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.

中文翻译：

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粘塑性椭圆物体撞击固体表面

这项理论和数值研究重点关注粘塑性椭圆毫米/厘米物体在无滑移条件下撞击固体表面后驱动其扩散的物理机制。二维撞击物体被描述为宾汉流体。二维数值模拟基于致力于多相非牛顿流体流动的变分多尺度方法。考虑到扩散动力学、能量预算和缩放定律，对所获得的结果进行了分析。他们表明，在可忽略的毛细管效应下，椭圆形物体的冲击动能在扩散过程中通过粘塑性效应消散，产生三种流态：惯性-粘性、惯性-塑性和混合惯性-粘塑性。这些状态受到撞击物体的初始纵横比的强烈影响，这揭示了使用形态来控制扩散的可能性。最后，结果总结在一个图表中，通过称为影响数的单个无量纲参数将对象的最大扩散和扩散时间与不同的扩散方式联系起来。