A numerical study of droplet dynamic behaviors on a micro-structured surface using a three dimensional color-gradient lattice Boltzmann model

Generalized equilibria for color-gradient lattice Boltzmann model based on higher-order Hermite polynomials: A simplified implementation with central moments

We propose generalized equilibria of a three-dimensional color-gradient lattice Boltzmann model for two-component two-phase flows using higher-order Hermite polynomials. Although the resulting equilibrium distribution function, which includes a sixth-order term on the velocity, is computationally cumbersome, its equilibrium central moments (CMs) are velocity-independent and have a simplified form. Numerical experiments show that our approach, as in Wen et al. [Phys. Rev. E 100, 023301 (2019)2470-004510.1103/PhysRevE.100.023301] who consider terms up to third order, improves the Galilean invariance compared to that of the conventional approach. Dynamic problems can be solved with high accuracy at a density ratio of 10; however, the accuracy is still limited to a density ratio of 1000. For lower density ratios, the generalized equilibria benefit from the CM-based multiple-relaxation-time model, especially at very high Reynolds numbers, significantly improving the numerical stability.

A Numerical Study of Micro-Droplet Spreading Behaviors on Wettability-Confined Tracks Using a Three-Dimensional Phase-Field Lattice Boltzmann Model

Wettability-confined tracks have been extensively used in open-surface microfluidic devices for their high capacity of transporting droplet pumplessly. Inspired by the experimental work of Sen et al. [ Langmuir 2018 , 34 , 1899 - 1907 ], in the present study, a three-dimensional phase-field lattice Boltzmann model is developed and used to investigate the spreading behaviors of microdroplet on a series of wettability-confined tracks. The experimental findings are successfully reproduced through our simulation, where three distinct stages of droplet spreading on the horizontal wettability-confined diverging track are fairly exhibited, that is, the initial stage with droplet front spreading quickly, the intermediate stage with both droplet front and bulge moving forward at a constant speed, and the final stage with droplet front decelerating gradually. Moreover, a parametric study of track divergence angle is further performed, and the influential mechanism of track divergence angle on droplet spreading is further revealed. It is demonstrated that track divergence is responsible for the Laplace pressure gradient and capillary force inside the droplet, which drives the droplet bulge to move forward on the diverging track. With an increase in divergence angle, the capillary force increases linearly, which increases the droplet spreading speed at the initial and intermediate stages, while the peak capillary force comes earlier, and consequently the final decelerating stage comes earlier. On the basis of the parametric study and droplet volume conservation rule, a power law relation between track divergence angle and droplet spreading is proposed, which helps to identify the start of final decelerating stage. Finally, the droplet spreading over various inclined tracks is explored, which can be achieved only when the capillary force at the beginning is larger than the droplet gravity component along the inclined track surface.