermal conductivity.
• Introduction of a new singular function, w(t), to model short-time behavior.

Main Results:

• A new singular function, w(t), is required to accurately describe the bulk viscosity correlation function in the hard sphere limit.
• The value a(n) approaches the square root of 2 in the hard sphere limit for both bulk and shear viscosity correlation functions.
• The qualitative behavior of the heat flux correlation function mirrors that of the shear stress correlation function.

Conclusions:

• The proposed model, including the w(t) function, accurately captures the transition to the hard sphere limit for transport coefficients.
• The derived w(t) function appears consistent across bulk viscosity, shear viscosity, and thermal conductivity.
• This work provides a more complete theoretical framework for understanding transport phenomena in dense fluids.