Drop Impact Velocity Research Articles

On some common features of drop impact on liquid surfaces

The impact of a drop on liquid surfaces is studied experimentally and theoretically in the region of the fully developed splashing. In order to reveal the influence of viscosity and target liquid depth on the resulting flow patterns, the experiments were carried out with water and 70% glycerol–water solution, and for different target liquid depths. Based on the experimental observations, a dynamic model of the central jet formation at the cavity collapse is developed. This model predicts an emergence of a liquid flow up into the central jet and simultaneously a small flow velocity downward and allows us to evaluate the velocities of these two flows. A theoretical model for the cavity submergence is presented. This model gives the constant velocity of the cavity submergence which is half the initial drop impact velocity. Analytical solution for the gravity–capillary cavity collapse has been derived and provides a good fit to the experimental results. Theoretical analysis and experiments have shown that the maximum cavity radius and the cavity collapse time depend on both the Froude number and the dimensionless capillary length.

Crater formation in soils by raindrop impact

AbstractThe process of crater formation by the impact of water drops on soil, sand and various other target material was studied. Craters of various shapes and sizes were observed on different target materials or conditions, ranging from circumferential depression to completely hemispherical shape. Crater shape was dependent upon target material, its flow stress or shear strength and the presence and thickness of water on the surface. Between 5 and 22 per cent of impact energy was spent on cratering, but the relationship between crater volume and kinetic energy of a raindrop was curvilinear, indicating a lower efficiency of impact energy in removing target material as the energy increases. Impact impulse, on the other hand, showed a more linear relationship with crater volume, and the ratio of impulse over crater volume (I/V) remained constant for the entire range of drop sizes, impact velocities, and surface conditions used in this study. Surface shear strength, represented by the penetration depth of fall‐cone penetrometer, appeared to be a key factor involved in this process. An equation was developed which related crater volume to cone penetration depth and impact impulse. Crater volume, which appeared to be a better indicator of the total amount of material dislodged by a raindrop than splash amount, can thus be predicted using this equation. Copyright © 2004 John Wiley & Sons, Ltd.

Single drop impaction on a solid surface

AbstractAn experimental and theoretical study is presented on spreading and retracting of a single drop impacting on a smooth surface at room temperature. The experimental study showed the influence of kinetic energy, liquid‐solid interaction, and energy dissipation on the impact process. The results are reported for Reynolds number from 180 to 5,513, Weber number from 0.2 to 176, four different liquids (distilled water, n‐Octane, n‐Tetradecane, and n‐Hexadecane), and four different surfaces (slide glass, uncoated silicon wafer, HMDS coated silicon wafer, and Teflon film). A theoretical model based on an energy balance was developed to predict the maximum spreading ratio at low impact velocity. The key novel feature of this model is that the shape of the drop is assumed to be a spherical cap during the spreading process. When compared to models in the literature, the present model not only gives better predictions for low drop impact velocities, but also in most cases gives predictions that are within 10% of the experimental data at high impact velocities.

Drop impact on a liquid–liquid interface

The effects of Reynolds number (Re) on the gravity-driven impact of a single drop onto a liquid–liquid interface were studied experimentally using the particle image velocimetry method. The liquid beneath the interface was identical to the drop liquid. Two liquids with different viscosities were used as the ambient above the interface resulting in viscosity ratios (drop to ambient) of 0.14 and 0.33. Index matching and a slight camera inclination were employed to eliminate optical distortion. Image planes were captured at a rate of 500 Hz, and velocity fields were determined from consecutive images. The flow Reynolds numbers based on drop impact velocity and ambient viscosity were 20 and 68 for the lower and higher viscosity ratios, respectively. During the approach toward the interface, the drop shape was more oblate for the higher Re case. At the same time, viscous stresses generated a vortex ring inside each drop and a wake behind it. Each wake contained a detached ring of similar sign to the ring inside the drop. The subsequent deformation of the drop and the interface due to impact was observed to be more radical in the higher Re case. The impingement and shearing of the trailing wake on the upper surface of each drop played a significant role in dissipating the vorticity inside both drops, and the vorticity dissipated faster for lower Re.

