Vapor-liquid phase transition in fluctuating hydrodynamics: The most probable transition path and its computation

Abstract

In this paper, we consider transition events between metastable states in fluid systems modeled by two-phase Navier-Stokes equations with thermal noise. The vapor-liquid phase transition which occurs during the vapor condensation is such an example. We propose a numerical method to compute the transition pathway. We first approximate the continuum hydrodynamics model by the smoothed particle hydrodynamics (SPH). In the SPH formulation, the dynamics of the system take the form of Langevin equations. This allows us to derive conditions that characterize the most probable transition pathway. Then we compute the most probable transition pathway by solving these conditions in the space of mass and momentum density fields using the string method. The force, which is needed to evolve the string in the space of the density fields, is computed by discretizing the deterministic model using the finite difference method. The numerical method is applied to study the condensation of vapor in a periodic cell and the Cassie-Wenzel transition on pillared solid substrates.