experimental comparisons between droplet-droplet

Atomization and Sprays, 19(5):409–423, 2009

EXPERIMENTAL COMPARISONS BETWEEN DROPLET-DROPLET COLLISION AND SINGLE-DROPLET IMPACTS ON A SOLID SURFACE E. Kompinsky and E. Sher The Pearlstone Center for Aeronautical Studies, Department of Mechanical Engineering, Ben-Gurion University, Beer-Sheva, Israel Original Manuscript Submitted: 11/13/2007; Final Draft Received: 5/20/2008 The behavior of droplet-droplet collision on dry and wet solid surfaces was studied experimentally. We show that the well-documented similarity between droplet-droplet collision on a solid surface and a single-droplet impact on a dry surface is limited to low impact velocities, while the similarity between droplet-droplet collision on a solid surface and a single-droplet impact on a wet surface is limited to high impact velocities. The major phenomenological differences between the above two cases, in terms of morphology, spreading behavior, secondary droplet formation, different crown behavior, and the formation of a central (Worthington) jet, are discussed here in detail.

INTRODUCTION Many applications involve droplet collision on a solid surface; among them are spray cooling, spray painting, spray coating, and ink-jet printing. Because of the many in uencing factors, the process of sprays’ interaction with a solid surface is complex in nature. Such factors include the impinging velocity, impinging angle, equilibrium surface tension, uid dynamic viscosity, and density, vapor pressure, wettability, droplets’ density number, and more. Extensive research has been done in the !eld of single-droplet impact on dry and wet solid surfaces (e.g., [1–8]). Most of the research work addressed low and high impact velocities on dry and wet surfaces. Crowns and their propagation and nonsplashing phenomena such as droplet deposition and spreading, receding (recoiling), jetting, !ngering, and rebounding were also studied in depth. Rioboo et al. [9] compared the dry and wet impact cases and showed that the two phenomena

are signi!cantly different in terms of morphology, spreading behavior, and secondary droplet formation. While the impact on a dry surface tends to exhibit only a radially extending lamella, the impact on a wet surface results in the formation of a corona that expands vertically and radially. Furthermore, the spreading velocity appears to be slower for impacts on wet than on dry surfaces. Rioboo et al. [10] reported experimental results concerning crown formation during liquid droplet impacts on wet surfaces. Based on their experimental observations, they determined the limit between deposition with or without crowns formation, and the limit between the formation of crowns, with or without splash. If the thickness of the !lm is much larger than the drop’s diameter, the droplet’s impact creates a crater in the liquid layer. When this crater recedes, it can lead to bubble entrapment in the liquid and to the formation of an uprising central jet. Such impacts can also lead to splash when this central jet breaks up into

——————— Correspondence concerning this article should be addressed to E. Sher, The Pearlstone Center for Aeronautical Studies, Department of Mechanical Engineering, Ben-Gurion University, Beer-Sheva, Israel; e-mail: [email protected] 1044–5110/09/35.00 c 2009 by Begell House, Inc.

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a single or several secondary droplets. However, the knowledge obtained by the single-droplet tests can hardly be applied to the actual spray jet impingement because it lacks the interaction effects between multiple droplets and the surface [11]. Another complication is associated with the short time scales of the deposition process. In cases of low impact velocities, the spreading phenomenon is probably controlled by surface tension, while in cases of high impact velocities, compressibility effects strongly affect the impact regime [12]. The present study focuses on the characterization of droplet-droplet collisions on a solid surface. A comparison with some single-droplet impacts on dry and wet surfaces was also conducted for both low and high impact velocities. First, experimental data of single-droplet impacts on dry and wet surfaces were obtained. We then compared the results with droplet-droplet collision observations applied for the same surfaces and conditions. EXPERIMENTAL SETUP The experiments were performed with deionized (DI) water droplets impinging vertically on a smooth nontreated aluminum at plate. The droplets and the surface were both at room temperature of 25◦ C. A droplet generator (medical injector with a needle) was used to initiate identical droplets having an initial droplet diameter of 3.2 mm. The injector was pressed slowly to form a dripping droplet underneath. The droplet detached from the injector due to its own weight. The shape of the falling droplet appeared to oscillate between spherical and a slightly ellipsoid shape. Impact velocities ranged from 0.4 to 2.7 m/s, which is a typical range of interest in many studies on the subject (e.g., Vadillo et al. [12] examined impact velocities lower than 1 m/s, Fujimoto et al. [11] examined impact velocities ranging from 0.8 to 3.1 m/s). Reynolds numbers ranged from 1440 to 8300, Weber numbers ranged from 8 to 300, and the Ohnesorge number (Oh) was 0.002. A long time interval (0.5–1 s) was set between the !rst and second droplets for the droplet-droplet collisions, such that the second droplet collided with a deposited resting droplet on the solid surface. No observable evaporation took place between the !rst

