Theoretical study of vapor-liquid homogeneous nucleation using stability analysis of a macroscopic phase

Stability analysis is generally used to verify that the solution to phase equilibrium calculations corresponds to a stable state (minimum of the free energy). In this work, tangent plane distance analysis for stability of macroscopic mixtures is also used for analyzing the nucleation process, reconciling thus this analysis with classical nucleation theories. In the context of the revised nucleation theory, the driving force and the nucleation work are expressed as a function of the Lagrange multiplier corresponding to the mole fraction constraint from the minimization problem of stability analysis. Using a van der Waals fluid applied to a ternary mixture, Lagrange multiplier properties are illustrated. In particular, it is shown how the Lagrange multiplier value is equal to one on the binodal and spinodal curves at the same time as the driving force of nucleation vanishes on these curves. Finally, it is shown that, on the spinodal curve, the nucleation work from the revised and generalized nucleation theories are characterized by two different local minima from stability analysis, irrespective of any interfacial tension models.