Hansen-Goos hard sphere equation of state: Difference between revisions

Latest revision as of 16:36, 3 May 2016

The Hansen-Goos hard sphere equation of state is given by ^[1] (Eq. 5):

\rho k_{B}T\kappa _{T}={\frac {(1-\eta )^{4}}{(1+2\eta -\gamma \eta ^{3}+\delta \eta ^{4})^{2}}}

where (Eq. 7)

\gamma =2(19-{\frac {B_{4}}{V^{3}}})\approx 1.270463

and (Eq. 8)

\delta =-{\frac {3}{7}}+{\frac {5\gamma }{8}}+{\frac {4}{7}}{\sqrt {1-{\frac {21\gamma }{32}}+{\frac {105\gamma ^{2}}{1024}}}}\approx 0.694605

and where $\kappa _{T}$ is the isothermal compressibility, $\rho$ is the number density and $\eta$ is the packing fraction.

@@ Line 1: / Line 1: @@
 The '''Hansen-Goos''' [[Equations of state for hard spheres | hard sphere equation of state]] is given by
-<ref>[http://dx.doi.org/10.1063/1.4947534  Hendrik Hansen-Goos "Accurate prediction of hard-sphere virial coefficients B6 to B12 from a compressibility-based equation of state", Journal of Chemical Physics '''144''' 164506 (2016);]</ref> (Eq. 5):
+<ref>[http://dx.doi.org/10.1063/1.4947534  Hendrik Hansen-Goos "Accurate prediction of hard-sphere virial coefficients B6 to B12 from a compressibility-based equation of state", Journal of Chemical Physics '''144''' 164506 (2016)]</ref> (Eq. 5):
 :<math> \rho k_B T \kappa_T = \frac{(1-\eta)^4}{(1+2\eta -\gamma \eta^3 + \delta \eta^4)^2}</math>
@@ Line 12: / Line 12: @@
 :<math> \delta = - \frac{3}{7} + \frac{5\gamma}{8} +\frac{4}{7} \sqrt{1- \frac{21 \gamma}{32} + \frac{105\gamma^2}{1024}} \approx 0.694605</math>
-and where <math>\kappa_T</math> is the [[Compressibility#Isothermal compressibility| isothermal compressibility]].
+and where <math>\kappa_T</math> is the [[Compressibility#Isothermal compressibility| isothermal compressibility]], <math>\rho</math> is the number density and <math>\eta</math>
+is the packing fraction.
 ==References==
 <references/>
 [[Category: Equations of state]]
 [[category: Hard sphere]]