and second droplets. The impaction plate area was about 100 × 70 mm. A high-speed CCD camera with a record rate of 2000 fps (frames per second) was used to obtain photographic observations. The camera was positioned at zero angle in front of the impaction plate. The lighting was generated mostly by a back light projector at the opposite side and positioned at about a 30 deg angle toward the impaction plate. The room standard uorescence lighting provided additional lighting. Impact velocity and droplet size measurements were obtained using image analysis software. The schematic experimental setup is shown in Fig. 1. The measured diameter is the wet diameter on (in contact with) the surface, and the measured height is the liquid’s peak height as illustrated in Fig. 2. In some cases, this may result in a slightly underestimated value. The length scale is shown on the left side of the !gure in which the distance between two lines is 1 mm. Based on the camera characteristics, such as the camera speed, number of pixels, and magni!cation, the measurements (diameter and height) are

Fig. 1 Schematic of experimental setup.

Fig. 2 Diameter and height measurements.

COMPARISONS BETWEEN DROPLET-DROPLET COLLISION AND SINGLE-DROPLET IMPACTS ON A SOLID SURFACE 411

estimated to be accurate within ±5%. Data from the high-speed camera was transferred to a PC for further analysis.

surface at a low impact velocity of 0.45 m/s (impact Re and We of 1440 and 8.9, respectively). The initial impact, deposition, spreading, receding, and oscillating phases are clearly shown in the gure And are explained as follows:

RESULTS AND DISCUSSION In this section, the behavior and evolution of the spreading droplet, its height, and its con guration as it impacts the surface are discussed in detail. Included are single-droplet impacts on dry and wet surfaces at low and high impact velocities. Furthermore, we examine droplet-droplet collisions on a solid surface at low and high impact velocities.

• In the rst phase, the deposition stage, which follows the initial impact, the droplet’s shape changes from spherical to a disklike shape, increasing its diameter and reducing its height above the surface. • The second phase is the spreading phase, during which the diameter and height continue to increase and reduce, respectively, but at a lower rate than in the former stage, due to energy dissipation mainly because of surface tension and viscous losses. The spreading stage ends as maximum spreading is reached

A Single-droplet Impact on a Dry Solid Surface Figure 3 shows the evolution of the diameter and height of a single-droplet impact on a dry solid Initial Impact

Deposition stage

Spreading stage

Receding stage

Oscillation stage

Diameter and Height [mm]

7 6

Diameter

5 4 3 2

Height

1 0 0

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40

60

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Time [ms] Fig. 3 Single-droplet low-velocity impact (0.45 m/s) on a dry surface.

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when the droplet, which has been transformed into a •at disk, has a maximum diameter and minimum height. The •at disk dwells for about 5 ms at this stage to form a lamella and a rim (the diameter shrinks and the height ascends). Roisman et al. [13] found that when the impinging Re ≫ 1, the kinetic energy at the end of the droplet’s spreading period does not vanish because a •uid motion still remains in the inner part of the droplet. At this stage, the shape of the droplet is that of a lamella (disk) as the inner part, and a rim on the outer perimeter, as shown in Fig. 4. Here, Rr is the disk radius, hr is the rim height, hl is the disk height, ar is the rim radius, θ is the contact angle between the droplet and the solid surface, Vl is the disk velocity, and Vr is the rim velocity. • During the receding phase (13–19 ms), the diameter seemingly shrinks rst by a low and then by a fast process to its minimum value. The diameter stays nearly constant at the beginning of the receding stage, as the liquid from the rim •ows toward the central lamella zone, while the height increases at a certain rate and is subsequently slightly decreased. The increase in the droplet’s height is caused by the returning of excessive liquid from the upper area of the rim into the central zone of the droplet due to surface tension. The liquid is forced upward, hence increasing the droplet’s height and widening its upper part. • An oscillation phase seems to follow the receding phase. The droplet toggles between spreading and receding motions, until equilibrium is attained. During these movements, the diameter and height act as opposite; when one increases, the other reduces and vice versa. As

