Henry's law, surface tension, and surface adsorption in dilute binary mixtures

Equilibrium properties of dilute binary fluid mixtures are studied in two-phase states on the basis of a Helmholtz free energy including the gradient free energy. The solute partitioning between gas and liquid (Henry's law) and the surface tension change $\Delta\gamma$ are discussed. A derivation of the Gibbs law $\Delta\gamma=-T\Gamma$ is given with $\Gamma$ being the surface adsorption. Calculated quantities include the derivatives $d T_c/dX$ and $d p_c/dX$ of the critical temperature and pressure with respect to the solute molar fraction $X$ and the temperature-derivative $(\p \gamma/\p T)_{{\rm cx},p}$ of the surface tension at fixed pressure $p$ on the coexistence surface. Here $(\p \gamma/\p T)_{{\rm cx},p}$ can be both positive and negative, depending on the solute molecular size and the solute-solvent interaction,and diverges on the azeptropic line. Explicit expressions are given for all these quantities in the van der Waals model.