Numerical Stability and Accuracy of Contact Angle Schemes in Pseudopotential Lattice Boltzmann Model for Simulating Static Wetting and Dynamic Wetting

Abstract

There are five most widely used contact angle schemes in the pseudopotential lattice Boltzmann (LB) model for simulating the wetting phenomenon: The pseudopotential-based scheme (PB scheme), the improved virtual-density scheme (IVD scheme), the modified pseudopotential-based scheme with a ghost fluid layer constructed by using the fluid layer density above the wall (MPB-C scheme), the modified pseudopotential-based scheme with a ghost fluid layer constructed by using the weighted average density of surrounding fluid nodes (MPB-W scheme) and the geometric formulation scheme (GF scheme). But the numerical stability and accuracy of the schemes for wetting simulation remain unclear in the past. In this paper, the numerical stability and accuracy of these schemes are clarified for the first time, by applying the five widely used contact angle schemes to simulate a two-dimensional (2D) sessile droplet on wall and capillary imbibition in a 2D channel as the examples of static wetting and dynamic wetting simulations respectively. (i) It is shown that the simulated contact angles by the GF scheme are consistent at different density ratios for the same prescribed contact angle, but the simulated contact angles by the PB scheme, IVD scheme, MPB-C scheme and MPB-W scheme change with density ratios for the same fluid-solid interaction strength. The PB scheme is found to be the most unstable scheme for simulating static wetting at increased density ratios. (ii) Although the spurious velocity increases with the increased liquid/vapor density ratio for all the contact angle schemes, the magnitude of the spurious velocity in the PB scheme, IVD scheme and GF scheme are smaller than that in the MPB-C scheme and MPB-W scheme. (iii) The fluid density variation near the wall in the PB scheme is the most significant, and the variation can be diminished in the IVD scheme, MPB-C scheme and MPB-W scheme. The variation totally disappeared in the GF scheme. (iv) For the simulation of capillary imbibition, the MPB-C scheme, MPB-W scheme and GF scheme simulate the dynamics of the liquid-vapor interface well, with the GF scheme being the most accurate. The accuracy of the IVD scheme is low at a small contact angle (44 degrees) but gets high at a large contact angle (60 degrees). However, the PB scheme is the most inaccurate in simulating the dynamics of the liquid-vapor interface. As a whole, it is most suggested to apply the GF scheme to simulate static wetting or dynamic wetting, while it is the least suggested to use the PB scheme to simulate static wetting or dynamic wetting.