Numerical investigation on the head-on collision between unequal-sized droplets with multiple-relaxation-time lattice Boltzmann model

Abstract

Droplet collision is a fundamental and important phenomenon in multiphase flow. Compared with equal-sized droplet collision, unequal-sized cases have been much less examined and understood. In the present study, the high density ratio lattice Boltzmann multiphase model proposed by Lee et al. (2010) and Lee (2009) is realized into the multiple-relaxation-time formulation in the axisymmetric cylindrical coordinate, which succeeds in achieving both high density ratio and low viscosity. Using this model, the head-on droplet collision between unequal-sized droplets is investigated from the aspects of the diameter ratio, Ohnesorge number (Oh), and the Weber number (We) by discussing their effects on the time-resolved evolutions of droplet shape, flow field, and the mixing process. It is found that the diameter ratio is crucial in determining the droplet dynamics and outcome, since at low diameter ratio the droplet deforms slightly and exhibits the characteristics of surface wave propagation. Whereas, as the diameter ratio increases the droplet deforms more largely and symmetrically, which is easier to result in reflexive separation, and gas bubble is likely to be entrapped in the droplet at medium diameter ratio. Besides, it is found that the initial smaller droplet tends to spread or penetrate more into the larger one with increasing diameter ratio, while the “mixing pattern” (whether axially nailed into, or penetrate/spread from the side) is not obviously affected by the diameter ratio. The Oh number is found to affect the mixing process more than the droplet dynamics and the outcome, since at low Oh number the smaller droplet penetrates axially into the larger one, at medium Oh number it tends to spread on the larger one’s surface, while at high Oh number it accumulates at its initial side. The effect of We number on mixing is found to be relevant with the Oh number and diameter ratio. As We number increases, at high Oh number the initial smaller droplet spreads more widely on the larger one’s surface; at low Oh number, the initial smaller droplet penetrates axially deeper into the larger one at low diameter ratio, while tends to spread on the larger one’s side surface at large diameter ratio.