Smoothed particle modelling of liquid-vapour phase transitions

Liquid-vapour phase transition in a simple fluid is studied using Smoothed Particle Hydrodynamics (SPH), a Lagrangian numerical method. A continuum fluid model displaying a liquid-vapour phase transition, based on the van der Waals equation of state with a squared density gradient capillary force and linear constitutive relations for viscosity and heat flux, is solved using SPH. The liquid vapour interface is intrinsically diffuse in both the analytical model and the numerical method. In SPH a continuous field is represented by interpolation over particles whose properties are smoothed over space and which interact with an environment dependent two-body potential. By applying SPH to the partial differential equations of continuum mechanics, a set of ordinary differential equations governing an N-body system of particles is obtained. A two dimensional SPH code was developed and used to simulate phase transitions. Temperature quenches were used to produce an instability driven decomposition into coexisting liquid and vapour. Stable coexisting vapour and liquid phases, with densities in good agreement with theory, are produced. Condensation emerges from the solution of the model with no explicit tracking of the vapour-liquid interface. Simulated fluids phase separate with a flow that appears realistic and without gross artifacts, containing droplets and bubbles which coalesce when driven together by flow. The kinetics of the growth of liquid domains in the phase separating fluid are divided into two regimes: an initial period in which density perturbations grow with an exponent close to one third, followed by a coarsening of liquid droplets where the exponent is strongly influenced by the quench depth. A three dimensional SPH code was developed in order to investigate the behaviour of the model when parameterised for water and used to simulate mesoscopic systems with length scales of the order of nanometres. When stable liquid vapour interfaces were formed for the continuum model of water, the density gradient and associated surface tension are resolved, however the surface tensions were found to be orders of magnitude too small. At coarse spatial resolution the interface is artificially broadened, leading to spuriously low surface tension. It is found that the spatial resolution must be of the order of the liquid-vapour interfacial width in order to accurately resolve density gradients and surface energy. Ultimately, liquid-vapour phase transitions can be modelled using SPH, however the microscopic width of the interface requires either microscopic simulation resolution or parameterisation to account for unresolved spatial scales