Drop Splashing Research Articles

Pattern identification in systems withS(1)symmetry

This work is devoted to pattern identification in systems with S(1) symmetry based on limited experimental data. As we demonstrate, such pattern identification is complicated by the lack of a theoretical basis as well as by the presence of experimental uncertainties, and possible overlapping and missing points in the data. The study is motivated by a recent finding of physical systems where instabilities of different wave numbers may coexist and thus lead to several single-wave-number patterns superimposed with a random phase-shift between them. As shown in this work, such patterns cannot be identified with Fourier analysis as well as direct measurement of the wave numbers is not possible. We present both a constructive theoretical approach, which establishes the conditions under which the structure of such patterns is identifiable, and an example of application-the crown structure analysis in the drop splash problem. For the latter study, an experimental setup is developed based on high-speed stereo photography, which produces data suitable for a quantitative analysis of the observed patterns.

Effect of chamber pressure on spreading and splashing of liquid drops upon impact on a dry smooth stationary surface

Liquid drop impacts on a smooth surface were studied at elevated chamber pressures to characterize the effect of gas pressure on drop spreading and splashing. Five common liquids were tested at impact speeds between 1.0 and 3.5 m/s and pressure up to 12 bars. Based on experiments at atmospheric pressure, a modification to the “free spreading” model (Scheller and Bousfield in AIChE Paper 41(6):1357–1367, 1995) has been proposed that improves the prediction accuracy of maximum spread factors from an error of 15–5%. At high chamber pressures, drop spreading and maximum spread factor were found to be independent of pressure. The splash ratio (Xu et al. in Phys Rev Lett 94:184505, 2005) showed a non-constant behavior, and a power-law model was demonstrated to predict the increase in splash ratio with decreasing impact speed in the low impact speed regime. Also, drop shape was found to affect splash promotion or suppression for an asymmetry greater than 7–8% of the equivalent drop diameter. The observations of the current work could be especially useful for the study of formation of deposits and wall combustion in engine cylinders.

A linear stability theory on time-invariant and time-dependent spatial domains with symmetry: the drop splash problem

This work is a combination of physical and analytical considerations of lin- ear stability pictures on time-invariant and time-dependent spatial domains with symmetry. The discussion is offered in the context of the Rayleigh-Taylor instability (of a fluid inter- face accelerated in the direction of a heavier phase) applied to the drop splash problem, which provides a natural ground for developing stability theory on time-dependent spatial domains with O(2) symmetry. The peculiarity of the underlying linear model common in a number of other interfacial instabilities - linear oscillator ftt + a(k)f = 0 in the wavenumber k-space - allows one to establish a direct correspondence between stability pictures on time-invariant and time-dependent spatial domains. The stability analysis also leads to a notion of frustration in (linear) stability patterns.

Splashing Characteristics of Monodisperse Sprays with Significant Viscosity Differences Impacting a Flat Surface

Drop impingement and splashing as a function of viscosity and, to a lesser extent, temperature are examined here. The working fluid is a mixture of water and glycerin with relative mass percentages varying from 0 to 100%, which spans a viscosity range of three orders of magnitude. First, a criterion that separates “on” and “off” for splashing as a function of glycerin percentage is expressed in terms of both Weber and Reynolds numbers and its highly nonlinear behavior is a function of the change in fluid viscosity. Next, the complex splashing characteristics of a rather simple monodisperse spray injected at a pressure of 2 bars onto a flat, 2-mm-diameter aluminum cylindrical rod are examined. Spatial variations in the fraction of splashed liquid, Sauter mean diameter, splashed droplet size distribution, and splash volume fraction as a function of radial distance for these mixtures are reported.

Thin film formation during splashing of viscous liquids

After impact onto a smooth dry surface, a drop of viscous liquid initially spreads in the form of a thick lamella. If the drop splashes, it first emits a thin fluid sheet that can ultimately break up into droplets causing the splash. Ambient gas is crucial for creating this thin sheet. The time for sheet ejection, t{ejt}, depends on impact velocity, liquid viscosity, gas pressure, and molecular weight. A central air bubble is trapped below the drop at pressures even below that necessary for this sheet formation. In addition, air bubbles are entrained underneath the spreading lamella when the ejected sheet is present. Air entrainment ceases at a lamella velocity that is independent of drop impact velocity as well as ambient gas pressure.

