Prandtl Number in Classical Hard-Sphere and One-Component Plasma Fluids
Sergey Khrapak1, Alexey Khrapak1
1Joint Institute for High Temperatures, Russian Academy of Sciences, 125412 Moscow, Russia.
Molecules (Basel, Switzerland)
|February 10, 2021
Summary
The Prandtl number, a key fluid property, was calculated for hard-sphere and plasma fluids. It increases towards the freezing point, reaching a near-universal value for simple dielectric fluids.
Area of Science:
- Thermodynamics
- Fluid Dynamics
- Statistical Mechanics
Background:
- The Prandtl number (Pr) is a dimensionless group crucial for heat transfer and fluid flow analysis.
- Understanding Pr in dense, strongly coupled systems is vital for predicting material behavior near phase transitions.
- Previous studies have primarily focused on dilute or weakly coupled regimes.
Purpose of the Study:
- To evaluate the Prandtl number for three-dimensional hard-sphere and one-component plasma fluids.
- To investigate the behavior of Pr across dilute, weakly coupled to dense, strongly coupled regimes.
- To determine the Prandtl number near the fluid-solid phase transition.
Main Methods:
- Numerical evaluation of the Prandtl number.
- Simulation of three-dimensional hard-sphere systems.
- Simulation of one-component plasma fluids.
Main Results:
- Numerical values of order unity were obtained for the Prandtl number in both systems.
- The Prandtl number consistently increases as the freezing point is approached.
- A quasi-universal Prandtl number of approximately 1.7 was observed for simple dielectric fluids near freezing.
Conclusions:
- The Prandtl number exhibits significant changes in dense, strongly coupled fluids.
- A quasi-universal value of the Prandtl number near freezing suggests common behavior in simple dielectric fluids.
- Further investigation into two-dimensional fluid systems is warranted.
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