Liu hard disk equation of state: Difference between revisions
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The global EoS for all phases: | The global EoS for all phases: | ||
<math>\eta >= 0.72 </math> | <math>\eta <= 0.72 </math> | ||
<math>Z=Z_{lh} </math> | |||
<math>\eta > 0.72 </math> | |||
<math>Z=Z_{solid} </math> | |||
where: | |||
<math>Z_{solid} = </math> | |||
==References== | ==References== | ||
Revision as of 19:50, 22 October 2020
The Liu equation of state for hard disks (2-dimensional hard spheres) is given by Eq. 1 of [1].
For the stable fluid:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Z_v = \frac{1 + \eta^2/8 + \eta^4/18 - 4 \eta^4/21}{(1-\eta)^2} }
where the packing fraction is given by Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \eta = \pi \rho \sigma^2 /4 } where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma} is the diameter of the disks.
The EoS for the stable fluid, liquid-hexatic transition region and hexatic:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Z_{lh} = Z_v + \frac{b_1 \eta^{m_1} + b_2 \eta^{m_2}}{(1-c \eta)} }
The global EoS for all phases: Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \eta <= 0.72 } Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Z=Z_{lh} } Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \eta > 0.72 } Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Z=Z_{solid} }
where: Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Z_{solid} = }