Length and time scales of a liquid drop impact and penetration into a granular layer (original) (raw)
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Scaling of liquid-drop impact craters in wet granular media
Combining high-speed photography with laser profilometry, we study the dynamics and the morphology of liquid-drop impact cratering in wet granular media-a ubiquitous phenomenon relevant to many important geological, agricultural, and industrial processes. By systematically investigating important variables such as impact energy, the size of impinging drops, and the degree of liquid saturation in granular beds, we uncover a scaling law for the size of impact craters. We show that this scaling can be explained by considering the balance between the inertia of impinging drops and the strength of impacted surface. Such a theoretical understanding confirms that the unique energy partition originally proposed for liquid-drop impact cratering in dry granular media also applies for impact cratering in wet granular media. Moreover, we demonstrate that compressive stresses, instead of shear stresses, control the process of granular impact cratering. Our study enriches the picture of generic granular impact cratering and sheds light on the familiar phenomena of raindrop impacts in granular media.
Length and time scales of a liquid drop
2013
Length and time scales of a liquid drop impact and penetration into a granular layer 1 Liquid drop impact and penetration into a granular layer are investigated with diverse liquids and granular materials. We use various size of SiC abrasives and glass beads as a target granular material. We also employ ethanol and glycerol aqueous solutions as well as distilled water to make a liquid drop. The liquid drop impacts the granular layer with a low speed (∼m/s). The drop deformation and penetration are captured by a high speed camera. From the video data, characteristic time scales are measured. Using a laser profilometry system, resultant crater morphology and its characteristic length scales are measured. Static strength of the granular layer is also measured by the slow pillar penetration experiment to quantify the cohesive force effect. We find that the time scales are almost independent of impact speed, but they depend on liquid drop viscosity. Particularly, the penetration time is proportional to the square root of the liquid drop viscosity. Contrastively, the crater radius is independent of the liquid drop viscosity. The crater radius is scaled by the same form as the previous paper, (
Morphology Scaling of Drop Impact onto a Granular Layer
Physical Review Letters, 2010
We investigate the impact of a free-falling water drop onto a granular layer. First, we constructed a phase diagram of crater shapes with two control parameters, impact speed and grain size. A low-speed impact makes a deeper cylindrical crater in a fluffy granular target. After high-speed impacts, we observed a convex bump higher than the initial surface level instead of a crater. The inner ring can be also observed in a medium impact speed regime. Quantitatively, we found a scaling law for a crater radius with a dimensionless number consisting of impact speed and density ratio between the bulk granular layer and water drop. This scaling demonstrates that the water drop deformation is crucial to understanding the crater morphology.
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 gran-ular 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. liquid impacts | granular impact cratering | jamming | liquid marble G ranular 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 Significance We provide a quantitative understanding of raindrop impacts on sandy surfaces—a ubiquitous phenomenon relevant to many important natural, agricultural, and industrial processes. Combining high-speed photography with high-precision laser profilometry, we investigate the dynamics of liquid-drop impacts on granular surfaces and monitor the morphology of resulting impact craters. Remarkably, we discover a quantitative similarity between liquid-drop impacts and asteroid strikes in terms of both the energy scaling and the aspect ratio of their impact craters. Such a similarity inspires us to apply the idea developed in planetary sciences to liquid-drop impact cratering, which leads to a model that quantitatively describes various features of liquid-drop imprints.
Morphology and scaling of impact craters in granular media
Physical Review Letters, 2003
We present the results of experiments on impact craters formed by dropping a steel ball vertically into a container of small glass beads. As the energy of impact increases, we observe a progression of crater morphologies analogous to that seen in craters on the moon. We find that both the diameter and the depth of the craters are proportional to the 1=4 power of the energy. The ratio of crater diameter to rim-tofloor depth is constant for low-energy impacts, but increases at higher energy, similar to what is observed for lunar craters.
