Numerical prediction of flake-particle displacement and orientation during droplet impact

• A fitting equation predicts flake-particle motion and orientation in droplet impact. • Dimensionless parameters (We, Re) govern particle displacement. • Generalized Reynolds number extends applicability to non-Newtonian fluids. • Validation confirms model accuracy for microscale droplet impact. • Findings provide a unified framework for droplet–particle interaction analysis. The behavior of flake particles within impacting droplets is crucial to industrial applications, including coating technologies. In this study, a numerical model is developed to predict both the displacement and orientation of flake particles in Newtonian and non-Newtonian droplets upon impact. A dimensionless equation for the particle displacement is derived using key parameters such as the Weber number and Reynolds number, while orientation behavior is captured using a semi-empirical model based on the initial Stokes number and initial particle orientation. The models are validated through computational fluid dynamics simulations under various fluid properties and impact velocities. To extend the models to non-Newtonian fluids, a generalized Reynolds number is introduced, incorporating shear-rate-dependent viscosity. Additionally, microscale-droplet simulations confirm the scalability of the models. These findings provide a unified framework for analyzing flake-particle dynamics during droplet impact and contribute to improving coating uniformity and efficiency in practical applications.