Phase segregation of liquid-vapor systems with a gravitational field

Phase separation in the presence of external forces has attracted considerable attention since the initial works for solid mixtures. Despite this, only very few studies are available which address the segregation process of liquid-vapor systems under gravity. We present here an extensive study which takes into account both hydrodynamic and gravitational effects on the coarsening dynamics. An isothermal formulation of a lattice Boltzmann model for a liquid-vapor system with the van der Waals equation of state is adopted. In the absence of gravity, the growth of domains follows a power law with the exponent 2/3 of the inertial regime. The external force deeply affects the observed morphology accelerating the coarsening of domains and favoring the liquid accumulation at the bottom of the system. Along the force direction, the growth exponent is found to increase with the gravity strength still preserving sharp interfaces since the Porod's law is found to be verified. The time evolution of the average thickness L of the layers of accumulated material at confining walls shows a transition from an initial regime where L≃t2/3 (t: time) to a late-time regime L≃gt5/3 with g the gravitational acceleration. The final steady state, made of two overlapped layers of liquid and vapor, shows a density profile in agreement with theoretical predictions.