Impact of drops of polymer solutions on small targets

The collision of drops of polymer solutions with small targets was studied experimentally. The tested liquids were aqueous solutions of polyethylene oxide (MW=4 000 000) at concentrations of 10, 100, 1000 wt ppm. The drop impact velocity was about 3.5 m/s, and the drop diameters were in the range of 2.6–3.8 mm. The target was a stainless steel disk of 3.9 mm diameter. The collision was monitored by means of high-speed photography technique. As in the case of pure water, a circular liquid lamella was formed, and then it retracted with formation of outwards-directed secondary jets. There was no significant difference between the values of the maximum diameter and the retraction velocity of the lamella in the cases of water and polymeric liquids. On the contrary, the polymeric additives drastically changed the character of the lamella retraction. The secondary jets were transformed into thinning filaments submitted to elastic stresses with an attached droplet. Then, depending on the polymer concentration, the filaments ruptured and the attached droplets escaped, or the liquid filaments pulled the attached droplets back and the whole liquid returned to the target. A splashing threshold has been derived for polymeric liquids based on the liquid relaxation time and the impact conditions.

Impact of water drops on small targets

The collision of water drops against small targets was studied experimentally by means of a high-speed photography technique. The drop impact velocity was about 3.5 m/s. Drop diameters were in the range of 2.8–4.0 mm. The target was a stainless steel disk of 3.9 mm diameter. The drop spread beyond the target like a central cap surrounded by a thin, slightly conical lamella bounded by a thicker rim. By mounting a small obstacle near the target, surface-tension driven Mach waves in the flowing lamella were generated, which are formally equivalent to the familiar compressibility driven Mach waves in gas dynamics. From the measurement of the Mach angle, the values of some flow parameters could be obtained as functions of time, which provided insight into the flow structure. The liquid flowed from the central cap to the liquid rim through the thin lamella at constant momentum flux. At a certain stage of the process, most of the liquid accumulated in the rim and the internal part of the lamella became metastable. In this situation, a rupture wave propagating through the metastable internal part of the lamella caused the rim to retract while forming outwardly directed secondary jets. The jets disintegrated into secondary droplets due to the Savart–Plateau–Rayleigh instability. Prior to the end of the retraction, an internal circular wave of rupture was formed. It originated at the target and then it propagated to meet the retracting rim. Their meeting resulted in a crown of tiny droplets. A theoretical analysis of the ejection process is proposed.

Spreading of an inviscid drop impacting on a liquid film

The evolution of the deforming liquid surface following the impact of a drop onto a film of the same liquid is analysed numerically using a boundary integral method assuming axisymmetric, inviscid flow. Surface tension and gravity are taken into account. At times comparable to, or larger than the impact time scale (based on initial drop radius and impact velocity), the section of the liquid surface bounded by the radially propagating crown or rim is predicted to approach a single central shape independent of film thickness. At times which are much smaller than the impact time scale, jetting behaviour is obtained in the neck region where the drop meets the film when the Weber number is large enough. The jet is found to move close to the film, and this suggests the possibility of bubble entrapment, confirming a previous report in the literature. The present results suggest the occurrence of a train of bubble rings from repeated near-reconnection events as the neck moves radially outwards under jetting conditions.

Development of a rainfall test rig as an aid in soil block weathering assessment

Continual changes in earth technology and the search for new trends in soil block weathering practices have resulted in the development of a rainfall test rig (RTR). By positioning the water-spraying nozzle at a fall-height of 2.0 m and water pressure of 0.5 kg/cm 2, the device generates a rainfall intensity of 150 mm/h. On application to the standard flour pellet, the RTR discharges spectra of rainfall in which the range of drop sizes, impact velocities and kinetic energy appropriate to natural rainfall conditions. This was applied to soil block samples arranged on a 0.9-m 2 adjustable soil block holder (platform). The results of testing two different soil block samples, stabilised with cement, lime and lime/gypsum at varying proportions and cured at both room temperature (RT) and elevated temperature (ET), under controlled and reproducible artificial rainfall conditions, are briefly discussed.

