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Phenomena of a drop impact on a restricted liquid surface
Experimental Thermal and Fluid Science 51 (2013) 332–341
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Experimental Thermal and Fluid Science journal homepage: www.elsevier.com/locate/etfs
Phenomena of a drop impact on a restricted liquid surface Jun Zou ⇑, YuLiang Ren, Chen Ji, XiaoDong Ruan, Xin Fu The State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, China
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Article history: Received 2 March 2013 Received in revised form 19 August 2013 Accepted 19 August 2013 Available online 28 August 2013 Keywords: Drop Reflected waves Surrounding wall Bounce Bubble entrapment
a b s t r a c t The behavior of drops impacting on a gas–liquid interface restricted by surrounding walls is studied using a high-speed video camera. The droplet diameter used in this experiment was 2.64 mm with impact Weber number of between 5 and 630. The highly purified water held by glass tubes of various inner diameters (6 mm, 8 mm, 12 mm, 17 mm and 26 mm) is used as the restricted target liquid. A special phenomenon of bubble entrapment is observed in our experiments. It is found that the bubble formation is not only dependent on the impact velocity of the drop, but also the distance from the surrounding walls to impact point. Moreover, because of the restricted effect of surrounding walls, the critical velocity for the occurrence of canopy bubble decreases sharply with the reduction of the tube size. Decreasing the inner diameter of tube also makes the drop bounce higher than that on a broad liquid surface with the same Weber number. Ó 2013 Elsevier Inc. All rights reserved.
1. Introduction Phenomena of liquid drops falling to solid or liquid surfaces are ubiquitous in nature. The studies of them are very important due to their relevance to a wide range of applications, such as inkjet printing, spray cooling, spray painting, and dissolved oxygen increment [1,2]. Generally speaking, the outcome of a drop impact on a liquid surface, including bouncing, coalescence, jetting and splashing, depends on the impact velocity of drops [3], liquid viscosity [4] and depth of the target liquid [5]. Among these influencing factors, the depth of liquid pool is the most commonly considered physical constraint. When the depth of the target liquid is small, due to the bottom effect the outcomes of drop impact is different in many aspects, such as the height of the rebounding jet [6], number of secondary droplets [7,8] and crown height [9], compared with drop impact on a deep liquid pool. There are a large number of published literatures focused on the phenomena of drop impact onto the liquid surface, however, within which the effect of surrounding wall is always ignored. Until recently, Zou et al. [10] found that the surrounding walls and drop oscillation played an important role in a unique phenomenon of large bubble entrapment during the drop (diameter 3.86 mm) impact on a restricted liquid surface. Moreover some up-to-date requirements in the field of tissue engineering make the research urgent. For example in organ printing, droplets holding cells are sprayed onto porous bioscaffolds that the growing tissues can be
attached to, which relate to a series of complex drop impact phenomena involving on solid and restricted liquid surfaces [11]. Recently, drop impact onto electrospun polymer nanofiber mats attracted attention of researchers [12], because of the unique outcome [13], and the application of this process for effective spray cooling [14]. In this paper, a study of the dynamics of drop impact onto a restricted liquid surface is presented. To understand the impact process, its behavior is recorded by a high-speed video camera. Several phenomena different from drop impact on the broad liquid surface were observed. Besides that, experimental results with a large range of impacting velocity are discussed in this paper, whose outcomes are described in detail and compared to the previous work of drop impact on liquid surfaces. In order to decrease the effect of drop oscillation, the drops with diameter = 2.64 mm was chosen as impact droplets. The effect of drop oscillation on the phenomenon of large bubble entrapment has been discussed detailedly in the previous work [10]. In the present paper, the study is based on the effect of the impact velocity of drop and tube diameter. The fluid viscosity and surface tension are also important influential factors on the outcomes, but that will be discussed in the future work. The main dimensionless parameters governing drop impact and employed in the present paper are
Dt ¼
Dt qV 2 D qVD We1=2 ; We ¼ ; Re ¼ ; Oh ¼ ; D r l Re 2=5
K ¼ We Oh ⇑ Corresponding author. Tel.: +86 57187953395. E-mail address: [email protected] (J. Zou). 0894-1777/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.expthermflusci.2013.08.016
; K 0 ¼ We0:375 Re0:25
where D and V denote the drop diameter and impact velocity, respectively. q, r and l denote the liquid density, surface tension
J. Zou et al. / Experimental Thermal and Fluid Science 51 (2013) 332–341
and kinetic viscosity, respectively. Dt is the inner diameter of the tube used for holding target liquid. Dt denotes the dimensionless distance of surrounding walls. We, Re and Oh denote Weber, Reynolds and Ohnesorge numbers respectively. K and K0 are important composite groups for drop impact [23,22].