Assessment of gas and liquid velocities induced by an impacting liquid drop

A two-phase flow model using the boundary element method was applied to investigate the physics of a liquid drop impacting onto a solid, dry plate. Xu et al. showed that air pressure plays an important role in splashing: as air pressure was reduced, splashing of an ethanol drop with a Weber number of 838 was suppressed. This remarkable observation provided the motivation for the current modeling effort. We numerically investigate how air pressure affects the behavior of an impacting drop. Surveying both inside and outside the impacting drop, velocities of both the liquid and gas are computed. Simulations show that gas speed, as it is displaced by the falling drop, is more than three times higher than the incoming drop speed. Air entrainment induced by the displaced gas seems to be an important contributor to corona formation, which always precedes any instability, fingering, or splashing of the liquid. To describe drop-impact phenomena, the maximum spreading diameter of the drop and the topology of the impacting fluid are reported as functions of Weber number and gas density.

Drop Impact, Spreading, Splashing, and Penetration into Electrospun Nanofiber Mats

Experiments were conducted to study peculiarities of drop impact onto electrospun polymer nanofiber mats. The nanofiber cross-sectional diameters were of the order of several hundred nanometers, the pore sizes in the mats of about several micrometers, and the mat thicknesses of the order of 200 microm. Polyacrylonitrile (PAN), a polymer which is partially wettable by water, was used to electrospin nanofiber mats. The experiments revealed that drop impact onto nanotextured surfaces of nanofiber mats produce spreading similar to that on the impermeable surfaces. However, at the end of the spreading stage, the contact line is pinned and drop receding is prevented. At higher impact velocities, prompt splashing events with formation of tiny drops were observed. It was shown that the splash parameter K(d) = We(1/2) Re(1/4) (with We and Re being the Weber and Reynolds numbers, respectively) previously used to characterize the experiments with drop impact onto smooth impermeable dry substrates can be also used to describe the onset of splash on substrates coated by nanofiber mats. However its threshold value K(ds) (in particular, corresponding to the minimal impact velocity leading to generation of secondary droplets) for the nanotextured surfaces is higher than that for dry flat substrates. In addition, water penetration and spreading inside wettable nanofiber mats after drop impact was elucidated and quantified. The hydrodynamics of drop impact onto nanofiber mats is important for understanding effective spray cooling through nanofiber mats, recently introduced by the same group of authors.

English

Solid freeform fabrication has the potential to construct ceramic parts, directly from computer aided design (CAD) data, without a mould or a die by the addition of material. Direct ceramic ink-jet printing is one of the techniques used in freeform fabrication. Ceramic tiles used in space vehicles can be produced by this method wherein a porous ceramic substrate (Al2O3/SiC) can be filled with a ceramic ink and processed subsequently. The success of this process depends on the systematic preparation of ceramic inks and the deposition of the ceramic ink on the substrate. In this paper, photographic studies were made on the characteristics of ceramic ink droplets when these are deposited on a porous ceramic substrate from a burette under gravity. For this investigation, ceramic inks were prepared using different amounts (0.25–3.0 vol. %) of an organic dispersant (oleic acid) added to a ceramic composition containing different amounts: (a) (7.5– 17.5 vol. %) of alumina and (b) (7.5–15.0 vol. %) of zirconia with ethyl alcohol as a carrier. From this study, the drop formation, sedimentation in the drop, spread of drop on the substrate, splashing of drop impinging a previous ceramic ink layer on the substrate, and merging of droplets after deposition, are observed. This method is useful for manufacturing of parts with ceramic fibres filled with ceramic particles and this study can provide inner details on the behaviour of ink drops.Defence Science Journal, 2009, 59(6), pp.675-682, DOI:http://dx.doi.org/10.14429/dsj.59.1575

