Van der Waals-Navier Stokes equation for boiling phenomena - Bubble formation by heating

By making use of a Simulation scheme incorporating the Navier-Stokes equation and the van der Waals equation, we study the combined dynamics of fluid motion and phase separation in a bubble generation process. The thermodynamic force for phase separation is taken into account by the entropy density of the van der Waals fluid, which is a function of local density and local energy. With this force and the surface tension, explicit forms of equations of motion are given for the density, momentum, and energy. In this scheme, we are able to treat gas and liquid states in a unified way and study a spontaneous bubble generation process by heating. In this paper, we demonstrate the processes of bubble generation in a pinpoint-heated one-dimensional system of water, and Study their characteristics. For example, before the bubble generation, a step-like pressure domain wall propagates from the the position where the liquid is heated. After further heating, thermodynamic instability takes place and a gas region is generated and expands. The temperature and pressure profiles around the domain boundary are investigated when the gas region is expanding. The conditions of the heating process for bubble generation are also studied.