2. Experimental setup The apparatus shown in Fig. 1 is used to investigate droplet impact upon a liquid surface restricted by surrounding walls, which has been used in the experiment of large bubble entrapments [10]. The droplet production system is comprised of: a syringe, flat tipped stainless steel needles, flexible transparent tube and a roller clamp. The flat tipped stainless needles is caught by a clamp which was mounted on a vernier height gauge (resolution: 0.02 mm and range 900 mm). The height gauge is installed to facilitate changing the droplet height and subsequently the droplet impact velocity. The roller clamp is attached to the flexible transparent tube to regulate the producing rate of droplets. Flat tipped stainless needles are connected to the flexible transparent tube to produce small droplets, which are formed at the tip of needles and detached off under their own weight. The highly purified water held by glass tubes of various inner diameters (6 mm, 8 mm, 12 mm, 17 mm, 26 mm) is used as the restricted target liquid, of which the depth hl is over 150 mm. Finally, the acquisition system including a high speed video camera (FASTCAM-ultima APX, USA) and a Nikkor 60-mm micro lens is employed to capture the images. Images are captured by the high speed video camera at a speed of 2000 fps (frames per second). Flickerless backlighting is produced by a high-intensity LED lamp with a thin sheet of drafting paper as a diffuser. The camera is connected to a computer by firewire cable. The control software is installed in the computer, and allows capturing and storing images. The environment pressure is kept at 101.3 kPa. The test liquid (comprising the target liquid and droplets) and laboratory temperature are kept at 25 °C, at which the surface tension coefficient and dynamic viscosity of the test liquid (highly purified water) are 0.07197 N/m and 0.8937 103 Pa s, respectively. The maximum temperature fluctuation is about ±2 °C. The temperature fluctuation has no significant effect on the surface tension coefficient and viscosity of water, below 1% and 5% respectively. The contact angle between the tube wall and the liquid is measured from images, which is 60.8° with uncertainty of 1°.
Fig. 1. Experimental setup.
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In the experiments, the drop is released from the needle, with an initial velocity of zero. After the detachment from the needle, the drop is then accelerated by gravity. The impact velocity V is measured from the images. By varying the impact height H, V could be controlled. The uncertainty of V is estimated to be 0.04 m/s. The droplet diameter was calculated by processing the images in image analyzer. The drop diameter D, is yielded from 1=3 , where Dx is the horizontal diameter and Dy is the D ¼ D2x Dy vertical diameter. The typical initial shape of the drop is shown in Fig. 1. We employ the same needle in all the experiments, producing drops with diameters of 2.64 mm, which is considered as a constant in the present study. The maximum standard deviation of drop diameter is found to be 0.04 mm. In this paper, the Weber numbers of drops range from 5 to 630. Considering the uncertainty of drop size and impact velocity, the error of Weber numbers is estimated to be less than 0.2. Each experimental point was performed several times (3 times as a minimum) to test the repeatability. 3. Results and discussion According to many investigations [1,15], the drop impact phenomena on liquid pool are divided into four main categories: Floating, bouncing, coalescence and splashing. When the droplet momentum is not enough to break the air film between the droplet and water surface, the floating or bouncing phenomena occur. With the further increase of Weber number, the coalescence occurs accompanied by the creation of a crater without breakup of the fluid or generation of secondary droplets. When the Weber number becomes large enough, the splashing appears, which can be subdivided into crown splashing, jet splashing and canopy bubble that crown close above the cavity [1]. A sketch of the outcomes resulting from the collision of a drop with the liquid surface is shown in Fig. 2, and the outcomes are described in the following section. First, for very low Weber number impact the floating and bouncing are described; secondly, the analysis of coalescence and splashing is presented; finally, the transition boundary of a regime map is discussed. 3.1. Floating and bouncing A few cases of droplets bouncing and floating upon a restricted liquid surface were observed in the experiment. When the Weber number is small enough, the droplet floats on the liquid surface. For the bouncing case, after several times of rebounds on the gas–liquid interface, the drop also floats on it, sometimes lasting for seconds before coalescence with the bulk liquid. In the paper, we focus more on the bouncing phenomenon.
Fig. 2. Phenomena of drop impact on a restricted liquid surface.
