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Generalized Green-Kubo formulas for fluids with impulsive, dissipative, stochastic, and conservative interactions
1Institute for Theoretical Physics, Universiteit Utrecht, 3508 TD Utrecht, The Netherlands.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 21, 2006
Summary
We generalized Green-Kubo expressions for thermal transport coefficients in complex fluids, applicable to various forces including hard sphere interactions. This provides a new framework for understanding heat transport dynamics.
Area of Science:
- Statistical Mechanics
- Complex Fluids
- Transport Phenomena
Background:
- The Green-Kubo formalism is a cornerstone for calculating transport coefficients from equilibrium time-correlation functions.
- Complex fluids exhibit intricate dynamics that challenge traditional transport theories.
- Understanding thermal transport is crucial for materials science and engineering.
Purpose of the Study:
- To generalize the Green-Kubo expressions for thermal transport coefficients in complex fluids.
- To develop a theoretical framework applicable to a wide range of interparticle forces.
- To investigate the specific case of hard sphere fluids.
Main Methods:
- Generalization of Green-Kubo formulas for thermal transport coefficients.
- Inclusion of instantaneous transport coefficients and time-correlation functions.
- Application of the streaming operator formalism for dynamical variables.
- Validation for conservative, impulsive, stochastic, and dissipative forces.
Main Results:
- A generalized Green-Kubo expression is derived, decomposing the thermal transport coefficient into an instantaneous part and a time-integral of a correlation function.
- The derived formulas are shown to be valid for diverse systems, including hard sphere fluids, Langevin fluids, and systems with conservative or dissipative forces.
- Conditions for the equality of conjugate currents and instantaneous coefficients are identified.
Conclusions:
- The generalized Green-Kubo expressions offer a versatile tool for studying thermal transport in complex fluids.
- The framework accommodates various interaction potentials and dynamical behaviors.
- The hard sphere fluid serves as a key application, demonstrating the utility of the new formalism.
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