SGT for pure components

When working with pure components, SGT implementation is direct as there is a continuous path from the vapor to the liquid phase. SGT can be reformulated with density as indepedent variable.

\[\sigma = \sqrt{2} \int_{\rho^\alpha}^{\rho_\beta} \sqrt{c_i \Delta \Omega} d\rho\]

Here, \(\Delta \Omega\) represents the grand thermodynamic potential, obtained from:

\[\Delta \Omega = a_0 - \rho \mu^0 + P^0\]

Where \(P^0\) is the equilibrium pressure.

In phasepy this integration is done using ortoghonal collocation, which reduces the number of nodes needed for a desired error. This calculation is done with the sgt_pure function and it requires the equilibrium densities, temperature and pressure as inputs.

>>> #component creation
>>> water =  component(name = 'Water', Tc = 647.13, Pc = 220.55, Zc = 0.229, Vc = 55.948, w = 0.344861
... ksv = [ 0.87185176, -0.06621339], cii = [2.06553362e-26, 2.64204784e-23, 4.10320513e-21])
>>> #EoS object creation
>>> eos = prsveos(water)

First vapor-liquid equilibria has to be computed. This is done with the psat method from the EoS, which returns the pressure and densities at equilibrium. Then the interfacial can be computed as it is shown.

>>> T = 350 #K
>>> Psat, vl, vv = eos.psat(T)
>>> rhol = 1/vl
>>> rhov = 1/vv
>>> sgt_pure(rhov, rhol, T, Psat, eos, full_output = False)
>>> #Tension in mN/m
... 63.25083234

Optionally, full_output allows to get all the computation information as the density profile, interfacial lenght and grand thermodynamic potential.

>>> solution = sgt_pure(rhol, rhov, T, Psat, eos, full_output = True)
>>> solution.z #interfacial lenght array
>>> solution.rho #density array
>>> solution.tension #IFT computed value