A multidimensional examination of phase separation in single-component fluids

Abstract

A thermodynamic instability in a homogeneous fluid can lead to spontaneous formation of distinct domains within the fluid. This process involves not only the spatial redistribution of fluid density but also transient exchanges of pressure, temperature, and energy. However, classical theoretical frameworks, such as the Ginzburg–Landau and Cahn–Hilliard models, lack incorporation of these essential thermodynamic aspects. To investigate the dynamics of multiple physical fields during phase separation, we numerically solve a two-dimensional van der Waals fluid model. Thermodynamic consistency is demonstrated by verifying the coexistence curve. While the equilibrium pressure remains similar across the unstable region of the isotherm, we demonstrate that the energy in the system depends on the initial density. Although the majority of energy is stored as heat at typical values of the heat capacity, high-density domains contain less specific energy compared to their low-density counterparts due to interparticle attraction. Consequently, the transition of low-density domains into high-density through the process of coalescence releases excess energy, which redistributes in the form of longitudinal waves and heat. We also highlight the role of parameters, such as heat capacity and thermal conductivity, in less intuitive phenomena, including elevated temperature fluctuations and memory preservation.