Morphology scaling of drop impact onto a granular layer

Experimental study of liquid drop impact on granular medium: Drop spreading/splashing and particle ejection

The impact of a liquid drop on a granular medium is a common phenomenon in nature and engineering. The possible splashing droplets and ejected particles could pose a risk of pathogen transmission if the water source or granular medium is contaminated. This work studies the liquid drop impact on the granular medium using high-speed photography and considers the effects of liquid properties, drop impact characteristics, and granular medium properties. Four flow regimes, including direct penetration, prompt splashing, spreading, and corona splashing, are observed and a regime map is created to identify their thresholds. The spreading regime can eject a large number of particles, and the corona splashing regime can produce splashing droplets in addition to the ejected particles. For the splashing droplets, their median diameters and velocities are in the ranges 0.11 to 0.21 and 0.15 to 0.37 of the diameter and velocity of the impact drop, and their median splashing angles range from 14° to 27°. Two particle ejection mechanisms are observed, falling squeeze and forward collision, driven by the collapsing and forward spreading of the liquid lamella, respectively. The particles ejected by the latter mechanism have larger ejection velocities, angles and distances from the impact center, which can facilitate their long-range transmission. In addition, the process of spreading and retracting of the lamella formed by the drop impact is also studied, and it is found that the maximum spreading diameter of the lamella is proportional to the crater diameter. These results improve the understanding of the phenomenon after the drop impact on the granular medium and the characteristics of the splashing droplets and ejected particles, contributing to the prediction and risk assessment of contaminated particle transmission.

Drop impact on wet granular beds: effects of water-content on cratering

Drop impact events on a wet granular bed show a rich variety by changing the substrate composition. We observe the drop impact onto dry/wet granular substrates with different grain sizes (50-400 μm) and water contents (0-22 vol%). Despite the fixed impactor conditions (impact velocity: 4.0 m s-1, water drop radius: 1.8 mm), the experiment reveals that the post-impact behaviors of both the impactor and target are strongly influenced by the substrate composition. We categorize these behaviors into several phases concerning liquid splashing and crater shapes left after the event. As these phases are relevant to each other, we measure the mechanical characteristics of the substrates and find that the onset of splashing and particle ejection is explained via the fracture of the substrate. Furthermore, we discuss several timescales of the event to understand the phase separations in more detail. Consequently, we find that the splashing phase and the crater shape are determined by competition among the timescales of impact, penetration, and contact.

Droplet jump from a particle bed

Drop tower experiments have been performed to study droplet jump from a particle bed across a wide range of fluid viscosities. Here the droplet jumps from the particle bed in response to the apparent step reduction from terrestrial gravity to microgravity when the experiment is dropped and enters free fall. The presence of a particle layer has been found to affect contact line dissipation and the overall jumping behavior of droplets. Additionally, the study has identified the impact of the Ohnesorge number (Oh) on droplet morphology. The investigation has yielded results that not only validate a modified version of the spring-mass-damper model for droplet rebound [Jha et al., Soft Matter, 2020, 16, 7270] but also extend its applicability to previously unexplored initial conditions. In particular, the model predicts droplet jump time and velocity. Moreover, the presence of particle layers has been found to effectively eliminate contact line dissipation without introducing substantial additional forms of dissipation. Experiments have been conducted at the Dryden Drop Tower facility at Portland State University. Particle beds have been constructed using polyethylene and polystyrene poly-dispersed spheres with diameters ranging from 125-150 μm and 600-1000 μm, respectively. The beds have been created by depositing a thin layer of particles on a glass substrate. The experimental conditions have allowed the exploration of a large parameter space of Bo0 1.8-8.6, We 0.05-1.40, and Oh 0.001-1.900.

Liquid Marbles and Drops on Superhydrophobic Surfaces: Interfacial Aspects and Dynamics of Formation: A Review

