Viscoplastic elliptical objects impacting a solid surface

Abstract

This theoretical and numerical study focuses on the physical mechanism driving the spreading of viscoplastic elliptical millimetric/centimetric objects after they impact a solid surface under no-slip conditions. The two-dimensional impacting objects are described as Bingham fluids. The two-dimensional numerical simulations are based on a variational multi-scale approach devoted to multiphase non-Newtonian fluid flows. The obtained results are analyzed considering the spreading dynamics, energy budgets and scaling laws. They show that, under negligible capillary effects, the impacting kinetic energy of the elliptical objects is dissipated through viscoplastic effects during the spreading process, giving rise to three flow regimes: inertio-viscous, inertio-plastic, and mixed inertio-visco-plastic. These regimes are strongly affected by the initial aspect ratio of the impacting objects, which reveals the possibility of using morphology to control spreading. Finally, the results are summarized in a diagram linking the object's maximum spreading and spreading time with different spreading regimes through a single dimensionless parameter called impact number.