Droplet spreading: Role of characteristic length scales and modified disjoining pressure

TL;DR

This study investigates how characteristic length scales influence droplet spreading predictions using a lubrication-based model, proposing a new scaling relation for disjoining pressure with high accuracy.

Contribution

It introduces a model that incorporates stage-specific characteristic length scales and proposes a novel scaling relation for disjoining pressure prediction.

Findings

Choice of characteristic scales affects accuracy of droplet spreading predictions.

Model predictions align well with experimental data for different substrates.

New scaling relation for disjoining pressure achieves ±5% error.

Abstract

The numerical prediction of droplet base radius and contact angle depends on the choice of characteristic radius and height of droplet. In this study, a developed model on the basis of lubrication approximation is used to investigate the effect of characteristic parameters on the spreading of droplets over substrates. Based on two main stages of spreading (initial and equilibrium), characteristic radius and height were first evaluated. The model predictions were then compared with experimental results in literature for both impermeable and permeable substrates. The study provides evidence that the choice of characteristic length scales based on either stage enables accurate prediction of the droplet base radius and contact angle. In addition, a new scaling relation for the predictions of the numerical disjoining pressure, with an error of $\pm$5\%, is proposed.