Liquid marbles (LMs) are droplets encapsulated with powders presenting varied roughness and wettability. These LMs have garnered a lot of attention due to their dual properties of leakage-free and quick transport on both solid and liquid surfaces. These droplets are in a Cassie-Baxter wetting state sitting on both roughness and air pockets existing between particles. They are also reminiscent of the state of a drop on a superhydrophobic (SH) surface. In this review, LMs and bare droplets on SH surfaces are comparatively investigated in terms of two aspects: interfacial and dynamical. LMs present a fascinating class of soft matter due to their superior interfacial activity and their remarkable stability. Inherently hydrophobic powders form stable LMs by simple rolling; however, particles with defined morphologies and chemistries contribute to the varied stability of LMs. The factors contributing to this interesting robustness with respect to bare droplets are then identified by tests of stability such as evaporation and compression. Next, the dynamics of the impact of a drop on a hydrophobic powder bed to form LMs is studied vis-à̀-vis that of drop impact on flat surfaces. The knowledge from drop impact phenomena on flat surfaces is used to build and complement insights to that of drop impact on powder surfaces. The maximum spread of the drop is empirically understood in terms of dimensionless numbers, and their drawbacks are highlighted. Various stages of drop impact-spreading, retraction and rebound, splashing, and final outcome-are systematically explored on both solid and hard surfaces. The implications of crater formation and energy dissipations are discussed in the case of granular beds. While the drop impact on solid surfaces is extensively reviewed, deep interpretation of the drop impact on granular surfaces needs to be improved. Additionally, the applications of each step in the sequence of drop impact phenomena on both substrates are also identified. Next, the criterion for the formation of peculiar jammed LMs was examined. Finally, the challenges and possible future perspectives are envisaged.

Cold granular targets slow the bulk freezing of an impacting droplet

When making contact with an undercooled target, a drop freezes. The colder the target is, the more rapid the freezing is supposed to be. In this research, we explore the impact of droplets on cold granular material. As the undercooling degree increases, the bulk freezing of the droplet is delayed by at least an order of magnitude. The postponement of the overall solidification is accompanied by substantial changes in dynamics, including the spreading-retraction process, satellite drop generation, and cratering in the target. The solidification of the wetted pores in the granular target primarily causes these effects. The freezing process over the pore dimension occurs rapidly enough to match the characteristic timescales of impact dynamics at moderate undercooling degrees. As a result, the hydrophilic impact appears "hydrophobic," and the dimension of the solidified droplet shrinks. A monolayer of cold grains on a surface can reproduce these consequences. Our research presents a potential approach to regulate solidified morphology for subfreezing drop impacts. It additionally sheds light on the impact scenario of strong coupling between the dynamics and solidification.

Scaling laws of plume-induced granular cratering

Extraterrestrial landing often requires firing a high-speed plume towards a planetary surface, and the resulting gas-granular interactions pose potential hazards to the lander. To investigate these jet-induced cratering dynamics, an experiment campaign covering a range of gas and granular properties relevant to the lunar and Martian environments was conducted in a large-scale vacuum chamber. Despite the variations in jet Mach number, mass flow rate, and composition of the granular phase investigated in this work, the observed time evolution of crater depth displays a consistent transition from an early-stage linear to a late-stage sublinear growth. To explain these scaling relations, a model that relates the kinetic energy gained by the particles per unit time to the power of the impinging jet is introduced. From this model, erosion rates and the critical depth at which the transition occurs can be extracted, and they are shown to depend on the gas impingement pressure, which was varied by changing ambient pressure, jet Mach number, mass flow rate, and nozzle height above the surface. These results highlight key mechanisms at work in the dynamics of plume-induced cratering and help to develop an understanding of optimal rocket engine firing times for future landings.

Soil Deformation after Water Drop Impact-A Review of the Measurement Methods

Water erosion is an unfavorable phenomenon causing soil degradation. One of the factors causing water erosion is heavy or prolonged rainfall, the first effect of which is the deformation of the soil surface and the formation of microcraters. This paper presents an overview of research methods allowing the study of microcraters as well as the process of their formation. A tabular summary of work on the measurements of various quantities describing the craters is presented. The said quantities are divided into three groups: (i) static quantities, (ii) dynamic quantities, and (iii) dimensionless parameters. The most important measurement methods used to study crater properties, such as (i) basic manual measurement methods, (ii) photography, (iii) high-speed imaging, (iv) profilometers, (v) 3D surface modelling, and (vi) computed tomography (CT) and its possibilities and limitations are discussed. The main challenges and prospects of research on soil surface deformation are also presented.

Key connection between gravitational instability in physical gels and granular media

We study gravitationally-driven (Rayleigh–Taylor-like) instability in physical gels as a model for the behavior of granular media falling under gravity; physical gels have a structural elasticity and may be fluidized, capturing both the solid and liquid properties of granular systems. Though ubiquitous in both industrial and natural contexts, the unique static and dynamic properties of granular media remain poorly understood. Under the action of a gravitational force, granular materials may flow while exhibiting heterogeneous rigidity, as seen during e.g., avalanches or landslides. Though the onset of this gravitational “instability” has been addressed, the mechanism behind its incidence is not yet understood. We find key quantitative similarities between Rayleigh–Taylor-like instability in physical gels and granular systems. In particular, we identify a common scaling law, showing that the instability is chiefly governed by the thickness of the flowable region.

