Effects of Imposing Contact Angle Schemes and Constructing a Special Ghost Fluid Layer on the Heated Substrate in Pseudopotential Lattice Boltzmann Simulation of Sessile Droplet Evaporation

Abstract

The primitive pseudopotential-based scheme (PP scheme), the modified pseudopotential-based scheme (MP scheme) and the improved virtual-density scheme (IVD scheme) are the three most widely used contact angle schemes to simulate wall wetting characteristics in the pseudopotential lattice Boltzmann (LB) model under isothermal conditions. In this paper, these three widely used contact angle schemes are applied to simulate the problem of sessile droplet evaporation on a heated substrate, which is a non-isothermal phase-change process where temperature varies spatially and temporally. It is found that (i) using the PP scheme (primitive pseudopotential-based scheme) and the MP scheme (modified pseudopotential-based scheme) may lead to algorithmic instability problems in certain ranges of contact angles, deformation of droplet interface shape or Marangoni vortices shape, generation of unphysical vortices near the heated substrate, or result in erroneous temperature distributions near droplet triple-phase line. (ii) The IVD scheme (improved virtual-density scheme) has better algorithmic stability than the PP scheme and MP scheme (primitive pseudopotential-based scheme and the modified pseudopotential-based scheme), where the droplet interface shape and Marangoni vortices shape are correct, the unphysical vortices and the erroneous temperature distribution near droplet triple-phase line disappear. (iii) If a special ghost fluid layer (as proposed in this paper) is constructed on the wall when the PP scheme or the MP scheme (primitive pseudopotential-based scheme or the modified pseudopotential-based scheme) is implemented, the instability of the numerical solution is improved, the deformation of droplet interface shape and the Marangoni vortices shape are corrected, and the unphysical vortices near the heated substrate and the erroneous temperature distribution near droplet triple-phase line disappear. The addition of such a special kind of ghost fluid layer at the heated wall is needed to ensure correct simulation results when using fluid-solid interaction force to implement contact angle schemes for simulation of wall wettability effects in non-isothermal phase-change process using the pseudopotential LB model.

Keywords: pseudopotential lattice Boltzmann model, droplet evaporation, contact angle scheme