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

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{| border="1"
 
{| border="1"
 
|-  
 
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| <math>b_1</math> || <math>- 1.04191 x 10^8</math>
+
| <math>b_1</math> || <math>- 1.04191 * 10^8</math>
 
|-  
 
|-  
| <math>b_2</math>|| <math>2.66813 x 10^8</math>
+
| <math>b_2</math>|| <math>2.66813 * 10^8</math>
 
|-  
 
|-  
 
| <math>m_1</math> || 53
 
| <math>m_1</math> || 53

Revision as of 21:11, 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{b_1 \eta^{m_1} + b_2 \eta^{m_2}}{(1-c \eta)}

The global EoS for all phases:

Z=Z_{lh} , \eta <= 0.72

Z=Z_{solid} , \eta > 0.72

where: Z_{solid} = \frac{2}{\alpha} + 1.9 + \alpha - 5.2 \alpha^2 + 114.48 \alpha^4

and \alpha = \frac{2}{3^{1/2} \rho \sigma^2}


b_1 - 1.04191 * 10^8
b_2 2.66813 * 10^8
m_1 53
m_2 56
c 0.75

References