Impact cratering in sand: comparing solid and liquid intruders

How does the impact of a deformable droplet on a granular bed differ from that caused by a solid impactor of similar size and density? Here, we experimentally study this question and focus on the effect of intruder deformability on the crater shape. For comparable impact energies, we show that the crater diameter is larger for droplets than for solid intruders but that the impact of the latter results in deeper craters. Interestingly, for initially dense beds of packing fractions larger than 0.58, we find that the resultant excavated crater volume is independent of the intruder deformability, suggesting an impactor-independent dissipation mechanism within the sand for these dense beds.

Explosion cratering in 3D granular media

Sudden release of energy in an explosion creates craters in granular media. In comparison with well-studied impact cratering in granular media, our understanding of explosion cratering is still primitive. Here, we study low-energy lab-scale explosion cratering in 3D granular media using controlled pulses of pressurized air. We identify four regimes of explosion cratering at different burial depths, which are associated with distinct explosion dynamics and result in different crater morphologies. We propose a general relation between the dynamics of granular flows and the surface structures of the resulting craters. Moreover, we measure the diameter of explosion craters as a function of explosion pressure, duration and burial depth. We find that the size of the craters is non-monotonic with increasing burial depth, reaching a maximum at an intermediate burial depth. In addition, the crater diameter shows a weak dependence on explosion pressure and duration at small burial depths. We construct a simple model to explain this finding. Finally, we explore the scaling relations of the size of explosion craters. Despite the huge difference in energy scales, we find that the diameter of explosion craters in our experiments follows the same cube root energy scaling as explosion cratering at high energies. We also discuss the dependence of rescaled crater sizes on the inertial number of granular flows. These results shed light on the rich dynamics of 3D explosion cratering and provide new insights into the general physical principles governing granular cratering processes.

A novel experimental setup for an oblique impact onto an inclined granular layer

We develop an original apparatus of the granular impact experiment by which the incident angle of the solid projectile and the 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 using 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.

Cratering response during droplet impacts on granular beds

This experimental work focuses on the cratering response of granular layers induced by liquid droplet impacts. A droplet impact results in severe granular layer deformation, crater formation and deposits in the vicinity of the impact center. High-precision three-dimensional imaging of the granular layer surface revealed important characteristics of liquid impacts on granular matter, such as singular asymmetric deformations of the layer. Our analysis also demonstrated that the impact energy and the granular packing, and its inherent compressibility, are not the unique parameters controlling the bed response, for which granular fraction heterogeneities may induce strong variations. Such heterogeneous conditions primarily influence the magnitude but not the dynamics of liquid impacts on granular layers. Finally, a general equation can be used to relate the enery released during cratering to both the impact energy and the compressibility of the granular matter. However, our results do not support any transition triggered by the compaction-dilation regime. Hence, higly detailed numerical simulations could provide considerable insights regarding the remaining questions related to heterogeneous packing conditions and its influence over the bulk compressibility and the compaction-dilation phase transition.

Impact cratering on a granular bed by hydrogel spheres having intermediate property between solid and liquid

We investigated the low speed impact on a granular bed by a hydrogel sphere and especially focused on the resultant crater diameter. Though the crater diameter depends only on the impact kinetic energy for the solid sphere impact cratering, it also depends on the elastic energy for the hydrogel sphere. The hydrogel sphere impact cratering is classified into two dynamics: small and large indentation of the sphere. For the small indentation, the crater diameter is proportional to the 1/4 power of the energy for ejecting granular materials, which is calculated by substituting the elastic energy stored in the sphere from the impact kinetic energy. Considering the force balance between the inertial force and the indentation, we derived the relation between the impact kinetic energy, Young's modulus, and the crater diameter. In the large limit of Young's modulus, the relation leads to the 1/4 power law observed in solid sphere impact. The dependency of Young's modulus on the crater diameter for the large indentation of the sphere is larger than the impact with small indentation.

Droplet impact on heated powder bed

The impact of droplets on a heated powder bed involves a wide range of phenomena with increasing complexity from spreading of liquid, to bubble nucleation, to more complex ones such as splashing, crater formation, and fluidization. In this study, we focus on the impact behaviors caused by elevation in temperature of the powder bed. We experimentally characterize the impact behaviors for wide ranges of the impact velocity and surface temperature of the powder bed. We reveal several phenomena specific to the impact on a heated powder bed such as rebound, ruptures of expanding liquid films, bubble nucleation, and fluidization. We also show that the maximum spreading diameter increases with the surface temperature of the powder bed and propose an empirical scaling law to describe such a relation.

