Viscoplastic drops impacting a free-slip surface

Abstract

This theoretical and numerical study investigates the physical mechanisms that drive the spreading of viscoplastic drops of millimetric to centimetric size after they collide with a solid surface under free-slip conditions and negligible capillary effects. These impacting drops are modeled as Bingham fluids. The numerical simulations are conducted using a variational multi-scale method tailored to multiphase non-Newtonian fluid flows. The results are analyzed by examining the dynamics of spreading, energy balance, and scaling laws. The findings indicate that the kinetic energy from the impact of the drops is dissipated through viscoplastic effects during the spreading process, leading to the emergence of three distinct flow regimes: inertio-viscous, inertio-plastic, and mixed inertio-visco-plastic. These regimes are heavily influenced by the initial aspect ratio of the impacting drops, suggesting that morphology can be used to control spreading behavior. The study concludes with a diagram that correlates the drop’s maximum spreading and spreading time with various spreading regimes using a single dimensionless quantity termed the impact parameter.