Figure 1

The equilibrium densities as a function of the normalized temperature, $T/T_c$, with $T_c$ the critical temperature. For the same value of $\epsilon =10/31$ in (6), we consider a one dimensional interface at constant pressure $P_0$, and report the liquid ($l$, left panel) and gas ($g$, right panel) densities as obtained with lattice Boltzmann simulations with $\psi$ given in (21). We then repeat the simulations with the $\psi \left(\rho \right)=1-e^{-\rho }$. The Maxwell prediction for the two cases has been obtained from the integral constraint ${\int }_{{\rho }_g}^{{\rho }_l}[P_0-\rho T-\frac{\mathcal{G}}{2}{\psi }^2\left(\rho \right)]\frac{d\rho }{{\rho }^2}$ and is reported with the black solid line.Reuse & Permissions

Figure 2

We report the relative error with respect to the thermodynamic (Maxwell) solutions for data analyzed in Fig. 1.Reuse & Permissions

Figure 3

The equilibrium chemical potentials as a function of the normalized temperature, $T/T_c$, with $T_c$ the critical temperature. For the same value of $\epsilon =10/31$ in (6), we consider a one dimensional interface at constant pressure $P_0$, and report the liquid ($l$) and gas ($g$) densities as obtained with lattice Boltzmann simulations with $\psi$ given in (21). We then repeat the simulations with the $\psi \left(\rho \right)=1-e^{-\rho }$. The chemical potential is computed from $\mu =f^{\prime }$ and $f$ given by (18). We then plot the difference between the two chemical potentials evaluated in the liquid ($l$) and gas ($g$) phase, normalized to the chemical potential in the gas phase. Note that thermodynamic equilibrium imposes the same chemical potential, i.e., $|{\mu }_l-{\mu }_g|/|{\mu }_g|=0$. The latter is well reproduced when we use the pseudopotential (21).Reuse & Permissions