Quantitative phase-field modeling for boiling phenomena

A phase-field model is developed for quantitative simulation of bubble growth in the diffusion-controlled regime. The model accounts for phase change and surface tension effects at the liquid-vapor interface of pure substances with large property contrast. The derivation of the model follows a two-fluid approach, where the diffuse interface is assumed to have an internal microstructure, defined by a sharp interface. Despite the fact that phases within the diffuse interface are considered to have their own velocities and pressures, an averaging procedure at the atomic scale, allows for expressing all the constitutive equations in terms of mixture quantities. From the averaging procedure and asymptotic analysis of the model, nonconventional terms appear in the energy and phase-field equations to compensate for the variation of the properties across the diffuse interface. Without these new terms, no convergence towards the sharp-interface model can be attained. The asymptotic analysis also revealed a very small thermal capillary length for real fluids, such as water, that makes impossible for conventional phase-field models to capture bubble growth in the millimeter range size. For instance, important phenomena such as bubble growth and detachment from a hot surface could not be simulated due to the large number of grids points required to resolve all the scales. Since the shape of the liquid-vapor interface is primarily controlled by the effects of an isotropic surface energy (surface tension), a solution involving the elimination of the curvature from the phase-field equation is devised. The elimination of the curvature from the phase-field equation changes the length scale dominating the phase change from the thermal capillary length to the thickness of the thermal boundary layer, which is several orders of magnitude larger. A detailed analysis of the phase-field equation revealed that a split of this equation into two independent parts is possible for system sizes ranging from micrometers and above. The split of the phase-field equation leads to two equations controlling independently the phase change and the shape of the phase-field profile across the diffuse interface. A new algorithm is presented to solve a fully coupled model, including advection, phase change, and surface tension effects. Good agreement is found among numerical simulations, analytical solutions, and experimental results.