Lattice Boltzmann simulation of droplet dynamics in a bifurcating micro-channel

The droplet dynamic in a bifurcating micro-channel, as one of the basic multiphase problems, is frequently encountered in the fields of science and engineering. Due to its great relevance to many important applications and also its fascinating physical phenomena, it has attracted the increasing attention in the past decades. However, this problem is still not fully understood since it is very complicated:the droplet behaviors may be influenced by several physical factors. To clearly elucidate the physics governing droplet dynamics in a bifurcating micro-channel, a detailed numerical study on this problem is conducted. The present investigation is based on our recently developed phase-field-based lattice Boltzmann multiphase model, in which one distribution function is used to solve the Cahn-Hilliard equation, and the other is adopted to solve the Navier-Stokes equations. In this paper, we mainly focus on the effects of the surface wettability, capillary number and outlet flux ratio on the droplet dynamics, and the volume of the generated daughter droplet is also presented. The numerical results show that when the capillary number is large enough, the droplet behaviors depend critically on surface wettability. For the nonwetting case, the main droplet breaks up into two daughter droplets, which then completely suspend in the branched channels and flow towards the outlet. While for the wetting case, the main droplet also breaks up into two daughter droplets at first, and then different behaviors can be observed. The daughter droplet undergoes a secondary breakup, which results in part of droplet adhering to the wall, and the remaining flowing to the outlet. The volume of the generated daughter droplet is also measured, and it is shown that it increases linearly with contact angle increasing. When the capillary number is small enough, the droplet remains at the bifurcating position, which does not break up. Finally, we also find that the outlet flux ratio affects the rupture mechanism of the droplet. When the outlet flux ratio is 1, the droplet is split into two identical daughter droplets. When the outlet flux ratio increases, an asymmetric rupture resulting in the generation of two different daughter droplets, will be observed. However, if the outlet flux ratio is larger enough, the droplet does not breakup, and flows into the branched channel where the fluid velocity is larger. Here we define a critical outlet flux ratio, below which the droplet breakup occurs, and above which the droplet does not break up. The relationship between the capillary number and the critical outlet flux ratio is examined, and it is found that the critical outlet flux ratio increases with capillary number increasing.