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(a)
(b)
Fig. 3. Bouncing sequence of a drop (D = 2.64 mm, We = 5.29) impact on the liquid surface in tubes of different inner diameter, (a) Dt = 8 mm Dt ¼ 3:03 , (b) Dt = 26 mm Dt ¼ 9:85 .
Fig. 3 shows the time-elapsed images of the impact of a water drop (D = 2.64 mm, We = 5.29) onto the restricted liquid surface in tubes. The inner diameters of tubes are 8 mm and 26 mm respectively. These images show that the droplet bounces on the liquid surface and produces waves. During the first several milliseconds of the impact, a crater can be seen, and the waves are generated. The waves propagate from the impact point, and reflect when they reach the wall. When the reflected waves from the walls arrive at the impact point, it means that a portion of impact energy stored in waves returns to the impact area interacting with the bouncing droplet at the moment. During drop collision with liquid surfaces, the kinetic energy of the drop is fractionally converted to restorable energy supplying
the motion of the drop away from the surface, and is mostly lost due to wave propagation and viscosity dissipation [5]. In order to measure the bouncing energy, a restitution coefficient is defined as e = V0 /V, where V0 is the take-off speed derived by (2gH0 gD)1/2, where H0 is the maximum bouncing height of the drop centroid. Jayaratne and Mason [16] deduced from their experiments that about 95% of kinetic energy was lost for a normal impact of drop (diameter 120–400 lm) on a broad liquid surface, rebound with an effective coefficient of restitution of about 0.2. Furthermore, with the increase of drop size, the coefficient of restitution decreases for the increase of energy loss during drop deformation [5]. Fig. 4 shows the effect of surrounding wall on the coefficient of restitution of drop bounce (D = 2.64 mm,
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50 40
0.4
30 0.2
20
Time after impact (ms)
0.6
The restitution coefficient e
60
e Tb Tw
10 0.0 2
4
6
8
10
Dt* Fig. 4. Effect of surrounding wall on the coefficient of restitution e, bounce time Tb, and converging time of the first wave Tw (We = 5.29).
We = 5.29). In our experiments, the restitution coefficient e of the drop impact on the target liquid surface Dt ¼ 2:27 is over 0.45 at the Weber number 5.29, which is at least 4 times than that for drop impact on the liquid surface held in a larger tubes Dt ¼ 9:85 . It is noticeable that when the distance from surrounding walls to impact point is over 6 times of drop radius, after a sharp descent the restitution coefficient e shows stable and is close to the experimental results of drop bouncing on a broad liquid surface [5]. Considering the sharp descent of restitution coefficient e in Fig. 4, one possible physical explanation is the wave effect. After the impact, surface waves produced by the drop impact propagate away from the impact point, until they are reflected back by the tube wall, as shown in Fig. 3. If the reflected waves reach the impact point before the drop rebounces from the liquid surface, the energy stored in the wave will give the drop a higher upward velocity. Therefore the condition for a higher restitution coefficient e should be Tb > Tw, where Tb denotes the time when the bouncing drop leaves the surface and Tw denotes the time when the first reflected wave converges. Tw can be evaluated as Dt/Vw, where Vw is the velocity of the first wave front, which can be measured according to the sequential pictures captured by high speed camera. The
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values of Tb and Tw with different tube diameters are shown in Fig. 4. When Dt is over 4.75, the value of Tw increases to outstrip the valve of Tb. It means the energy stored in reflected waves cannot be timely fed back to the drops to enhancing the bouncing behavior, which is represented by a obvious sudden decrease of the restitution coefficient e for the tube size Dt over 4.54, as shown in Fig. 4. 3.2. Coalescence and splashing Fig. 5 shows the time-elapsed images of the impact of a water drop (D = 2.64, We = 12.5) onto the liquid surface in the tube Dt ¼ 6:44 . These images show that the drop coalesces with the liquid and produces a crater. No jet and secondary droplets are produced during and after impact. As the droplet merges in the target liquid surface, a crater forms and wave is generated. Surface waves expands outward at first, and then is reflected by the wall, concentrating toward the impact point, making the crater bottom rough and ‘‘striped’’ (Fig. 5, 24–38 ms). It is noticeable the second crater occurs after the first one produced by drop impact (Fig. 5, 72 ms). According to our observation, the second crater is always shallower than the first one impacted by the drop. Fig. 6a, shows the sequence images of the impact of a water droplet with the Weber number of 115 onto the liquid surface in the tube Dt ¼ 4:54 . The impact exhibits a different behavior to that shown in the previous sequence of images (Fig. 4) due to the increasing impact velocity. A crater with a higher depth is formed at 13 ms, which then collapses and develops into a jet without bubble entrapment. The jet reaches a maximum height at 50 ms, breaking up and producing one droplet, and then slumps downward. The slumping jet impacts the liquid surface, forming a crater again, which expands to its highest depth at 76 ms. For the first crater generated by drop impact, the top edge of crater expands from the impact point until reaching the tube wall. However, for the second crater almost the whole liquid surface descends except that near the tube wall. The reflected surface wave can be easily observed moving along the crater surface, concentrating toward the crater bottom (Fig. 6a, 66–76 ms). When the bottom of the crater becomes cone shape, a tiny bubble pinches off the bottom of crater due to the focusing reflected wave.