Crater formation during raindrop impact on sand

After a raindrop impacts on a granular bed, a crater is formed as both drop and target deform. After an initial, transient, phase in which the maximum crater depth is reached, the crater broadens outwards until a final steady shape is attained. By varying the impact velocity of the drop and the packing density of the bed, we find that avalanches of grains are important in the second phase and hence affect the final crater shape. In a previous paper, we introduced an estimate of the impact energy going solely into sand deformation and here we show that both the transient and final crater diameter collapse with this quantity for various packing densities. The aspect ratio of the transient crater is however altered by changes in the packing fraction.

Liquid-Grain Mixing Suppresses Droplet Spreading and Splashing during Impact

Would a raindrop impacting on a coarse beach behave differently from that impacting on a desert of fine sand? We study this question by a series of model experiments, where the packing density of the granular target, the wettability of individual grains, the grain size, the impacting liquid, and the impact speed are varied. We find that by increasing the grain size and/or the wettability of individual grains the maximum droplet spreading undergoes a transition from a capillary regime towards a viscous regime, and splashing is suppressed. The liquid-grain mixing is discovered to be the underlying mechanism. An effective viscosity is defined accordingly to quantitatively explain the observations.

Rheological characterization of digested sludge by solid sphere impact

An impact method was applied to investigate the rheological characteristics of digested sludge and reveal its transient dynamics. A high-speed camera allowed visualizing the dynamic impact process and observing interaction between impacting sphere and targeted sludge. A damping oscillation was observed after the impact. The crater diameter followed an exponential function, while the crater depth varied as a logarithmic function of both sphere diameter and free fall height. Furthermore, the viscosity and elasticity of digested sludge were evaluated by establishing a simplified impact drag force model. The impact elastic modulus was consistent with the Young's modulus measured by a penetrometer. The impact viscosity was reasonable as the estimated impact shear stress was greater than the yield stress of digested sludge resulting in the formation of crater. The impact method offers an alternative way to reveal the viscoelasticity of digested sludge through a dynamic process.

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.

Raindrop impact on sand: a dynamic explanation of crater morphologies

As a droplet impacts upon a granular substrate, both the intruder and the target undergo deformation, during which the liquid may penetrate into the substrate. These three aspects together distinguish it from other impact phenomena in the literature. We perform high-speed, double-laser profilometry measurements and disentangle the dynamics into three aspects: the deformation of the substrate during the impact, the maximum spreading diameter of the droplet, and the penetration of the liquid into the substrate. By systematically varying the impact speed and the packing fraction of the substrate, (i) the substrate deformation indicates a critical packing fraction ϕ* ≈ 0.585; (ii) the maximum droplet spreading diameter is found to scale with a Weber number corrected by the substrate deformation; and (iii) a model of the liquid penetration is established and is used to explain the observed crater morphology transition.

Aerosol generation by raindrop impact on soil

Aerosols are investigated because of their significant impact on the environment and human health. To date, windblown dust and sea salt from sea spray through bursting bubbles have been considered the chief mechanisms of environmental aerosol dispersion. Here we investigate aerosol generation from droplets hitting wettable porous surfaces including various classifications of soil. We demonstrate that droplets can release aerosols when they influence porous surfaces, and these aerosols can deliver elements of the porous medium to the environment. Experiments on various porous media including soil and engineering materials reveal that knowledge of the surface properties and impact conditions can be used to predict when frenzied aerosol generation will occur. This study highlights new phenomena associated with droplets on porous media that could have implications for the investigation of aerosol generation in the environment.

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.

Experimental investigation into the impact of a liquid droplet onto a granular bed using three-dimensional, time-resolved, particle tracking