Fig. 4 Model of spreading droplet on a surface.

the time advances, the oscillation amplitude diminishes. Worth noting is the longer time scale of the forth phase as compared to the preceding phases (see also Ref. 12). The process repeatability is demonstrated by observing the time evolution of ve different experiments under identical experimental conditions as shown in Fig. 5. The repeatability of the process phases, the absolute values of the droplet diameter and height, and the associated time scales seem to be convincing with a quite high con dence. The effect of the impact velocity (impact Reynolds and Weber numbers) on the diameter and height evolutions is shown in Figs. 6 and 7, respectively. In these gures, the initial drop diameter D0 and the impact drop velocity V0 have been used to normalize the relevant parameters. It seems that as the impact velocity increases, the droplet tends to spread over a wider area and the spreading stage becomes more dominant (14.4 mm in diameter for the highest impact Reynolds and Weber numbers versus 6.6 mm for the lowest). This is attributed to the higher ratio between the kinetic energy of the droplet and its surface tension. Following the maximum spread is the receding stage that appears to be much weaker for the high velocity case; no oscillations after receding have been observed. The receding stage of the lower impact Reynolds and Weber numbers case seems to differ from the other two cases in its second vigorous fast stage, in which excessive liquid from the upper area of the rim returns inward into the central zone of the droplet due to surface tension. The liquid is forced upward, hence increasing the droplet’s height. We assume that since the spreading area of the droplet for the higher impact case is much larger (due to higher ratio of inertia to surface tension forces), the liquid lm thickness is much lower and the shear stresses there hinder the inward •ow. The equilibrium shape of the droplet tends to be more like a spherical cap (stronger receding) for the lower impact Reynolds and Weber numbers’ case (Re = 1440, We = 8.9), while it tends to be more disklike (weaker receding) for the higher impact Reynolds and Weber numbers’ case (Re = 8300, We = 300) as schematically shown in Fig. 8. The effects of the Reynolds and Weber numbers on the



8 Diameter

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Diameter 3 Height 1 Height 4

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Fig. 5 Single-droplet low-velocity impact (0.45 m/s) on a dry surface: process repeatability.

5

2.6m/s

4 Impact velocity = 1.8m/s

3 0.45m/s

2 1 0 0

2

4 6 Dimensionless Time [t/(Dp/ vo)]

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Fig. 6 Diameter evolution of single-droplet impacts on a dry surface.

Dimensionless Height [H/Dp]

1.2 1 0.8 0.6

Impact velocity = 0.45m/s

0.4 0.2

2.6m/s 1.8m/s

0 0

2

4 6 8 Dimensionless Time [t/(Dp/ vo)]

Fig. 7 Height evolution of single-droplet impacts on a dry surface.

10

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R

h

Dm

Dm

(a)

(b)

Fig. 8 Assumed equilibrium shape of a single droplet impacted on a dry surface for high (a) and low (b) impact velocities.

impact and collision outcomes will be discussed further in the following sections. A Single-droplet Impact on a Wet Solid Surface Figure 9 shows the evolution of the diameter and height of a single-droplet impact on a wet solid surface at a low impact velocity of 0.45 m/s. The lm thickness is 1 mm and the droplet diameter is 3.2 mm. It seems that when the droplet hits the wet surface at low impact velocity, it deforms and spreads continuously at a stable rate, while increasing its diameter and reducing its height above the wet surface until it vanishes and becomes a part of the surface liquid pool. When a droplet impacts on a wet surface at a higher impact velocity (Fig. 10), a high enough

pressure region is formed near the free liquid surface around the droplet from which a circular liquid lm in the shape of a crown emerges (Fujimoto et al. [11] expected such a behavior for dropletdroplet collision case, while it was assumed to be pretty much the same as for a wet surface impact). While observing the images taken during the crown formation phase, we noticed that the crown, which mostly consists of the liquid’s original [14], spreads upward and outward. The rim at the top of the crown ejects liquid ngerlike lms that eventually break into secondary droplets (crown splash). The droplet that hits the liquid lm forms a crater, the boundary of which is the crown walls. The impact energy is used to form the crown, and is then dissipated by the t tension. The crown does not collapse but gradually descends back into the liquid lm from which it


14 12 Diameter 10 8 6 4 Height 2 0 0

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Time [ms]

Fig. 9 Single-droplet impact at low velocity (0.45 m/s) on a wet surface; lm thickness, 1 mm.