Fig. 5. Coalescence sequence of a drop (D = 2.64 mm, We = 12.5) impact on the liquid surface in the tube of Dt = 17 mm Dt ¼ 6:44 .
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(a)
(b)
Fig. 6. Outcomes of a drop (D = 2.64 mm, We = 115) impact onto the liquid surface in tubes of different inner diameter or broad liquid surface, (a) Dt = 12 mm Dt ¼ 4:54 , (b) Dt = 17 mm Dt ¼ 6:44 , (c) broad surface.
Comparing with primary bubble entrapment, the bubble size in Fig. 6a is similar, but the time of its appearance is delayed to be after the collapse of second crater. This special phenomenon of bubble entrapment was not reported in previous literatures of drop
impact on liquid surface. Primary bubble entrainment is believed to be caused by capillary waves converging along the cavity wall, whose timing has a delicate balance with the rebounding of the cavity bottom [17,18]. In the case of bubble entrapment in
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(c)
Fig. 6 (continued)
1.0
0.8
Dr (mm)
Fig. 6a, called the delayed bubble entrapment, the wave can be found, while the bubble appears just together with the contracting of cavity bottom (Fig. 6a, 76–83 ms). Therefore, the formation mechanism of delayed bubble is similar to primary bubble. However, delayed bubble entrapment also has some special features. There is no high-speed jet observed after the delayed bubble entrapment, while primary bubble entrapment always appears together with one. This absence implies that the converging of surface wave, which is perhaps the reflected wave from the wall, is weaker at cavity bottom. The appearance of delayed bubble is sensitive to the tube diam eter Dt , only observed with tube diameter of 12 mm Dt ¼ 4:54 in the experiments. Fig. 6b shows the behavior of drop impacting on the liquid surface in the tube Dt ¼ 6:44 with the same Weber number as Fig. 6a. After the concentration of the surface wave, the phenomenon of high-speed jet break appears (Fig. 6b, 93 ms) instead of bubble entrapment (Fig. 6a, 83 ms). The case of broad liquid surface is also given in Fig. 6c for comparison, where no phenomenon is observed after the first jet break. Fig. 7 shows how the diameter Dr of delayed bubbles varies with the impact Weber number of drops. At the initial stage the bubble size increases with the impact Weber number. When the impact Weber number of drop is over 130, the data show a decline trend. Fig. 8 shows time elapsed images of the impact of a drop with the Weber number of 267 onto the liquid surface in the tube Dt ¼ 4:54 . With the increase of Weber number, a very thin crown rises around the impact point during an early stage of the impact (Fig. 8, 1 ms). Small droplets are ejected from the top edge of the crown and splash to the tube wall. At 29 ms, a bubble is formed during the cavity collapses, which is a primary bubble entrapment. Then a jet rises from the center of the cavity. After that the second crater develops and collapses, but there is no occurrence of both bubble (Fig. 6a, 83 ms) and jet (Fig. 6b, 93 ms).
0.6
0.4
0.2
0.0
80
100
120
140
160
180
200
220
We Fig. 7. Sizes of the delayed bubbles (Dt = 12 mm, Dt ¼ 4:54).
Fig. 9a shows time elapsed images of a drop of We = 490 impact on the liquid surface in the tube Dt ¼ 4:54 . Unlike the previous two cases (Figs. 6a and 8), an obvious crown rises around the impact point. The crater looks more like a hemisphere during its expansion compared to those in Figs. 6a and 8. At 16 ms, it almost occupied the whole tube in radial direction. At the same time, the expansion of the impact crater causes a continual rise of liquid surface in the tube. Finally, the rising crown collapses toward impact point and closes above the cavity, forming a canopy bubble. Its formation mechanism is different from the bubbles formed in Figs. 6a and 8, which are both due to the pinch-off of the cavity, while the canopy bubble is formed by the crown collapsing inward. As shown in Fig. 9b, no canopy forms under the same condition
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Fig. 8. Crown splash sequence of a drop (D = 2.64 mm, We = 267) onto the liquid surface in tubes, Dt = 12 mm Dt ¼ 4:54 .
