Pontier Alexandre, Blosse Sarah, Viroulet Sylvain, Lacaze Laurent
Institut de Mécaniques des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, 31400 Toulouse, France.
Soft Matter. 2025 Jul 23;21(29):5935-5946. doi: 10.1039/d4sm00917g.
This paper explores crater formation resulting from the impact of a liquid drop on a densely packed granular bed composed of lightweight polystyrene beads. Several regimes based on the drop impact velocity and diameter , and the grain diameter are identified. These regimes are discussed in terms of several dimensionless numbers, including a Froude number Fr, which compares the droplet's kinetic energy to its potential energy at impact, the Weber number We, which compares the inertial to capillary forces, and the size ratio /. At low We, Fr, and /, the dimensionless crater diameter / follows a power-law scaling as We, consistent with previous studies on droplet impacts on granular surfaces, where the crater size reflects the maximum droplet spreading observed on a solid surface. This situation is thus analysed using a so-called signature approach. In this situation, the crater size is also shown to quantitatively depend on /. When We exceeds a critical value We(/), the scaling deviates from We and the crater size depends mainly on /. This transition is discussed in connection with the onset of droplet splashing. For larger /, a different power-law scaling emerges with an exponent smaller than 1/4, regardless of the value of Fr or We, and the splash transition no longer occurs under these conditions. This is consistent with other studies, highlighting the significant amount of energy transfer in crater formation, therefore referred to as the energetic approach. Overall, the final crater size is found to depend strongly on / among the droplet impact characteristics. To unify part of these observations, the role of local dissipation due to grain contact friction during crater formation is incorporated. This leads to the definition of a new dimensionless number , which combines the effects of grain-to-drop size ratio / and droplet inertia ( Fr). This parameter enables the collapse of / data onto a single curve for the range of parameters investigated in this study.
本文探讨了液滴撞击由轻质聚苯乙烯珠粒组成的密集堆积颗粒床时形成坑洼的情况。根据液滴撞击速度、直径以及颗粒直径确定了几种模式。这些模式通过几个无量纲数进行讨论，包括弗劳德数Fr，它将液滴的动能与其撞击时的势能进行比较；韦伯数We，它将惯性力与毛细力进行比较；以及尺寸比/。在低We、Fr和/的情况下，无量纲坑洼直径/遵循与We相关的幂律标度，这与先前关于液滴撞击颗粒表面的研究一致，在该研究中坑洼尺寸反映了在固体表面观察到的最大液滴铺展情况。因此，这种情况使用所谓的特征方法进行分析。在这种情况下，坑洼尺寸也显示出定量地依赖于/。当We超过临界值We(/)时，标度偏离We，坑洼尺寸主要取决于/。结合液滴飞溅的开始对这种转变进行了讨论。对于较大的/，无论Fr或We的值如何，都会出现指数小于1/4的不同幂律标度，并且在这些条件下飞溅转变不再发生。这与其他研究一致，突出了坑洼形成过程中大量的能量转移，因此称为能量方法。总体而言，发现最终坑洼尺寸在液滴撞击特性中强烈依赖于/。为了统一部分这些观察结果，考虑了坑洼形成过程中由于颗粒接触摩擦导致的局部耗散的作用。这导致定义了一个新的无量纲数，它结合了颗粒与液滴尺寸比/和液滴惯性（Fr）的影响。对于本研究中所研究的参数范围，该参数能够将/数据汇聚到一条单一曲线上。
