A three dimensional smooth particle hydrodynamics model of the nanoscale condensation of water

Abstract

Mesoscopic, coarse grained models of phase transitions are of interest for their potential to simulate the transient fine scale structure associated with rapid phase transitions and the equilibrium properties of multi-phase systems. The van der Waals square gradient model provides a convenient equation of state for a fluid with a liquid and vapour phase. A three dimensional smooth particle hydrodynamics code was developed in order to investigate the fidelity with which this numerical technique captures the behaviour of the van der Waals model, parameterised for water in conditions of liquid-vapour coexistence. Our code is capable of modelling small to medium sized systems of the order of several thousands of particles in three dimensions, at scales of 10-100 nanometres. Lagrangian methods such as smooth particle hydrodynamics (SPH) are capable of simulating flows with complex structure naturally. Smooth particle methods represent the fluid as a collection of 'particles' representing macroscopic fluid elements and carrying mass, momentum and thermal energy. The equations of motion governing the smooth particles are derived from the continuum (Navier-Stokes) equations. The pressure and heat flux tensors are determined using linear constitutive relations and an equilibrium equation of state. Specific substances are modelled by the selection of this equation of state and of parameters for the constitutive relations. Lagrangian particle methods bring their own set of numerical challenges for which algorithmic solutions are implemented, including artificial viscosity, anti-clumping measures and the use of different length scales for different components of the equation of state. The smooth particle equations of motion for a phase separating fluid are solved using parameters derived for water. The condensation of a liquid phase from the water vapour naturally from the solution of the model, with no explicit tracking of the vapour-liquid interface required. Using the smooth particle code to solve the continuum equations of motion for this model of water, we are able to produce droplets and planar gas-liquid interfaces under a variety of boundary conditions. By controlling the mean temperature of the fluid and the volume of the periodic box, the fluid can be taken to arbitrary points on the phase diagram. Expansion may be used to induce boiling, while temperature quenches can be used to produce an instability driven decomposition into coexisting liquid and vapour.