(D = 2.64 mm, We = 490) if the liquid surface is not restricted. The canopy phenomenon is seldom observed during drop impact on a broad liquid surface, which happens only for the drops close to the terminal velocity [19,20]. But it can be observed frequently for the drop impact on the liquid surface in tubes, especially in smaller tubes. An explanation can be based on the restricting effect of the wall. The wall is a radial restriction to the cavity, so it makes the radial expansion of both the cavity and the crown stop soon. At the same time, because of the expansion of cavity the liquid near tube wall is squeezed upward, sending more liquid into the crown. The two effects speed up the crown to collapse inward, favoring the occurrence of canopy bubble.
3.3. Transition boundaries of regimes The outcomes of drop impact on liquid surfaces have been mapped by many researchers based on most relevant non-dimensional parameters or the combination of them. In the paper, the impact outcomes have been compared with those of Liow [21], Huang and Zhang [22], and Okawa et al. [23] which show the transition between different boundaries for a normal impact. Liow [21] suggested that the transitions between bounce and coalescence should occur at We = 8. Huang and Zhang [22] suggested that the transitions between jet formation and coalescence should occur at K0 = 28 and that the transition between jet formation and splashing occurs at K0 = 70. Okawa et al. [23] suggested that the splashing limit occurs at K = 2100.
The different impact behaviors are presented in Fig. 10 according to the impact Weber number and tube diameter. An alternative representation using K0 and K is shown in Figs. 11 and 12. The notation of infinity represents cases of drops impacting on broad liquid surface, whose results are similar to large tubes Dt ¼ 9:85 . The We Dt map can be divided into four regions: bounce, coalescence/jet, splash and canopy, as shown in Fig. 10. Generally speaking, canopy occurs in small tubes with high Weber numbers, while the other three kinds of outcomes appear in order when the Weber number increases. Fig. 10 shows that the Weber number boundaries of the bounce, coalescence/jet and splash regions are independent from Dt . The explanation could be that the deviation of these three regions is determined by a rapid process after the impact. The tube wall makes little effect on the early stages of the impacting process, so the kinetic energy of the drop is the major factor to distinguish bounce, coalescence and splash. On the other hand, the value of Dt does play an important role in the development of the cavity forming after the impact. That is the reason of the complex outcomes inside the coalescence/jet region, where the formation of jet and the following phenomena are very dependent on the dynamics of the cavity. According to our experimental results (Fig. 10), coalescence occurs at a low Weber number for the impact on liquid surfaces in tubes of five different diameters. By comparing the impact outcomes with Liow’s thresholds [21], the coalescence threshold seems to fit with his results (We = 8). As shown in Fig. 11, Huang and Zhang [22] suggested that the transitions between coalescence and jet formation for drop impact
J. Zou et al. / Experimental Thermal and Fluid Science 51 (2013) 332–341
339
(a)
(b)
Fig. 9. Sequence of a drop (D = 2.64 mm, We = 490) impact onto a) the liquid surface in the tube of Dt = 12 mm Dt ¼ 4:54 , b) broad liquid surface.
on the broad liquid surface should occur at K0 = 28. For the case of drop impact on restricted liquid surface in tubes, as shown in Fig. 11, the transition threshold of K0 increases as a function of the tube diameter from Dt ¼ 3:03 to 6:44. Except for the smallest tube size Dt ¼ 3:03 , all the critical value for coalescence to jet
formation is above the results suggested by Huang and Zhang. Moreover, the tube wall gives birth to a special phenomenon of delayed bubble entrapment only appearing in the tube of Dt ¼ 6:44, whose region is below the limit of crown splash and coincidence with the phenomenon of jet break at the first impact.
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Fig. 10. Distribution of the impact regimes obtained in this work on a We Dt map.
Fig. 11. Distribution of the impact regimes obtained in this work on a K 0 Dt map.
Fig. 12. Distribution of the impact regimes obtained in this work on a K Dt map.
