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Pressure in multicomponent LBM

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    The total pressure in a multicomponent system is given by

    P = (rho1 + rho2)/3 + (g11*psi1^2 + g22psi2^2 + g12*psi1*psi2 + g12*psi2*psi1)/6

    What would be the pressure for a single component?

    In a single component LBM the pressure is,

    P = rho/3 + g11*psi1^2/6

    How do you interpret the additional two terms (g12*psi1*psi2) that appear in multicomponent LBM in the context of partial pressures?


    Hi Azmir,

    please be aware that thermodynamically speaking, in a multicomponent mixture, there are no “partial pressures”. The partial pressure is just a simplification of a component’s fugacity in the mixture which is related to the component’s chemical potential. I would recommend to derive a free energy (Helmholtz energy) from the bulk pressure term you showed above and then derive chemical potentials for components 1 and 2. As you are using the pseudopotential model, you need to take into account how the psi_i are a function of the rho_i.
    All in all, this looks like another mixing rule for a multicomponent equation of state.

    Kind regards

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