A phase-change model for diffusion-driven mass transfer problems in incompressible two-phase flows

Abstract

We present a VOF-based numerical method for incompressible Direct Navier–Stokes (DNS) equations for diffusion-driven phase-change flows. A special emphasis is placed on the treatment of velocity discontinuities across the interface. A novel algorithm is presented to smoothly extend the liquid velocity field across the interface in a way that the interface can be transported by a divergence-free velocity field. The transport of species is treated with a two-scalar approach and special attention is paid to the advection and diffusion steps in order to prevent artificial mass transfer. The methodology is implemented in the open-source code Basilisk and is validated against analytical and semi-analytical models. The relative errors on the relevant quantities are generally below 1% for the finest grids. The method is finally applied to study the growth of electrochemically generated bubbles on planar electrodes and the effect of contact angles and number of nucleation sites is investigated.