Akira Onuki ∗ Department of Physics, Kyoto University, Kyoto 606-8502, Japan (Dated: February 7, 2009)
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 ∆γ are discussed. A derivation of the Gibbs law ∆γ = −T Γ is given with Γ being the surface adsorption. Calculated quantities include the derivatives dT c /dX and dp c /dX of the critical temperature and pressure with respect to the solute molar fraction X and the temperature-derivative (∂γ/∂T ) cx,p of the surface tension at fixed pressure p on the coexistence surface. Here (∂γ/∂T ) 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. Near the solvent critical point, it is proportional to (dp c /dX)/K Kr , where K Kr is the Krichevskii parameter. Explicit expressions are given for all these quantities in the van der Waals model.