J. Zou et al. / Experimental Thermal and Fluid Science 51 (2013) 332–341
As the impact Weber number increases further than the region of jet break, the crown splashing occurs. As shown in Fig. 10, for larger tubes Dt ¼ 4:54; 6:44 and 9:85 , the crown splashing threshold is around We = 225 for drops with diameter of 2.64 mm, which is independent of the distance from surrounding walls to the impact point. In the smaller tubes Dt ¼ 2:27 and 3:03 , the phenomenon of crown splashing is not observed. As shown in Fig. 11, splashing appears around the line of K0 = 70, fitting well with the results of Huang and Zhang [22]. Okawa et al. [23] suggested K = 2100 as a threshold for splashing. In Fig. 12, our experimental results shows that splashing occurs around K = 2600, higher than the line suggested by Okawa et al. The canopy phenomenon is seldom observed during drop impact on a broad liquid surface. However because of the restricted effect of surrounding walls, the required velocities for the occurrence of canopy decrease sharply with the reduction of the tube size. As shown in Fig. 10, the critical impact Weber number of canopy is only 192 for the drop impact on the liquid surface in the tube of inner diameter 8 mm Dt ¼ 3:03 , but is out of regulating range of our experimental setup (the maximum of impact Weber number = 630) for the case of the drop impact on the li quid surface in the tubes of inner diameter 17 mm Dt ¼ 6:44 and 26 mm Dt ¼ 9:85 . With the present experimental results, the lower limit of the canopy region is estimated to be We ¼ 173Dt 321:8 .
4. Conclusions An experimental study was conducted for water droplet impact on restricted liquid surfaces held in tubes. The droplet impact Weber number was varied between 5 and 630, the tube diameter was changed between 6 mm and 26 mm. By analyzing images of the drop impact, the behavior of the impact process for the range of conditions studied was extracted. In addition, information relating to the coefficient of restitution for drop bounce and the size of delayed bubble entrapment was discussed. The critical Weber numbers for the coalescence to crown splash seem independent of the distance of surrounding walls to impact point under the range of studied here. However, decreasing the distance causes difference in impact outcome, especially for the canopy bubble formation, whose critical velocity decrease sharply to a value easier to reach. Moreover, decreasing distance can reduce the travelling time of the reflected wave, making drop bounce higher. It is interesting that, within a certain distance range, the second crater is observed, perhaps followed by delayed bubble entrapment or jet formation. The impact Weber number of the drop also appears to influence the size of the delayed bubble entrapped.
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Acknowledgments This work is supported by the National Natural Science Foundation for Excellent Youth Scholars of China (No. 51222501), the Science Fund for Creative Research Groups of the National Natural Science Foundation of China (No. 51221004). References [1] M. Rein, Phenomena of liquid drop impact on solid and liquid surfaces, Fluid Dyn. Res. 12 (1993) 61–93. [2] A.L. Yarin, Drop impact dynamics: splashing, spreading, receding, bouncing, Annu. Rev. Fluid Mech. 38 (2006) 159–192. [3] M. Hsiao, S. Lichter, L.G. Quintero, The critical Weber number for vortex and jet formation for drops impinging on a liquid pool, Phys. Fluids 31 (1988) 3560– 3562. [4] Q. Deng, A.V. Anilkumar, T.G. Wang, The role of viscosity and surface tension in bubble entrapment during drop impact onto a deep liquid pool, J. Fluid Mech. 578 (2007) 119–138. [5] J. Zou, P.F. Wang, T.R. Zhang, X. Fu, X.D. Ruan, Experimental study of a drop bouncing on a liquid surface, Phys. Fluids 23 (2011) 044101. [6] J. Shin, T.A. McMahon, The tuning of a splash, Phys. Fluids A 2 (1990) 1312– 