5

Crown

Height [mm]

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Central column

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Film thickness = 1.5mm

1 1mm 0 0

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Time [ms] Fig. 10 Height evolution of single-droplet impacts at high velocity (2.6 m/s) on a wet surface.

has emerged. When the crown descends and the crater is •lled, a high-pressure region is developed at the center of impact, thus resulting in a central liquid column erection from the •lm. This central column is assumed to consist of the original droplet and some portion of the surrounding liquid •lm [14]. The central liquid column can further break up into several secondary droplets. This central column emerges only once, while consuming a large part of the energy gained as a result of the sinking of the crown, as well as of the surface ten-

sion and kinetic energy of the incoming liquid that •lls the crater. Another result of such an impact are the generated ripples that propagate outward onto the liquid •lm. Figures 10 and 11 show the effect of the •lm thickness (in the relevant range of droplet-droplet collision) on the height and diameter evolutions. Except for the small effect on the diameter where the droplet spreads faster with the thicker •lm, no other noticeable difference has been observed. The diameter increases at a decreasing rate until the

20

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Time [ms] Fig. 11 Diameter evolution of single-droplet impacts at high velocity (2.6 m/s) on a wet surface.

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Diameter (of the wet area) [mm]

crown descends and vanishes in the liquid •lm. The general behavior of the height for the two liquid •lms’ thicknesses seems to be similar (Fig. 10). It seems that the crown peaks are quite similar, but the central column jet of the shallower pool appears much earlier than that of the deeper pool, while its intensity is much lower. This is attributed to the crater size that follows the crown absorption; the crater was observed to be larger for the thicker •lm. The thickness of the liquid •lm seems to play an important role in the central column generation and evolution with time, and therefore droplet-droplet collision on a solid surface should be considered with appropriate care. The thickness-

to-diameter ratio was examined for the case where a single-droplet impacts on a wet surface at high impact velocity. It was found that when this ratio increases (within the same order of magnitude), the height evolution is slower and a larger crater is formed. Low-Velocity Impact of Droplet-Droplet Collision on a Solid Surface When a droplet having a low impact velocity collides with a previously deposited resting droplet on a solid surface (Figs. 12 and 13), the initial diameter and the initial height of the wet trace are

10 Droplet-droplet collision 8 6 Single droplet impact 4 2 0 0

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40 60 Time [ms]

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Fig. 12 Diameter evolution of a single-droplet impact on a dry surface and a droplet-droplet collision on a solid surface, at low impact velocity (0.45m/s).

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Time [ms] Fig. 13 Height evolution of a single-droplet impact on a dry surface and a droplet-droplet collision at low impact velocity (0.45 m/s).


equal to the equilibrium diameter and height of the previous droplet accordingly (the initial height as depicted in the •gures is the sum of the previously deposited droplet equilibrium height and the initial height of the incoming droplet). The wet trace seems to further expand only when the colliding droplet spreads and reaches the initial trace size. In the case discussed, the impact velocity is low, the collision is nonviolent, and the droplets merge gently. Subsequently, the wet diameter further expands while the droplet transforms into w and afterward into lamella and a rim structure (Fig. 14) similarly to the case of a single droplet having a low-velocity impact on a dry surface. We can try to compare a low impact velocity dropletdroplet collision on a solid surface (Figs. 12 and 13) with the low-velocity single-droplet impact on a wet surface (as shown in Fig. 9); but as can be clearly seen, there is no resemblance between these apparently similar occurrences. While for the single-droplet case there is a continuous spreading (increasing diameter when reducing the height) until the droplet vanishes smoothly into the liquid •lm, in the droplet-droplet case the resulting behavior is much different and actually very similar to the single-droplet, low velocity impact on a dry solid surface. This is only logical since the equilibrium diameter and mass of the •rst droplet

