Combined dynamic-kinematic validation of droplet-wall impact modeling

TL;DR

This paper introduces a combined dynamic contact angle model that improves droplet impact predictions by integrating geometric and kinematic metrics, validated through simulations and experiments on water-glycerol droplets impacting sapphire glass.

Contribution

It presents a novel combined model merging Hoffman-Voinov-Tanner law with Hoffman function-based approach for better droplet impact simulation accuracy.

Findings

Hoffman function-based model captures receding dynamics more accurately.

Generalized Hoffman-Voinov-Tanner law matches maximum spreading within 7%.

Radial velocity errors during receding are significantly reduced with the new model.

Abstract

Many numerical studies validate droplet wall impact using only maximum spreading diameter, yet this metric alone cannot ensure correct droplet dynamics. We present a combined dynamic contact angle (DCA) model that merges the geometric accuracy of the generalized Hoffman-Voinov-Tanner law with the kinematic consistency of a Hoffman function-based approach, improving predictions of droplet spreading and receding. We simulate water-glycerol droplet impact on sapphire glass at Weber numbers 20 -- 250 and assess both contact angle formulations. Simulated radial velocity fields are processed in Python using SciPy and compared with Particle Image Velocimetry measurements in the longitudinal section of the spreading droplet. The Hoffman function-based model captures the main droplet kinematic trends and provides more consistent receding dynamics. The generalized Hoffman-Voinov-Tanner law matches the maximum spreading diameter within 7%. However, during receding, it shows a median absolute error in radial velocity up to three times higher than that of the Hoffman function-based solution. Average radial velocity and spreading velocity can differ from experimental trends even when maximum spreading is reproduced. These findings support validation combining geometric and kinematic metrics and motivate the combined model for predicting spreading and receding. Using the maximum spreading factor $\beta_{max}$ as the ratio of the maximum spreading diameter over the initial droplet diameter and the characteristic capillary number $Ca_{char}$ defined from the mean internal horizontal velocity at 300 micrometer above the substrate, we introduce a $(\beta_{max},\,Ca_{char})$ diagram to relate spreading characteristics to internal flow dynamics. We hypothesize that, given sufficient data, the contact-line geometry may be used to estimate internal kinematics.