1317. [7] A.B. Wang, C.C. Chen, Splashing impact of a single drop onto very thin liquid films, Phys. Fluids 12 (2000) 2155–2158. [8] G.E. Cossali, M. Marengo, A. Coghe, S. Zhdanow, The role of time in single drop splash on thin film, Exp. Fluids 36 (2004) 888–900. [9] S. Mukherjee, J. Abraham, Crown behavior in drop impact on wet walls, Phys. Fluids 19 (2007) 052103. [10] J. Zou, C. Ji, B.G. Yuan, Y.L. Ren, X.D. Ruan, X. Fu, Large bubble entrapment during drop impacts on a restricted liquid surface, Phys. Fluids 24 (2012) 057101. [11] V. Mironov, T. Boland, T. Trusk, G. Forgacs, R.R. Markwald, Organ printing: computer-aided jet-based 3D tissue engineering, Trends Biotechnol. 21 (2003) 157–161. [12] C.M. Weickgenannt, Y.Y. Zhang, S. Sinha-Ray, I.V. Roisman, T. GambaryanRoisman, C. Tropea, A.L. Yarin, Inverse-Leidenfrost phenomenon on nanofiber mats on hot surfaces, Phys. Rev. E 83 (2011) 036310. [13] A.N. Lembach, H.B. Tan, I.V. Roisman, T. Gambaryan-Roisman, Y.Y. Zhang, C. Tropea, A.L. Yarin, Drop impact, spreading, splashing, and penetration into electrospun nanofiber mats, Langmuir 26 (2010) 9516–9523. [14] S. Sinha-Ray, Y. Zhang, A.L. Yarin, Thorny devil nanotextured fibers: the way to cooling rates on the order of 1 kW/cm2, Langmuir 27 (2011) 215–226. [15] S.K. Alghoul, C.N. Eastwick, D.B. Hann, Normal droplet impact on horizontal moving films: an investigation of impact behavior and regimes, Exp. Fluids 50 (2011) 1305–1316. [16] O.W. Jayaratne, B.J. Mason, The coalescence and bouncing of water drops at an air/water interface, Proc. R. Soc. Lond. A 280 (1964) 545–565. [17] H.C. Pumphrey, P.A. Elmore, The entrainment of bubbles by drop impacts, J. Fluid Mech. 220 (1990) 539–567. [18] H.N. Oguz, A. Prosperetti, Bubble entrainment by the impact of drops on liquid surfaces, J. Fluid Mech. 219 (1990) 143–179. [19] G.J. Franz, Splashes as sources of sound in liquids, J. Acoust. Soc. Am. 31 (1959) 1080–1096. [20] O.G. Engel, Crater depth in fluid impacts, J. Appl. Phys. 37 (1966) 1798–1808. [21] J.L. Liow, Splash formation by spherical drops, J. Fluid Mech. 427 (2001) 73– 105. [22] Q. Huang, H. Zhang, A study of different fluid droplets impacting on a liquid film, Pet. Sci. 5 (2008) 62–66. [23] T. Okawa, T. Shiraishi, T. Mori, Production of secondary drops during the single water drop impact onto a plane water surface, Exp. Fluids 41 (2006) 965–974.
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Experimental Thermal and Fluid Science journal homepage: www.elsevier.com/locate/etfs
Phenomena of a drop impact on a restricted liquid surface Jun Zou ⇑, YuLiang Ren, Chen Ji, XiaoDong Ruan, Xin Fu The State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, China
a r t i c l e
i n f o
Article history: Received 2 March 2013 Received in revised form 19 August 2013 Accepted 19 August 2013 Available online 28 August 2013 Keywords: Drop Reflected waves Surrounding wall Bounce Bubble entrapment
a b s t r a c t The behavior of drops impacting on a gas–liquid interface restricted by surrounding walls is studied using a high-speed video camera. The droplet diameter used in this experiment was 2.64 mm with impact Weber number of between 5 and 630. The highly purified water held by glass tubes of various inner diameters (6 mm, 8 mm, 12 mm, 17 mm and 26 mm) is used as the restricted target liquid. A special phenomenon of bubble entrapment is observed in our experiments. It is found that the bubble formation is not only dependent on the impact velocity of the drop, but also the distance from the surrounding walls to impact point. Moreover, because of the restricted effect of surrounding walls, the critical velocity for the occurrence of canopy bubble decreases sharply with the reduction of the tube size. Decreasing the inner diameter of tube also makes the drop bounce higher than that on a broad liquid surface with the same Weber number. Ó 2013 Elsevier Inc. All rights reserved.