Particle Impact and Breakup in Aircraft Measurement

Abstract Measurements of cloud particle properties from aircraft by optical and impact techniques are subject to artifacts following particle breakup prior to detection. The impact kinetic energy to surface energy ratio (ℒ) provides a breakup criterion at ℒ ≥ 7 for water and ice with major fragmentation for ℒ > 100. This applies to optical imaging probes for particle concentration, size, and projected area spectra measurement. Uncertainty arises should impacting particles shatter and disperse, defeating the intent of the original measurements. Particle shatter is demonstrated in Formvar replicas (University of North Dakota Citation) and video records of particle approach and impact on the Cloudscope (NCAR C-130, NASA DC-8) at airspeeds of 130 and 200 m s−1. Sufficient impact kinetic energy results in drop splash and ice shatter, with conversion to surface energy and ultimately thermal energy through viscous dissipation and ice defect production occurring down to the molecular scale. The problem is minimized in design by reducing the regions responsible for particle breakup to a minimum and locating sensors in regions inaccessible to shatter fragments.

Crown-forming instability phenomena in the drop splash problem

The objective of this work is to study the fundamental instability behind the crown formation in the problem of drop splashing on a pre-existing liquid film. Based on experimental and theoretical insights, we demonstrate that the most plausible instability mechanism is of the Richtmyer–Meshkov type associated with a nearly impulsive acceleration of the interface. We also discover frustration phenomena in the wave number selection of the crown spike structure and study the corresponding bifurcation picture.

Splashing on elastic membranes: The importance of early-time dynamics

We study systematically the effect of substrate compliance on the threshold for splashing of a liquid drop using an elastic membrane under variable tension. We find that the splashing behavior is strongly affected by the tension in the membrane and splashing can be suppressed by reducing this tension. The deflection of the membrane upon droplet impact is measured using a laser sheet, and the results allow us to estimate the energy absorbed by the film upon drop impact. Measurements of the velocity and acceleration of the spreading drop after impact indicate that the splashing behavior is set at very early times after, or possibly just before, impact, far before the actual splash occurs. We also provide a model for the tension dependence of the splashing threshold based on the pressure in the drop upon impact that takes into account the interplay between membrane tension and drop parameters.

Dynamics of Drop Impact on a Rectangular Slot

Drop impact on substrates is of scientific importance and plays a central role in both microscale and large-scale applications, e.g., ink-jet printing and spray coating. For over 100 years, researchers have studied situations where drops impact planar substrates, a beautiful free surface flow resulting in either drop deposition or splashing. By contrast, drop impact on nonplanar substrates, e.g., spheres, has become of interest only recently. Here, the impact of drops of several liquids with a slot of width comparable to the drop diameter that is dug into an otherwise planar substrate is studied experimentally as a function of impact velocity. Two different kinds of splashing arise in the new experiments: an internal splash similar to that observed on planar substrates and a new, external splash, where some of the drop liquid splashes out of the slot. Phase diagrams that delineate regimes of drop spreading and splashing are presented. Simple scaling arguments are also developed to rationalize the findings.

Liquid drop splashing on smooth, rough, and textured surfaces

Splashing occurs when a liquid drop hits a dry solid surface at high velocity. We report experimental studies of how the splash depends on the roughness and the texture of the surfaces as well as the viscosity of the liquid. For smooth surfaces, there is a "corona" splash caused by the presence of air surrounding the drop. There are several regimes that occur as the velocity and liquid viscosity are varied. There is also a "prompt" splash that depends on the roughness and texture of the surfaces. A measurement of the size distribution of the ejected droplets is sensitive to the surface roughness. For a textured surface in which pillars are arranged in a square lattice, experiment shows that the splashing has a fourfold symmetry. The splash occurs predominantly along the diagonal directions. In this geometry, two factors affect splashing the most: the pillar height and spacing between pillars.

