We introduced a mass transfer calculation into the improved lattice Boltzmann method (LBM) for incompressible two-phase flows. To confirm the validity of the developed method, an unsteady mass transfer problem in a single droplet was simulated, and the numerical result was found to be in good agreement with the analytical solution. Subsequently, the mass transfer calculation method was applied to simulate collisions of binary droplets containing a very small amount of another miscible liquid, and the mass concentration distributions were investigated. In particular, we focused on the rotational separation phenomenon, i.e. colliding droplets coalesce, rotate generally by more than 180 degrees, and then separate from each other. It was found that the mass of the miscible liquid in each separated droplet is affected by the angular momentum at the collision. Furthermore, we defined and calculated the weighted angular momentum of the rotating droplets, which extracts the angular momentum in the high concentration region. The result showed that as the offset distance or the collision speed increases, the high concentration region of the droplets retains most of their pre-collisional angular momentum, which finally leads to enhancement of the mass transfer of the miscible liquid.
Saito et al. (Sun,) studied this question.