Van der Waals gas bubble as a dynamical system.

Abstract

A van der Waals fluid contained in a bubble under constant surface tension and temperature is formulated as a dynamical system. The temperature and surface tension determine the nature of the equilibrium solutions. The bifurcation set is a cusp where the cusp point is a shifted critical point, thus modifying the van der Waals critical point. When the temperature is above the shifted critical temperature the model is valid for all radii; otherwise, the model is not valid for sufficiently small radii. The Hamiltonian is used to discuss the problem of using a Maxwell construction to determine a phase transition in a bubble.