Granular impact cratering by liquid drops: Understanding raindrop imprints through an analogy to asteroid strikes

When a granular material is impacted by a sphere, its surface deforms like a liquid yet it preserves a circular crater like a solid. Although the mechanism of granular impact cratering by solid spheres is well explored, our knowledge on granular impact cratering by liquid drops is still very limited. Here, by combining high-speed photography with high-precision laser profilometry, we investigate liquid-drop impact dynamics on granular surface and monitor the morphology of resulting impact craters. Surprisingly, we find that despite the enormous energy and length difference, granular impact cratering by liquid drops follows the same energy scaling and reproduces the same crater morphology as that of asteroid impact craters. Inspired by this similarity, we integrate the physical insight from planetary sciences, the liquid marble model from fluid mechanics, and the concept of jamming transition from granular physics into a simple theoretical framework that quantitatively describes all of the main features of liquid-drop imprints in granular media. Our study sheds light on the mechanisms governing raindrop impacts on granular surfaces and reveals a remarkable analogy between familiar phenomena of raining and catastrophic asteroid strikes.Granular impact cratering by liquid drops is likely familiar to all of us who have watched raindrops splashing in a backyard or on a beach. It is directly relevant to many important natural, agricultural, and industrial processes such as soil erosion (1, 2), drip irrigation (3), dispersion of microorganisms in soil (4), and spray-coating of particles and powders. The vestige of raindrop imprints in fossilized granular media has even been used to infer air density on Earth 2.7 billion years ago (5). Hence, understanding the dynamics of liquid-drop impacts on granular media and predicting the morphology of resulting impact craters are of great importance for a wide range of basic research and practical applications.Directly related to two long-standing problems in fluid and granular physics research, i.e., drop impact on solid/liquid surfaces (6–9) and granular impact cratering by solid spheres (10–16), liquid-drop impact on granular surfaces is surely more complicated. Although several recent experiments have been attempted to investigate the morphology of liquid-drop impact craters (17–21), a coherent picture for describing various features of the impact craters is still lacking. Even for the most straightforward impact-energy (E) dependence of the size of liquid-drop impact craters, the results remain controversial and incomplete (17, 19, 20). Katsuragi (17) and Delon et al. (19) reported that the diameter of liquid-drop impact craters D_c scales as the 1/4 power of the Weber number of liquid drops, which yields D_c ～ E^1/4, quantitatively similar to the energy scaling for low-speed solid-sphere impact cratering (10, 11). However, because the energy balance of liquid-drop impacts is different from that of solid-sphere impacts, the energy scaling argument used for solid-sphere impact cratering cannot be applied to explain the 1/4 power. Instead, Katsuragi argued that the power arises from the scaling of the maximal spreading diameter of the impinging drop, which coincidently follows the same 1/4 scaling with E (22). However, a later study by Nefzaoui and Skurtys showed that D_c is not equal to the maximal spreading diameter and a different scaling with D_c ～ E^0.18 was found (20). Although covering a larger dynamic range of E, Nefzaoui and Skurtys only investigated the scaling dependence on E and failed to provide a full scaling for D_c. The origin of the strange 0.18 scaling in liquid-drop impact cratering is still unclear. Finally, in addition to the diameter of impact craters, other important properties of liquid-drop impact craters such as the depth of impact craters and the shape of granular residues inside craters have not been systematically explored so far.The challenges faced in the study of liquid-drop impact on granular surfaces are mainly due to the large number of relevant parameters involved in the process, the inability of existing methods for resolving the 3D structure of impact craters, and the difficulty in extending the dynamic range of E in experiments. Here, we investigate the dynamics of liquid-drop impacts on granular surfaces across the largest range of impact energy that has been probed so far, which covers more than four decades from the drop deposition regime to the drop terminal velocity regime. Through a systemic study using different liquid drops and granular particles at various ambient pressures, we obtain a full dimensionless scaling for the diameter of liquid-drop impact craters. Surprisingly, we find that this scaling follows the well-established Schmidt–Holsapple scaling rule associated with asteroid impact cratering (23). Moreover, by combining high-speed photography with high-precision laser profilometry, we nonintrusively measure the depth of impact craters underneath the impinging drop. The measurement reveals that liquid-drop impact craters and asteroid impact craters exhibit a self-similar shape despite their enormous length difference over seven orders of magnitude. These remarkable findings inspire us to apply the physical insight developed for asteroid impact cratering to the problem of liquid-drop impact cratering. The insight, in combination with the concepts of liquid marble (24) and particle jamming transition (25, 26), leads to a simple coherent model that quantitatively captures all of the main features of liquid-drop imprints in granular media including the diameter and the depth of impact craters and the shape of granular residues.