Constructing a ghost fluid layer for implementation of contact angle schemes in multiphase pseudopotential lattice Boltzmann simulations for non-isothermal phase-change heat transfer

Abstract

The PP scheme (primitive pseudopotential-based scheme), the MP scheme (modified pseudopotential-based scheme) and the IVD scheme (improved virtual-density scheme) are the three most widely used contact angle schemes in pseudopotential lattice Boltzmann (LB) models to simulate wetting characteristics of multiphase flow over solid surfaces under isothermal conditions. In this paper, we apply these schemes to simulate the problem of sessile droplet evaporation on a heated substrate, which is an example of non-isothermal phase-change heat transfer process. It is found that the substrate heating effect destabilizes algorithms of these schemes in certain ranges of contact angles of a heated substrate. The droplet interface shapes simulated by the PP scheme and the MP scheme are inaccurate at obtuse contact angles due to large fluid density variations near the wall. The spurious currents near the droplet triple-phase contact line are very large in the MP scheme, causing the deformation of the Marangoni vortex shape inside the droplet and the erroneous droplet interface temperature distribution near the triple-phase contact line. The addition of a special ghost fluid layer on the wall proposed in this study can improve numerical stability of the PP and the MP schemes for application under non-isothermal conditions as well as under high saturated liquid/vapor density ratios. Although the IVD Scheme (with the nearest fluid layer temperatures above the heated wall chosen for calculating the effective mass of wall nodes) is also stable at low liquid/vapor density ratios, its numerical stability at high density ratios is not as robust as those of the PP and the MP schemes if a special ghost fluid layer is added in these schemes. It is shown that by adding such a special ghost fluid layer on the wall, large near-wall fluid density variations diminish in the PP and MP schemes and accurate droplet interface shapes can be recovered at obtuse contact angles. The spurious current in the MP schemes can be also reduced and accurate Marangoni vortex shapes in the droplet and droplet interface temperature distribution near the triple-phase contact line can be predicted.