Kinematic Closure of Drop Impact

TL;DR

This paper derives a unified scaling law for droplet impact spreading, accurately predicting maximum spreading ratios across different regimes by directly using energy balance principles.

Contribution

It introduces a self-consistent model based on energy balance to predict maximum droplet spreading, unifying inertio-capillary and inertio-viscous regimes.

Findings

The model quantitatively matches experimental and literature data.

It provides a regime-independent prediction without adjustable prefactors.

Abstract

Existing models for droplet impact prescribe the spreading contact time and effective spreading velocity from asymptotic arguments, which prevents a self-consistent prediction of the maximum spreading ratio across regimes. Here, the total spreading time and characteristic spreading velocity are derived directly from the energy balance, with explicit capillary and viscous contributions. Multiplying this time and velocity to obtain the maximum spreading diameter yields a closed, unified scaling law for the maximum spreading ratio of wetting drops across inertio-capillary and inertio-viscous regimes. The resulting expression quantitatively collapses the present measurements and literature data over wide ranges of Weber and Ohnesorge numbers, droplet sizes, and surface wettabilities without prefactors that need to be adjusted to a certain regime.