Three-dimensional mesoscopic investigation of directional coalescence of two droplets impacting on a wall with wettability difference

In this work, a three-dimensional (3D) nonorthogonal pseudopotential lattice Boltzmann method (LBM) was proposed to investigate the coalescence dynamics of two droplets impacting on a wall with wettability difference. The influences of the wettability difference, Weber number, offset distance on the low-wettability side on the coalescence dynamics and the contact-line evolution processes were systematically examined. Both symmetric and asymmetric distributions of the droplet-coalescence behaviors were considered. Our findings reveal that the wettability difference has a significant influence on the asymmetric-retracting and wetting-equilibrium stages, identifying three modes: pin-slip, slip and no-rebound, and slip and rebound. The rebound time is dominated by the high-wettability wall. At a larger Weber number, droplets exhibit a large retracting velocity, which results in increased pumping velocity and earlier rebound time. In addition, a dramatic retraction of the three-phase contact line (TPCL) on the low-wettability wall is observed, leading to the detachment of the liquid bridge from the low-wettability wall, and the formation of a cavity. With increasing offset distance on the low-wettability wall, three different evolution modes are found: coalescence-rebound, coalescence-separation, and non-coalescence. A power function relationship is reported between the Weber number $\text{We}$ and the offset distance $L^{*}$ both on the high-wettability wall and low-wettability wall for three modes of coalescence behavior with $\text{We}\sim L^{*\alpha }$. The value of the exponent $\alpha$ ranges from 4.6 to 7.4. This study showcases the effectiveness of the 3D nonorthogonal pseudopotential LBM in predicting the complex interface phenomena and characteristics of the multiphase flow structures under investigation.