are very limited and could not act as a new liquid •lm when the second incoming droplet arrives. The incoming droplet does “feel” the previously deposited one, but very quickly it “feels” the dry surface surroundings. As can be seen in Fig. 12, the •rst droplet’s equilibrium diameter is about 6 mm, whereas when the second droplet impacts, the system exceeds this value almost instantly and the dry surface surroundings dictate the resembling behavior to the single-droplet, low-velocity impact on a dry surface. Following the maximum spread is the receding phase (Fig. 15) where the diameter decreases to its minimal value, after which an oscillation period develops until system stabilization is reached and a new equilibrium diameter is attained. The image in the circles shows the shape, contact angle, and liquid volume in the droplet’s rim area. As compared to the dry surface impact case, dropletdroplet collision tends to reach equilibrium after a longer period of spreading and resending.

High-Velocity Impact of Droplet-Droplet Collision on a Solid Surface Figures 16 and 17 compare the diameter and height evolutions of a droplet-droplet collision with those

Fig. 14 Part of the spreading stage of a droplet-droplet collision on a solid surface with low collision velocity (0.45 m/s).

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Fig. 15 Part of the receding stage of a droplet-droplet collision on a solid surface with low collision velocity (0.45 m/s). Droplet-droplet collision

Diameter [mm]

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Time [ms] Fig. 16 Diameter evolution of a single-droplet impact on a wet surface ( lm thickness, 1 mm) and a droplet-droplet collision at high impact velocity (2.6 m/s).

5 Crown evolution

Height [mm]

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Dropletdroplet collision

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Single droplet impact

1 0 0

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Time [ms] Fig. 17 Height evolution of a single-droplet impact on a wet surface ( lm thickness, 1 mm) and a droplet-droplet collision at high impact velocity (2.6 m/s).


of a single-droplet impact on a wet solid surface (1 mm •lm thickness) at a high impact velocity of 2.6 m/s (impact Re and We numbers of 8300 and 300, respectively). In Fig. 16, the diameter in the droplet-droplet case starts from zero as compared to the equilibrium diameter of the previous droplet. In this case, the •rst droplet had spread to become so s !""# $ " % a reasonable con•dence. In both cases, the droplet that hits the liquid •lm forms a crater where the boundary of which is the crown walls that are developed and spread upward and outward. A rim at the top of the crown ejects liquid •ngerlike •lms that eventually break into secondary tiny droplets (crown splash). For the single-droplet case, when the crown descends and the crater is •lled, a part of the energy gained as a result of the sinking of the crown is used to erect a central liquid column that consequently breaks up into several secondary tiny droplets. It seems that the crown peaks are fairly similar, but for the droplet-droplet collision case, no central uprising column jet emerges after the crown sinking. It seems that in this case the crown collapses outward onto the dry surrounding surface and there is almost no energy left to get the liquid back into the center of impact and no crater is left open in the central area that needs to be closed. We have also noticed that in the droplet-droplet collision case, the crown reaches a point where

it ceases to expand and collapses outward, while for the single-droplet case it expands continuously until descending gradually into the liquid •lm. While for the droplet-droplet collision case with the low impact velocity the collision consequences developed in a slower manner than in the singledroplet impact on a dry surface case (Figs. 12 and 13), it seems that for the droplet-droplet collision case with the high impact velocity the collision consequences develop faster that those for the single-droplet impact on a wet surface. The difference in the crown expansion behaviors is attributed to the different liquid •lm area and thickness on the surface. For the single impact case, the liquid •lm is much larger than the trace of a previous droplet in the droplet-droplet collision case. The crown’s expansion in the droplet-droplet collision is strongly affected by boundary effects. The thickness of the liquid •lm and the liquid pool size seem to play an important role in the crown and central column generation and evolution with time. The effect of the impact velocity on the diameter and height evolutions is shown in Figs. 18 and 19, respectively. For the lower velocity case (0.45 m/s), the droplet appears to merge, spread, recede, and oscillate with no crown formation. Its evolution sequences are similar to the singleimpact dry surface case with low impact velocity. For the higher-velocity cases (1.7 and 2.6 m/s), the collision results in a crown that propagates to

Dimensionless Diameter [D/Dp]

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Impact velocity = 0.45m/s

1 0 0

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Fig. 18 Diameter evolution of droplet-droplet collisions on a solid surface.

