Coalescence speed of two equal-sized nanobubbles

In this work, we use molecular dynamics (MD) simulations coupled with continuum-based theoretical analysis to study the coalescence dynamics of two equal-sized nanobubbles (NBs). We first derive a governing equation for the evolution of the capillary bridge radius between two coalescing NBs from the axisymmetric Navier-Stokes equation. To verify the prediction from the governing equation, we carry out MD simulations of the coalescence of two NBs in a Lennard-Jones fluid system and directly measure the bridge radius, rb, as a function of time, t. By varying the bubble diameter, we change the NB Ohnesorge number from 0.46 to 0.33. In all cases, we find the theoretical prediction overestimates the expansion speed of the capillary bridge at early time of NB coalescence. However, once we take into account the curvature-dependent surface tension and restrict the minimum principal radius at the capillary bridge to the size of the atom in the model liquid, the theoretical prediction agrees with the MD data very well in both early time and later time of the coalescence process. From the theoretical model, we find neither liquid viscous force nor liquid inertial force dominates at later time of coalescence of the model NBs. In this case, the MD simulation results show rb(t) t0.76 ± 0.04 with the scaling exponent considerably higher than that in the scaling law rb(t) t0.5 for the viscous and inertial dominated regimes. The diameter ratio of fully merged NB to that of the original NB is about 2, which is different from 23 for the coalescence of millibubbles and microbubbles.