Kinematic Closure of Drop Impact
Abstract
Predicting how far a liquid droplet spreads upon impacting a solid surface is governed by a complex competition between inertia, surface tension, and viscous dissipation. Existing models typically estimate this maximum spreading diameter by prescribing the spreading time or velocity from a decoupled asymptotic limit, restricting predictive accuracy across regimes. Here, we formulate a reduced kinematic description by resolving both the characteristic spreading time and spreading velocity from an energy balance coupling capillary storage and viscous dissipation. Unifying these two asymptotically constrained closures via the kinematic relation Dmax = Vs ts yields a compact, parameter-free approximation for the maximum spreading ratio that bridges the inertio-capillary and inertio-viscous regimes. We quantify the accuracy of this reduced closure against the exact implicit energy relation and demonstrate that it quantitatively collapses our experimental measurements alongside extensive literature data across wide ranges of Weber and Ohnesorge numbers, droplet sizes, and surface wettabilities without adjustable prefactors.
Related
- Universal mapping of drop impact spreading from wetting to Leidenfrost regimes
- The ejected volume and drop statistics by bubble bursting in a sessile drop
- Compound drop impacts on substrates of different temperatures
- Pressure-drop localization and momentum insulation in liquid-gas coexistence Poiseuille flow
- On the rise of a Taylor bubble-drop assembly in a vertical tube
BibTeX
@misc{abbot2026kinematic,
title = {{Kinematic Closure of Drop Impact}},
author = {Mete Abbot and Daniel Bonn},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.11797},
eprint = {2605.11797},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.11797},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Kinematic Closure of Drop Impact
AU - Mete Abbot
AU - Daniel Bonn
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2605.11797
UR - https://arxiv.org/abs/2605.11797
AB - Predicting how far a liquid droplet spreads upon impacting a solid surface is governed by a complex competition between inertia, surface tension, and viscous dissipation. Existing models typically estimate this maximum spreading diameter by prescribing the spreading time or velocity from a decoupled asymptotic limit, restricting predictive accuracy across regimes. Here, we formulate a reduced kinematic description by resolving both the characteristic spreading time and spreading velocity from an energy balance coupling capillary storage and viscous dissipation. Unifying these two asymptotically constrained closures via the kinematic relation D_max = V_s t_s yields a compact, parameter-free approximation for the maximum spreading ratio that bridges the inertio-capillary and inertio-viscous regimes. We quantify the accuracy of this reduced closure against the exact implicit energy relation and demonstrate that it quantitatively collapses our experimental measurements alongside extensive literature data across wide ranges of Weber and Ohnesorge numbers, droplet sizes, and surface wettabilities without adjustable prefactors.
ER -