落下水滴の水面衝突による気泡音の発生

When a water droplet impacts on a water surface, subsequently underwater sounds are induced. Generally it is recognised that the sounds are caused by the oscillation of air bubbles entrained by the drop impact depending on the drop diameter dD and impact velocity Vimp which creates the (dD-Vimp) plane. There are two categories of the (dD - Vimp) combination for the bubble sounds. One is the sound due to an oscillating bubble entrained in the regular (dD-Vimp) region, another concerned with that resulting from a bubble entrained in the irregular (dD-Vimp) region.Suikinkutsu is a kind of traditional musical instruments which has been set up at a Japanese garden since the Edo period. The sound generated by Suikinkutsu seems to be connected with the bubble sound in the irregular (dD-Vimp) region which is a subject of the present paper.

Boundary integral prediction of the spreading of an inviscid drop impacting on a solid surface

Axisymmetric spreading of an idealised inviscid liquid drop impinging on a horizontal solid surface is analysed (including surface tension) using a boundary integral method for Weber numbers ( We), based on initial drop radius and impact velocity, ranging from 3 to 100. Progressive accumulation of liquid in a rim around the periphery of the spreading inviscid drop is predicted. The effect diminishes with increasing Weber number, and is negligible when We=50. It is concluded that the experimentally observed rim at Weber numbers exceeding this value is due solely to viscous retardation. For We⩾10, the calculated reduction in drop height with time is found to be almost independent of Weber number, and agrees extremely well with experimental data despite the absence of viscous effects in the calculations. The inviscid spreading rate increases with increasing Weber number, and a simple model predicts a dimensionless limiting value of 2 at large times as We→∞. The viscous reduction in the radius of spreading, determined by subtracting the measured and calculated (inviscid) values, is found to be approximately linear in time during most of the primary deformation. Derived values of the slope m can be fitted by m=0.5We Re −0.5 for We less than about 40. Modification of the calculated inviscid spreading radius using a linear viscous correction provides an improved prediction of drop spreading.

Vapor Breakthrough from Liquid Drops Impacting Air-Permeable Chemical Protective Fabric

The interaction between drop impact and vapor breakthrough for several kinds of air-permeable fabric composites (an outer shell with an adsorbent liner) is determined under convective flow conditions. Vapor breakthrough is measured using methyl sali cylate, a chemical agent simulant, for static and dynamic liquid drop placement on either the shell fabric alone or in combination with an activated carbon-loaded foam liner backing. Vapor concentration, detected by means of a photo-ionizer, is used to determine breakthrough curves, while image analysis provides a quantitative charac terization of the impact behavior of the liquid drops by measuring liquid spreading. splashing, and breakthrough. Drop impact velocities up to 6 m/s are measured on cotton/Kevlar®/nylon and cotton/nylon twill weave outer shell fabrics. For static drops, fabric composites with an outer wicking fabric give much lower total vapor breakthrough than do nonwicking fabrics, whereas for dynamic drops at subterminal impact velocities, the difference between nonwicking and wicking shell fabrics is re duced because of surface spreading and splashing. There is an inverse correlation be tween wetted area and vapor breakthrough due to localized vapor saturation of the adsorbent liner fabric. Below a critical drop velocity of 4.5 m/s, there is no direct liquid penetration through the shell fabric.

