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≤ We≤1790 and 10∘≤θ≤90∘. The simulations reproduce the principal features observed experimentally and identify five post-impact regimes in the We--θ plane: deposition, front splashing, side splashing, side-front splashing, and crown splashing. The deposition--front-splashing transition is described by the tangential-inertial parameter Ks=Wecosθ, with Ksc≈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 WeNc≈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 ds,med/D∼ We−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 Ns∼ We9/5, 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.
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BibTeX
@misc{xiong2026splashingregime,
title = {{Splashing-regime transitions and secondary-droplet scaling in oblique drop impacts on a deep pool}},
author = {Ying Xiong and Yang Zhang and Lingling Xie and Xiaolei Li},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.29762},
eprint = {2608.29762},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29762},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Splashing-regime transitions and secondary-droplet scaling in oblique drop impacts on a deep pool
AU - Ying Xiong
AU - Yang Zhang
AU - Lingling Xie
AU - Xiaolei Li
PY - 2026
DA - 2026/09/19
PB - arXiv
DO - 10.48550/arxiv.2608.29762
UR - https://arxiv.org/abs/2608.29762
AB - 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≤ We≤1790 and 10^∘≤θ≤90^∘. The simulations reproduce the principal features observed experimentally and identify five post-impact regimes in the We--θ 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=Wecosθ, with K_s^c≈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 We_N^c≈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,med/D∼ We^−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∼ We^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.
ER -