Coalescence dynamics of two unequal size water droplets in air

Coalescence dynamics of two water droplets falling under gravity in air, is studied for various diameter ratio (d$_{\mathrm{bottom}}$/d$_{\mathrm{top}})$ D$_{\mathrm{r}}=$0.15-6 and Ohnesorge number Oh$=$0.001-0.025 at a Bond number Bo$=$0.092. Axisymmetric simulations are done using sharp interface level set method based in-house code. We presented a regime map for the various Oh and D$_{\mathrm{r}}$, with partial coalescence at smaller as well as larger values of D$_{\mathrm{r}}$ and full coalescence at intermediate value of D$_{\mathrm{r}}$. For a transition in the coalescence dynamics, the present work reports a smaller and a larger critical value of D$_{\mathrm{r}}$ as compared to one critical D$_{\mathrm{r}}$ (the larger one) reported in the literature. Over the range of Oh studied here, there is a monotonic increase in both the critical D$_{\mathrm{r}}$ with increasing Oh -- from 1.5 to 5.7 for the larger critical D$_{\mathrm{r}}$ and from 0.3 to 0.4 for the smaller critical D$_{\mathrm{r}}$. The pinch-off height of satellite droplet is larger for partial coalescence at the larger D$_{\mathrm{r}}$ as compared to that at the smaller D$_{\mathrm{r}}$. The partial coalescence regime at the smaller D$_{\mathrm{r}}$ is presented here for the first time.