Difference between revisions of "Liu hard disk equation of state"

From SklogWiki
Jump to: navigation, search
Line 2: Line 2:
 
<ref>[https://arxiv.org/abs/2010.10624]</ref>.
 
<ref>[https://arxiv.org/abs/2010.10624]</ref>.
  
For stable fluid:
+
For the stable fluid:
 
:<math>Z_v = \frac{1 + \eta^2/8 + \eta^4/18 - 4 \eta^4/21}{(1-\eta)^2} </math>
 
:<math>Z_v = \frac{1 + \eta^2/8 + \eta^4/18 - 4 \eta^4/21}{(1-\eta)^2} </math>
  
 
where the packing fraction is given by <math>\eta = \pi \rho \sigma^2 /4 </math> where <math>\sigma</math> is the diameter of the disks.
 
where the packing fraction is given by <math>\eta = \pi \rho \sigma^2 /4 </math> where <math>\sigma</math> is the diameter of the disks.
  
The EoS for stable fluid, liquid-hexatic transition region and hexatic:
+
The EoS for the stable fluid, liquid-hexatic transition region and hexatic:
:<math>Z = \frac{1 + \eta^2/8 + \eta^4/18 - 4 \eta^4/21}{(1-\eta)^2} </math>
+
:<math>Z_lh = Z_v + \frac{1 + \eta^2/8 + \eta^4/18 - 4 \eta^4/21}{(1-\eta)^2} </math>
  
  

Revision as of 20:38, 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:

Z_v = \frac{1 + \eta^2/8 + \eta^4/18 - 4 \eta^4/21}{(1-\eta)^2}

where the packing fraction is given by \eta = \pi \rho \sigma^2 /4 where \sigma is the diameter of the disks.

The EoS for the stable fluid, liquid-hexatic transition region and hexatic:

Z_lh = Z_v + \frac{1 + \eta^2/8 + \eta^4/18 - 4 \eta^4/21}{(1-\eta)^2}


References