Impact cratering depends on projectile-to-grain and grain-to-grain interactions during the very short time of impact. This study investigates the effects of different media composition, namely the ratio between beach sand and silica sand of the impacted medium, on crater diameter and depth. Pure silica sand, pure beach sand, and ratios of 1:2, 1:1 and 2:1 of silica:beach sand were tested, and a plastic ball was dropped from various heights for different media. The recorded crater diameters and depths indicate that impact cratering is a more complex process than previously thought mainly because of the increased randomness in grain-to-grain contacts and force chain distributions produced by mixing different granular materials. It seems that mixtures of smaller grains and larger grains create a quasi-alloy state where smaller grains fill in the gaps between larger grains to increase the number of grain-to-grain contacts and force chains, and hence increase the rigidity of the medium. An equal partitioning of silica sand and beach sand seem to maximize this effect, as the medium with a volume ratio of 1:1 silica:beach sand has the smallest scaling factor for crater diameter. Although the crater depths result did not follow the 1/3 to 1/4 scaling factor proposed by previous studies, the shallower depths with larger compositions of silica sand confirm that crater depth decreases as grain sizes increase. The data also suggest that the quasi-alloy state of mixed medium redirects the energy of the projectile from deeper penetrations instead to wider and shallower displacements of sand.
Unified force law for granular impact cratering
Nature Physics, 2007
Experiments on the low-speed impact of solid objects into granular media have been used both to mimic geophysical events [1-5] and to probe the unusual nature of the granular state of matter [6-9]. While the findings are all strikingly different from impact into ordinary solids and liquids, no consensus has emerged regarding the interaction between medium and projectile. Observation that the final penetration depth is a power of the total drop distance was interpreted by a stopping force that is a product of powers of depth and speed [6]. Observation that the penetration depth is linear in initial impact speed was interpreted by a force that is linear in speed [7]. Observation that the stopping time is constant was interpreted by a force that is constant but proportional to the initial impact speed [8]. Observation that depth vs time is a sinusoid for a zero-speed impact was interpreted by a force that is proportional to depth [9]. These four experimental results, as well as their interpretations, would all seem to be in conflict. This situation is reminiscent of highspeed ballistics impact in the 19 th and 20 th centuries, when a plethora of empirical rules were proposed [10,11]. To make progress, we developed a means to measure projectile dynamics with 100 nm and 20 s precision. For a 1-inch diameter steel
A novel experimental setup for an oblique impact onto an inclined granular layer
Review of Scientific Instruments
We develop an original apparatus of the granular impact experiment by which the incident angle of the solid projectile and inclination angle of the target granular layer can be systematically varied. Whereas most of the natural cratering events occur on inclined surfaces with various incident angles, there have not been any experiments on oblique impacts on an inclined target surface. To perform systematic impact experiments, a novel experimental apparatus has to be developed. Therefore, we build an apparatus for impact experiments where both the incident angle and the inclination angle can be independently varied. The projectile-injection unit accelerates a plastic ball (6 mm in diameter) up to v i 100 m s −1 impact velocity. The barrel of the injection unit is made with a three-dimensional printer. The impact dynamics is captured by high-speed cameras to directly measure the impact velocity and incident angle. The rebound dynamics of the projectile (restitution coefficient and rebound angle) is also measured. The final crater shapes are measured using a line-laser profiler mounted on the electric stages. By scanning the surface using this system, a three-dimensional crater shape (height map) can be constructed. From the measured result, we can define and measure the characteristic quantities of the crater. The analyzed result on the restitution dynamics is presented as an example of systematic experiments using the developed system.
Unified force law for granular impact cratering 48 PUBLICATIONS 463 CITATIONS SEE PROFILE
Experiments on the low-speed impact of solid objects into granular media have been used both to mimic geophysical events [1-5] and to probe the unusual nature of the granular state of matter [6-9]. While the findings are all strikingly different from impact into ordinary solids and liquids, no consensus has emerged regarding the interaction between medium and projectile. Observation that the final penetration depth is a power of the total drop distance was interpreted by a stopping force that is a product of powers of depth and speed [6]. Observation that the penetration depth is linear in initial impact speed was interpreted by a force that is linear in speed [7].
Low-Speed Impact Craters in Loose Granular Media
Physical Review Letters, 2003 dsim(rhob3/2Db2H)1/3d\sim({\rho_{b}}^{3/2}{D_{b}}^{2}H)^{1/3}dsim(rhob3/2Db2H)1/3. The scaling with properties of the medium is also established. The crater depth has significance for granular mechanics in that it relates to the stopping force on the ball.