<i>Coalescence speed of two equal-sized nanobubbles</i>

We use molecular dynamics (MD) simulations coupled with continuum-based theoretical analysis to study the coalescence dynamics of two equal-sized nanobubbles (NBs). By varying the bubble diameter, we change the NB Ohnesorge number from 0.46 to 0.33 and directly measure the bridge radius, r_b, as a function of time, t. In all cases, we find the prediction from the axisymmetric Navier-Stokes equation 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 r_b(t)∝t^0.76±0.04 with scaling exponent considerably higher than that in the scaling law r_b(t)∝t^0.5 for the viscous and inertial dominated regimes.