DISR imaging and the geometry of the descent of the Huygens probe within Titan's atmosphere

The Descent Imager/Spectral Radiometer (DISR) provided 376 images during the descent to Titan and 224 images after landing. Images of the surface had scales between 150 m/pixel and 0.4 mm/pixel, all of which we assembled into a mosaic. The analysis of the surface and haze features in these images and of other data gave tight constraints on the geometry of the descent, particularly the trajectory, the tip and tilt, and the rotation of the Huygens probe. Huygens moved on average in the direction of 2 ∘ north of east from 145 to 50 km altitude, turning to 5 ∘ south of east between 30 and 20 km altitude, before turning back to east. At 6.5 km altitude, it reversed to WNW, before reversing back to SE at 0.7 km altitude. At first, Huygens was tilting slowly by up to 15 ∘ as expected for a descent through layers of changing wind speeds. As the winds calmed, tilts decreased. Tilts were approximately retrieved throughout the main-parachute phase, but only for 160 specific times afterwards. Average swing rates were 5 ∘ / s at high and low altitudes, but 13 ∘ / s between 110 and 30 km altitude. Maximum swing rates were often above 40 ∘ / s , far above the design limit of 6 ∘ / s , but they caused problems only for a single component of DISR, the Sun Sensor. The excitation of such high swing rates on the stabilizer parachute is not fully understood. Before the parachute exchange, the rotational rate of Huygens smoothly approached the expected equilibrium value of 3 rotations per vertical kilometer, although clockwise instead of counterclockwise. Starting at 40 s after the parachute exchange until landing, Huygens rotated erratically. Long-term averages of the rotational rate varied between 2.0 and 4.5 rotations/km. On time scales shorter than a minute, some 100 strong rotational accelerations or decelerations created azimuthal irregularities of up to 180 ∘ , which caused DISR to take most exposures at random azimuths instead of pre-selected azimuths. Nevertheless, we reconstructed the azimuths throughout the 360 rotations during the descent and for each of some 3500 DISR exposures with a typical accuracy near 2 ∘ . Within seconds after landing, the parachute moved into the field of view of one of the spectrometers. The observed light curve indicated a motion of the parachute of 0.3 m/s toward the SSE. DISR images indicated that the probe did not penetrate into the surface, assuming a level ground. This impact of Huygens must have occurred on major rocks or some elevated area. The unexpected raised height increases ice-rock sizes by 40% with respect to estimations made in 2005 [Tomasko, M.G., Archinal, B., Becker, T., Bézard, B., Bushroe, M., Combes, M., Cook, D., Coustenis, A., de Bergh, C., Dafoe, L.E., Doose, L., Douté, S., Eibl, A., Engel, S., Gliem, F., Grieger, B., Holso, K., Howington-Kraus, E., Karkoschka, E., Keller, H.U., Kirk, R., Kramm, R., Küppers, M., Lanagan, P., Lellouch, E., Lemmon, M., Lunine, J., McFarlane, E., Moores, J., Prout, G.M., Rizk, B., Rosiek, M., Rueffer, P., Schröder, S.E., Schmitt, B., See, C., Smith, P., Soderblom, L., Thomas, N., West, R., 2005. Rain, winds and haze during the Huygens probe's descent to Titan's surface. Nature 438, 765–778]. During the 70-min surface phase, the tilt of Huygens was 3 ∘ , changing by a small fraction of a degree. The apparent horizon looking south to SSW from the landing site was 1– 2 ∘ above the theoretical horizon, sloping by 1 ∘ up to the left (east). Our best guess puts the horizon as a 1–2 m high hill in 30–50 m distance. We detected the refraction from warm, rising air bubbles above our illuminated spot. Bright, elongated, cm-sized objects appear occasionally on the surface. If real, they could be rain drop splashes or fluffy particles blown across Titan's surface.

