Effects of initial conditions on the coalescence of micro-bubbles

The effects of initial conditions on the coalescence of two equal-sized air micro-bubbles ( R0) in water are studied using the lattice Boltzmann method. The focus is on effects of two initial set-ups of parent bubbles, separated by a small distance d and connected with a neck bridge radius r0, on the neck bridge growth at the early stage of the bubble coalescence. A sophisticated free energy lattice Boltzmann method model based on the Cahn-Hilliard diffuse interface approach is employed. This lattice Boltzmann method model has been demonstrated suitable for handling a large density ratio of two fluids up to 1000 and capable of minimizing the nonphysical spurious current. In both initial scenarios, the neck bridge evolution exhibits a half power-law scaling, [Formula: see text] after a development time. The half power-law agrees with the recent analytical prediction and experimental results. It has been found that smaller initial separation distance or smaller initial neck bridge radius results in faster growth of neck bridge and bubble coalescence, which is similar to the effects of these two initial scenarios on droplet coalescence. The physical mechanism behind each behavior has been explored. For the initial connected case, faster neck growth and longer development time corresponding to smaller initial neck radius is due to the significant bias between the capillary forces contributed by the meniscus curvature and the neck bridge curvature, whereas in the case of initial separated scenario, faster growth and shorter development time corresponding to shorter separation distance is due to the formation of elongated neck bridge. The prefactor A0 that represents the growth of neck bridge radius at the characteristic time ti captured in each case is in good agreement with the experimental results.