Effect of adjuvants on glyphosate wash-off from white birch foliage by simulated rainfall

Abstract The effect of six surfactant adjuvants on glyphosate wash‐off from white birch (Betula papyrifera Marsh.) foliage was studied at 2 and 6 h after treatment with end‐use mixtures of Vision® at the rate of 1 kg of active material in 35 L per ha area of leaf surface. The investigation consisted of two parts. In Part I, C‐labeled herbicide was used to determine the maximum amount of wash‐off ('Worst Case Scenario') by rinsing treated foliage with water. At 2 h after treatment ca 84% of the applied amount was washed off when no adjuvant was present, and at 6 h the washable amount decreased only to ca 72%. Out of the six adjuvants tested, only Silwet® L‐77, an organosilicone copolymer surfactant, provided the greatest increase in rain protection, since the amount washed off decreased to 51 and 42% at 2 and 6 h rain‐free periods respectively. In Part II of the investigation, non‐radiolabeled herbicide was used, and glyphosate wash‐off was examined at 2 and 6 h after treatment using cumulative rain of 1 and 5 mm. Under 1 mm rainfall, irrespective of rain drop sizes and impact velocity, ca 68% was washed off at 2 h after treatment, and ca 59% at 6 h. Under 5 mm rain, ca 78% and 70% were washed off at 2 and 6 h respectively. Cumulative rainfall played a greater role in glyphosate wash‐off than rainfall intensity. Again only the Silwet adjuvant lowered the amount washed off markedly. A rain‐free period of more than 6. h might be needed when a rainfastening adjuvant was not added to the end‐use mixtures of Vision formulation.

Bubble entrainment by the impact of drops on liquid surfaces

The impact of a drop on the plane surface of the same liquid is studied numerically. The accuracy of the calculation is substantiated by its good agreement with available experimental data. An attempt is made to explain the recent observation that, in a restricted range of drop radii and impact velocities, small air bubbles remain entrained in the liquid. The implications of this process for the underwater sound due to rain are considered. The numerical approach consists of a new formulation of the boundary-element method which is explained in detail. Techniques to stabilize the calculation in the presence of strong surface-tension effects are also described.

Further studies of the underwater noise produced by rainfall

A study of the sound produced by water drops striking a water surface has confirmed some earlier results [Pumphrey et al., J. Acoust. Soc. Am. 85, 1518 (1989)]. In particular, for a certain well‐defined range of drop sizes and impact velocities, drops will predictably and repeatedly entrain bubbles; this phenomenon has been named regular entrainment. In the present study, various fixed drop diameters have been used to investigate how bubble frequency, dipole strength, and time between drop impact and bubble formation vary with impact velocity. It is found that as impact velocity is increased through the point where entrainment begins, both frequency and dipole strength decrease to a minimum value and then rise again as the highest velocity at which entrainment occurs is approached. Both terms show increased variability near the critical upper and lower velocities. The frequency tends to increase monotonically as drop size is reduced; drops that entrain bubbles at their terminal velocities tend to produce frequencies near 14 kHz, which is also the peak frequency of the natural rainfall spectrum. Finally, the time between drop impact and bubble formation was found to increase monotonically as drop size or impact velocity increases. [Work supported by Office of Naval Research.]

The Fracture and Aerosol Release of Impacted HLW Glasses and HLW Canisters

ABSTRACTThe fracture and release mechanism of radioactive aerosols of HLW glass and HLW canisters are studied experimentally by laboratory scale and full scale drop tests. The experimental conditions model the conditions of accidental drops in a deep salt repository. The laboratory scale drop tests have a scaling factor of 1:10. Accelerated probes of simulated HLW glass impact on a ground plate and the size distributions of broken fines and released aerosols are measured by sieving and scanning electron microscopy (SEM) of aerosol samples.The impact velocity is determined as the dominating impact parameter. Further parameters tested, such as waste glass composition, cooling time (residual thermal stresses), probe temperature at impact, and ground characteristics, show no measurable influence. Source terms of released respirable aerosols are evaluated for two reference cases, borehole drop (impact velocity v = 80 m/s) and reloading hall drop (v = 14 m/s), the values being 0.1 % and to 2.10-4 % respectively of the glass probe mass. The full scale drop tests are performed with European Standard HLW canisters. The canisters keep their integrity in all tests up to drop heights of 14 m. On opening the canisters, the broken fines are analyzed by sieving. The results are in good agreement with the small scale tests and confirm their acceptability for use in a safety analysis.

