Hansen-Goos hard sphere equation of state: Difference between revisions
Carl McBride (talk | contribs) (Created page with "The '''Hansen-Goos''' hard sphere equation of state is given by <ref>[http://dx.doi.org/10.1063/1.4947534 Hendrik Hansen-Goos "Accur...") |
Carl McBride (talk | contribs) m (Slight tidy) |
||
| Line 1: | Line 1: | ||
The '''Hansen-Goos''' [[Equations of state for hard spheres | hard sphere equation of state]] is given by | 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>[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> | :<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> | :<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== | ||
<references/> | <references/> | ||
[[Category: Equations of state]] | [[Category: Equations of state]] | ||
[[category: Hard sphere]] | [[category: Hard sphere]] | ||
Latest revision as of 15:36, 3 May 2016
The Hansen-Goos hard sphere equation of state is given by [1] (Eq. 5):
- 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 \rho k_B T \kappa_T = \frac{(1-\eta)^4}{(1+2\eta -\gamma \eta^3 + \delta \eta^4)^2}}
where (Eq. 7)
- 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 \gamma = 2(19- \frac{B_4}{V^3}) \approx 1.270463 }
and (Eq. 8)
- 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 \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 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 \kappa_T} is the isothermal compressibility, 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 \rho} is the number density and 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} is the packing fraction.