Three-dimensional tracking and modeling of flake particle migration during droplet impact

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• Flake particle motion was experimentally analyzed in droplets. • A dimensionless model was developed to predict flake particle migration. • A novel imaging method enabled 3D particle height estimation from brightness. • 3D tracking of flake particles within droplets was experimentally achieved. • Migration model was extended to non-Newtonian fluids using effective viscosity. Aluminum flake particles in automotive paints critically influence the coating’s appearance through their distribution and orientation. However, their migration behavior during droplet impact remains unclear due to complex internal flows and optical distortions. In this study, we develop an experimental method to visualize and track the three-dimensional (3D) positions of multiple flake particles within a droplet as it impacts a solid surface. We estimate the particle height from the brightness in the bottom-view images, enabling 3D trajectory reconstruction. The analysis shows that the radial initial position predominantly affects the maximum migration distance, while the initial height has minimal influence. Furthermore, we derive a predictive equation using dimensional analysis based on Buckingham’s π theorem and validate it for Newtonian and non-Newtonian fluids by incorporating effective viscosity from the generalized Reynolds number. The experimental results closely matched the numerical simulations, confirming the model’s reliability. This work provides a novel experimental approach and quantitative insights into flake particle migration, contributing to improved control of coating processes using flake pigments.