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

TL;DR

This paper investigates the equilibrium properties of dilute binary fluid mixtures, focusing on surface tension, adsorption, and phase behavior, deriving key relations and explicit expressions within the van der Waals model.

Contribution

It provides a theoretical framework for understanding surface phenomena and phase changes in dilute mixtures, including derivations of the Gibbs law and explicit formulas in the van der Waals model.

Findings

Derivation of the Gibbs law relating surface tension change and surface adsorption.

Explicit expressions for critical temperature and pressure derivatives with respect to solute concentration.

Surface tension derivative can be positive or negative, diverging on the azeotropic line.

Abstract

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.