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Dimensionless Height [H/Dp]

1.5 2.6m/s 1.2 Crown

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Impact velocity = 0.45m/s 0.6 0.3

1.7m/s

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Dimensionless Time [t/(Dp/v0)] Fig. 19 Height evolution of droplet-droplet collisions on a solid surface.

a certain level until it ceases and falls outward. The early part of the evolution is very similar to the single-impact wet surface case with high velocity, while the later part seems to be somewhat different since it lacks the central column part. The Weber number can be thought of as a measure of the relative importance of the •uid’s inertia compared to its surface tension, whereas the Reynolds number is the ratio of inertial forces to viscous forces. Both of them (We and Re) are important and relevant parameters that affect the consequent collision behavior. For the same •uid and initial droplet’s dimensions, the main parameter that affects the collision outcome is the impact velocity. While the Reynolds number depends linearly on the impact velocity, the Weber number depends on its value raised by a power of two. Thus, when the impact velocity increases from 0.45 to 2.6 m/s, the Reynolds number increases from 1440 to 8300 and the Weber number from 8.9 to 300. The difference between the low and high impact velocity collision outcomes is therefore fundamental. While the lower impact velocity droplet-droplet collision does not evolve a crown propagation or splash and resembles a single-droplet impact on a dry surface, the high impact velocity droplet-droplet collision does evolve a crown propagation or splash, and resembles a single-droplet impact on a wet surface.

Figures 20 and 21 visually summarize our •ndings. Worth noting are the later stages of a singledroplet impact on a wet surface for high impact velocity (2.6 m/s). Figure 22 shows the development of a central liquid column after crown descent as discussed above. CONCLUSIONS This work compares droplet-droplet collisions on a solid surface, having low or high impact velocities, with single-droplet impacts on dry and wet solid surfaces. In general, similarities are found for the case of low impact velocity between dropletdroplet collision and a single-droplet impact on a dry surface. For the case of high impact velocity, similarities are found between droplet-droplet collision and a single-droplet impact on a wet surface. However, despite the resemblance, there are some signi•cant differences between the compared cases. The major phenomenological differences between the above two cases are, in terms of morphology, spreading behavior, secondary droplet formation, different crown behavior, and the formation of a central (Worthington) jet. Differences in diameter and height evolution values, in local maximums, minimums, and timing, in crown behavior, and in central liquid jet characteristics were determined.


a) Low impact velocity:

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Fig. 20 Different cases for low impact velocity of 0.45 m/s; time is in milliseconds.

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Fig. 21 Different cases for high impact velocity of 2.6 m/s; time is in milliseconds.


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Fig. 22 Later stages of a single-droplet impact on a wet surface, for impact velocity of 2.6 m/s. Shown is the development of a central liquid column after crown descent.

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8. A. L.Yarin, Droplet Impact Dynamics, Annu. Rev. Fluid Mech., vol. 38, pp. 159–192, 2006. 9. R. Rioboo, M. Marengo, G. E. Cossali, and C. Tropea, Comparison of Droplet Impact: Dry and Wet Cases, ILASS-Europe 2000, Darmstadt, 2000. 10. R. Rioboo, C. Bauthier, J. Conti, M. Voue, and J. Coninck, Experimental Investigation of Splash and Crown Formation during Single Droplet Impact on Wetted Surfaces, Exp. Fluids, vol. 35, pp. 648–652, 2003. 11. H. Fujimoto, T. Ogino, H. Takuda, and N. Hatta, Collision of a Droplet with a Hemispherical Static Droplet on a Solid, Int. J. Multiphase Flow, vol. 27, pp. 1227–1245, 2001. 12. D. Vadillo, E. Canot, B. Lopez, and A. Soucemarianadin, Collisions of Single and Multiple Drops onto Solid Walls, LEGI, France, 2004. 13. I. V. Roisman, R. Rioboo, and C. Tropea, Normal impact of a liquid droplet on a dry surface: model for spreading and receding, Proc. of the Royal Society A, vol. 458, pp. 1411–1430. 2002. 14. A. M. Worthington, A Study of Splashes, Longmans, Green, London, 1908.