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Phase Transition in the Boltzmann-Vlasov Equation
A C Fowler1,2
11MACSI, University of Limerick, Limerick, Ireland.
Journal of Statistical Physics
|April 2, 2019
Summary
This study shows that strong inter-molecular attraction can destabilize uniform gas states, explaining phase transitions. The research uses a modified Boltzmann equation for typical gas densities.
Area of Science:
- Statistical Mechanics
- Kinetic Theory
- Thermodynamics
Background:
- Phase transitions are crucial phenomena in physics.
- Understanding the kinetic theory basis of phase transitions is complex.
- Previous models often simplified inter-molecular interactions.
Purpose of the Study:
- To explain phase transitions using a modified Boltzmann equation.
- To investigate the role of inter-molecular attraction in gas stability.
- To analyze the conditions under which a uniform gas state becomes unstable.
Main Methods:
- Studied a form of the Boltzmann equation incorporating a Vlasov term for inter-molecular attraction.
- Analyzed the evolution equation for the one-particle distribution function.
- Utilized an approximation valid for typical gas densities where the ratio of molecular diameter to mean inter-particle distance is small.
Main Results:
- Demonstrated that a uniform gas state becomes unstable when inter-molecular attraction is sufficiently strong.
- Showed that the collision term is negligible for fluctuations at the molecular spacing scale.
- An explicit approximate solution was derived and its validity discussed.
Conclusions:
- Inter-molecular attraction is a key factor in destabilizing uniform gas states, leading to phase transitions.
- The derived approximation provides a foundation for understanding these phenomena.
- Future work can extend these results to finite amplitude effects.
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