Bubble entrainment from bursting bubbles

MacIntyre observed in 1972 that when a large bubble setting on a pool of water bursts it deposits a ring of small bubbles on the surface. He explained the presence of these small bubbles as resulting from splashing film drops although he did not have any photographs to substantiate his explanation. A consideration of film drop diameter and impact velocity indicates that film drops should not splash, so research was undertaken to use high-speed photography to photograph bursting bubbles. The photographs do not show evidence of film drops splashing but instead reveal that the small bubbles result from the breakage of an unstable toroidal bubble formed when the original bubble bursts.

Rainfall measurements using underwater ambient noise

Observations are made which show that the underwater ambient noise spectrum generated by rain has a unique spectral shape which can be distinguished from other noise sources. Furthermore, the relationship between spectral level and rainfall is quantifiable. The spectral shape is dominated by a broad peak at 15 kHz, but also depends on the drop size distribution in the rain. A numerical study of the acoustic physics of a drop splash is used to explain the observed spectra. There are two contributions to underwater sound from the impact. The first contribution is from an initial acoustic water hammer pulse. The magnitude of this pulse depends on drop size, shape, and impact velocity. The contribution to the underwater sound spectrum is white and is very large for large drops. The second contribution occurs because at impact the incompressible continuity equation is not satisfied. Once this equation is satisfied, the splash is no longer an acoustic source. Numerically, the time required to closely satisfy this equation is roughly constant for all drop sizes at their terminal velocity. This time interval causes a low-frequency rolloff at roughly 15 kHz in the sound spectrum.

Splash Erosion Modeling: Physical Analyses

ABSTRACT A comprehensive relationship for the splash erosion process was derived from dimensional analysis. The processes which occur in both the drop-solid and the drop-liquid-solid domains were described with analytical relationships and simplified models. The models con-sider raindrop, sediment and system parameters affect-ing splash erosion. The effects of drop mass and impact velocity, slope gradient, water depth and time were evaluated using experimental data available.

Heat transfer to liquid drops from a small diameter channel at temperatures in the film boiling range

An experimental study to determine the values of heat transfer per drop for small drops of water, methanol, and acetone falling down a heated channel of small diameter. Channel temperatures ranged from 118°K to 269°K above saturation, and channel diameters were smaller than drop diameters. Values of heat transfer per drop exhibited a maximum at a saturation excess of approximately 200°K for all three fluids. The occurrence of a maximum is assumed to be due to the effect of vapor viscosity on the growth of the vapor film. The occurrence of the maxima at a common value of saturation temperature excess is thought to occur because of the effect of vapor thermal conductivity, vapor density, modified heat of vaporization, and vapor viscosity on the rate of growth of the vapor film. It was also found that heat transfer per drop is independent of channel length. High-speed motion pictures and visual observations lead to the assumption that all appreciable heat transfer takes place in a very short period of time after the drop first contacts the channel. The maximum values of heat transfer per drop were found to be related to fluid properties, drop impact velocity, and geometry by the following relationship: (Q D) max(d/D) 3·088 d 3λ VFρ L = 0·232 (N sigma;) 0·256 (N μ) −1·632 (N ρ) −2·264 (We) −0·245 .

An experimental study of factors which promote coalescence of two colliding drops suspended in water-I

The factors which determine whether two colliding drops will coalesce or rebound have been studied experimentally for 3.4 mm dia. anisole drops in water, using an apparatus designed to permit control of drop size, impact velocity and collision angle. Analysis of high speed movies showed that for relative approach velocities of 1.9–11.2 cm/sec, the apparent drop contact time was less than 70 msec. The probability of coalescence during this short time interval was a function of the phase and amplitude of the drop oscillations at moment of contact. The results have been analyzed using a modification of the conventional Stefan-Reynolds type film thinning equation derived for rigid interfaces. This relationship, although indicating more thinning for coalescences than rebounds, fails to predict fast enough thinning rates to validate the model. Part II gives detailed derivations for a thinning model in which interfaces are free to move, and shows how the results given in Part I can be explained by film thinning.