An experimental investigation into the interaction that occurs between an impacting water droplet and a granular bed of loose graded sand has been carried out. High-speed imaging, three-dimensional time-resolved particle tracking, and photogrammetric surface profiling have been used to examine individual impact events. The focus of the study is the quantification and trajectory analysis of the particles ejected from the sand bed, along with measurement of the change in bed morphology. The results from the experiments have detailed two distinct mechanisms of particle ejection: the ejection of water-encapsulated particles from the edge of the wetted region and the ejection of dry sand from the periphery of the impact crater. That the process occurs by these two distinct mechanisms has hitherto been unobserved. Presented in the paper are distributions of the particle ejection velocities, angles, and transport distances for both mechanisms. The ejected water-encapsulated particles, which are few in number, are characterized by low ejection angles and high ejection velocities, leading to large transport distances; the ejected dry particles, which are much greater in number, are characterized by high ejection angles and low velocities, leading to lower transport distances. From the particle ejection data, the momentum of the individual ballistic sand particles has been calculated; it was found that only 2% of the water-droplet momentum at impact is transferred to the ballistic sand particles. In addition to the particle tracking, surface profiling of the granular bed postimpact has provided detailed information on its morphology; these data have demonstrated the consistent nature of the craters produced by the impact and suggest that particle agglomerations released from their edges make up about twice the number of particles involved in ballistic ejection. It is estimated that, overall, about 4% of the water-droplet momentum is taken up in particle movement.

Penetration of projectiles into granular targets

Energetic collisions of subatomic particles with fixed or moving targets have been very valuable to penetrate into the mysteries of nature. But the mysteries are quite intriguing when projectiles and targets are macroscopically immense. We know that countless debris wandering in space impacted (and still do) large asteroids, moons and planets; and that millions of craters on their surfaces are traces of such collisions. By classifying and studying the morphology of such craters, geologists and astrophysicists obtain important clues to understand the origin and evolution of the Solar System. This review surveys knowledge about crater phenomena in the planetary science context, avoiding detailed descriptions already found in excellent papers on the subject. Then, it examines the most important results reported in the literature related to impact and penetration phenomena in granular targets obtained by doing simple experiments. The main goal is to discern whether both schools, one that takes into account the right ingredients (planetary bodies and very high energies) but cannot physically reproduce the collisions, and the other that easily carries out the collisions but uses laboratory ingredients (small projectiles and low energies), can arrive at a synergistic intersection point.

Impact on porous targets: penetration, crater formation, target compaction, and ejection

Using a granular-mechanics code, we study the impact of a sphere into a porous adhesive granular target, consisting of monodisperse silica grains. The model includes elastic repulsive, adhesive, and dissipative forces, as well as sliding, rolling, and twisting friction. Impact velocities of up to 30 m/s and target filling factors (densities) between 19% and 35% have been systematically studied. We find that the projectile is stopped by an effective drag force which is proportional to the square of its velocity. Target adhesion influences projectile stopping only below a critical velocity, which increases with adhesion. The penetration depth depends approximately logarithmically on the impact velocity and is inversely proportional to the target density. The excavated crater is of conical form and is surrounded by a compaction zone whose width increases but whose maximum value decreases with increasing target density. Grain ejection increases in proportion with impactor velocity. Grains are ejected which have originally been buried to a depth of 8R(grain) below the surface; the angular distribution favors oblique ejection with a maximum around 45°. The velocity distribution of ejected grains features a broad low-velocity maximum around 0.5-1 m/s but exhibits a high-velocity tail up to ~15% of the projectile impact velocity.

Simulation of granular jets: is granular flow really a perfect fluid?

We perform three-dimensional simulations of the impact of a granular jet for both frictional and frictionless grains. Small shear stress observed in the experiment [X. Cheng et al., Phys. Rev. Lett. 99, 188001 (2007)] is reproduced through our simulation. However, the fluid state after the impact is far from a perfect fluid, and thus the similarity between granular jets and quark gluon plasma is superficial because the observed viscosity is finite and its value is consistent with the prediction of the kinetic theory.

Building designed granular towers one drop at a time

A dense granular suspension dripping on an imbibing surface is observed to give rise to slender mechanically stable structures that we call granular towers. Successive drops of grain-liquid mixtures are shown to solidify rapidly upon contact with a liquid absorbing substrate. A balance of excess liquid flux and drainage rate is found to capture the typical growth and height of the towers. The tower width is captured by the Weber number, which gives the relative importance of inertia and capillary forces. Various symmetric, smooth, corrugated, zigzag, and chiral structures are observed by varying the impact velocity and the flux rate from droplet to jetting regime.

Impact of liquid droplets on granular media

The crater formation due to the impact of a water droplet onto a granular bed has been experimentally investigated. Three parameters were tuned: the impact velocity, the size of the droplet, and the size of the grains. The aim is to determine the influence of the kinetic energy on the droplet pattern. The shape of the crater depends on the kinetic energy at the moment the droplet starts to impact the bed. The spreading and recession of the liquid during the impact were carefully analyzed from the dynamical point of view, using image analysis of high-speed video recordings. The different observed regimes are characterized by the balance between the impregnation time of the water by the granular bed by the water and the capillary time responsible for the recession of the drop.