Splashing-regime transitions and secondary-droplet scaling in oblique drop impacts on a deep pool

Abstract

Oblique drop impact onto a deep liquid pool produces asymmetric crowns, directional jetting, and splashing transitions that cannot be characterized by the total impact inertia alone. We numerically investigate water drops impacting a quiescent deep pool over $41\le We\le 1790$ and $10^{\circ }\le \theta \le 90^{\circ }$. The simulations reproduce the principal features observed experimentally and identify five post-impact regimes in the $We$--$\theta$ plane: deposition, front splashing, side splashing, side-front splashing, and crown splashing. The deposition--front-splashing transition is described by the tangential-inertial parameter $K_s=We\cos \theta$, with $K_s^c\approx 120$. This criterion follows from the competition between downstream crown-rim inertia and capillary retraction at the Taylor--Culick velocity. The transition from front to side-front splashing is instead governed primarily by normal impact inertia, with a critical normal Weber number $W{e}_N^c\approx 318$. Beyond these regime transitions, the secondary-droplet statistics reveal fragmentation behavior common to the different splashing regimes. The droplet-size distributions are positively skewed, and the median diameter follows $d_{s,\mathrm{med}}/D\sim W{e}^{-3/5}$. Second-order velocity structure functions support a scale-dependent capillary--inertial description of rim and ligament breakup. Combined with mass conservation, this scaling gives $N_s\sim W{e}^{9/5}$, providing a numerical explanation for the secondary-droplet-number scaling observed experimentally. Thus, directional impact inertia governs the macroscopic selection of splashing regimes, whereas the secondary-droplet populations across these regimes exhibit a common capillary--inertial fragmentation scaling.

28 pages, 13 figures