Scaling law in the inviscid coalescence of unequal-size droplets

Droplet coalescence is an essential multiphase flow process in nature and industry. For the inviscid coalescence of two spherical droplets, our experiment shows that the classical 1/2 power-law scaling for equal-size droplets still holds for the unequal-size situation of small size ratios, but it diverges as the size ratio increases. Employing an energy balance analysis, we develop the first theory for asymmetric droplet coalescence, yielding a solution that collapses all experimental data of different size ratios. This confirms the physical relevance of the new set of length and time scales given by the theory. The functionality of the solution reveals an exponential dependence of the bridge's radial growth on time, implying a scaling-free nature. Nevertheless, the small-time asymptote of the model is able to recover the classical power-law scaling, so that the actual bridge evolution still follows the scaling law asymptotically in a wide parameter space. Further analysis suggests that the scaling-free evolution behaviour emerges only at late coalescence time and large size ratios. © The Author(s), 2025. Published by Cambridge University Press.