Experimental investigation on splashing and nonlinear fingerlike instability of large water drops

Abstract The fluid physics of the splashing and spreading of a large-scale water drop is experimentally observed and investigated. New phenomena of drop impact that differ from the conventional Rayleigh–Taylor instability theory are reported. Our experimental data shows good agreement with previous work at low Weber number but the number of fingers or instabilities begins to deviate from the R–T equation of Allen at high Weber numbers. Also observed were multiple waves (or rings) on the spreading liquid surface induced from pressure bouncing (or pulsation) within the impacting liquid. The first ring is transformed into a radially ejecting spray whose initial speed is accelerated to a velocity of 4–5 times that of the impacting drop. This first ring is said to be “splashing,” and its structure is somewhat chaotic and turbulent, similar to a columnar liquid jet surrounded by neighboring gas jets at relatively high impact speed. At lower impact speeds, splashing occurs as a crown-shaped cylindrical sheet. A second spreading ring is observed that transforms into fingers in the circumferential direction during spreading. At higher Weber number, the spreading of a third ring follows that of the second. This third ring, induced by the pressure pulsation, overruns and has fewer fingers than the second, which is still in a transitional spreading stage. Several important relationships between the drop impact speed, the spray ejection speed of the first ring, and the number of fingers of the second and third rings are presented, based on data acquired during a set of drop impact experiments. Issues related to the traditional use of the R–T instability are also addressed.

Thermal Effects in the Splashing of Drops under a Reduced Pressure Environment

A Comment on Letter by X. Lei Xu, Wendy W. Zhang, and Sidney R. Nagel, Phys. Rev. Lett. 94, 184505 (2005). The authors of the Letter offer a Reply.Received 14 December 2005DOI:https://doi.org/10.1103/PhysRevLett.96.179401©2006 American Physical Society

Drop Splashing on a Dry Smooth Surface

The corona splash due to the impact of a liquid drop on a smooth dry substrate is investigated with high-speed photography. A striking phenomenon is observed: splashing can be completely suppressed by decreasing the pressure of the surrounding gas. The threshold pressure where a splash first occurs is measured as a function of the impact velocity and found to scale with the molecular weight of the gas and the viscosity of the liquid. Both experimental scaling relations support a model in which compressible effects in the gas are responsible for splashing in liquid solid impacts.

Raindrop-impact-induced erosion processes and prediction: a review

Raindrop-impact-induced erosion is initiated when detachment of soil particles from the surface of the soil results from an expenditure of raindrop energy. Once detachment by raindrop impact has taken place, particles are transported away from the site of the impact by one or more of the following transport processes: drop splash, raindrop-induced flow transport, or transport by flow without stimulation by drop impact. These transport processes exhibit varying efficiencies. Particles that fall back to the surface as a result of gravity produce a layer of pre-detached particles that provides a degree of protection against the detachment of particles from the underlying soil. This, in turn, influences the erodibility of the eroding surface. Good understanding of rainfall erosion processes is necessary if the results of erosion experiments are to be properly interpreted. Current process-based erosion prediction models do not deal with the issue of temporal variations in erodibility during a rainfall event or variabilities in erodibility associated with spatial changes in dominance of the transport processes that follow detachment by drop impact. Although more complex erosion models may deal with issues like this, their complexity and high data requirement may make them unsuitable for use as general prediction tools. Copyright © 2005 John Wiley & Sons, Ltd.

Drop impact on a hot surface: effect of a polymer additive

The impact of a drop on a hot surface is studied for Weber numbers between 20 and 220, and wall temperatures between 120 and 180°C. Drops of pure water are compared with drops of a dilute polyethylene oxide water solution (0.02% M). The additive is shown to inhibit drop splashing, the ejection of secondary droplets and mist formation. As previously observed, the polymer can also prevent drops from bouncing off a cold wall. This is no longer true if the wall is above the dynamic Leidenfrost temperature, which is lower for the polymer solution.

The role of time in single drop splash on thin film

This paper reports on an experimental study of the impact of water drops on thin liquid films. The morphology of the impact was studied by still photography, and quantitative results were obtained by a proper image analysis technique. The time evolution of various parameters like the crown diameter, the crown height, and the secondary drop diameters are reported, and these experimental parameters are correlated and compared to available theoretical models. A particular set-up of the acquisition system allowed us to photograph the splash from below the solid wall, allowing the first estimation of the crown thickness and the total number of jets protruding from the crown rim as a function of time. The results indicate that, for the range of the parameters investigated, there is not a strong dependence on the film thickness. The evolution of the crown height depends on the impact Weber number, whereas its growing velocity and the crown thickness evolution are almost independent of Weber number.