1. Introduction Phenomena of liquid drops falling to solid or liquid surfaces are ubiquitous in nature. The studies of them are very important due to their relevance to a wide range of applications, such as inkjet printing, spray cooling, spray painting, and dissolved oxygen increment [1,2]. Generally speaking, the outcome of a drop impact on a liquid surface, including bouncing, coalescence, jetting and splashing, depends on the impact velocity of drops [3], liquid viscosity [4] and depth of the target liquid [5]. Among these influencing factors, the depth of liquid pool is the most commonly considered physical constraint. When the depth of the target liquid is small, due to the bottom effect the outcomes of drop impact is different in many aspects, such as the height of the rebounding jet [6], number of secondary droplets [7,8] and crown height [9], compared with drop impact on a deep liquid pool. There are a large number of published literatures focused on the phenomena of drop impact onto the liquid surface, however, within which the effect of surrounding wall is always ignored. Until recently, Zou et al. [10] found that the surrounding walls and drop oscillation played an important role in a unique phenomenon of large bubble entrapment during the drop (diameter 3.86 mm) impact on a restricted liquid surface. Moreover some up-to-date requirements in the field of tissue engineering make the research urgent. For example in organ printing, droplets holding cells are sprayed onto porous bioscaffolds that the growing tissues can be
attached to, which relate to a series of complex drop impact phenomena involving on solid and restricted liquid surfaces [11]. Recently, drop impact onto electrospun polymer nanofiber mats attracted attention of researchers [12], because of the unique outcome [13], and the application of this process for effective spray cooling [14]. In this paper, a study of the dynamics of drop impact onto a restricted liquid surface is presented. To understand the impact process, its behavior is recorded by a high-speed video camera. Several phenomena different from drop impact on the broad liquid surface were observed. Besides that, experimental results with a large range of impacting velocity are discussed in this paper, whose outcomes are described in detail and compared to the previous work of drop impact on liquid surfaces. In order to decrease the effect of drop oscillation, the drops with diameter = 2.64 mm was chosen as impact droplets. The effect of drop oscillation on the phenomenon of large bubble entrapment has been discussed detailedly in the previous work [10]. In the present paper, the study is based on the effect of the impact velocity of drop and tube diameter. The fluid viscosity and surface tension are also important influential factors on the outcomes, but that will be discussed in the future work. The main dimensionless parameters governing drop impact and employed in the present paper are
Dt ¼
Dt qV 2 D qVD We1=2 ; We ¼ ; Re ¼ ; Oh ¼ ; D r l Re 2=5
K ¼ We Oh ⇑ Corresponding author. Tel.: +86 57187953395. E-mail address: [email protected] (J. Zou). 0894-1777/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.expthermflusci.2013.08.016
; K 0 ¼ We0:375 Re0:25
where D and V denote the drop diameter and impact velocity, respectively. q, r and l denote the liquid density, surface tension
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and kinetic viscosity, respectively. Dt is the inner diameter of the tube used for holding target liquid. Dt denotes the dimensionless distance of surrounding walls. We, Re and Oh denote Weber, Reynolds and Ohnesorge numbers respectively. K and K0 are important composite groups for drop impact [23,22].
2. Experimental setup The apparatus shown in Fig. 1 is used to investigate droplet impact upon a liquid surface restricted by surrounding walls, which has been used in the experiment of large bubble entrapments [10]. The droplet production system is comprised of: a syringe, flat tipped stainless steel needles, flexible transparent tube and a roller clamp. The flat tipped stainless needles is caught by a clamp which was mounted on a vernier height gauge (resolution: 0.02 mm and range 900 mm). The height gauge is installed to facilitate changing the droplet height and subsequently the droplet impact velocity. The roller clamp is attached to the flexible transparent tube to regulate the producing rate of droplets. Flat tipped stainless needles are connected to the flexible transparent tube to produce small droplets, which are formed at the tip of needles and detached off under their own weight. The highly purified water held by glass tubes of various inner diameters (6 mm, 8 mm, 12 mm, 17 mm, 26 mm) is used as the restricted target liquid, of which the depth hl is over 150 mm. Finally, the acquisition system including a high speed video camera (FASTCAM-ultima APX, USA) and a Nikkor 60-mm micro lens is employed to capture the images. Images are captured by the high speed video camera at a speed of 2000 fps (frames per second). Flickerless backlighting is produced by a high-intensity LED lamp with a thin sheet of drafting paper as a diffuser. The camera is connected to a computer by firewire cable. The control software is installed in the computer, and allows capturing and storing images. The environment pressure is kept at 101.3 kPa. The test liquid (comprising the target liquid and droplets) and laboratory temperature are kept at 25 °C, at which the surface tension coefficient and dynamic viscosity of the test liquid (highly purified water) are 0.07197 N/m and 0.8937 103 Pa s, respectively. The maximum temperature fluctuation is about ±2 °C. The temperature fluctuation has no significant effect on the surface tension coefficient and viscosity of water, below 1% and 5% respectively. The contact angle between the tube wall and the liquid is measured from images, which is 60.8° with uncertainty of 1°.
Fig. 1. Experimental setup.
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In the experiments, the drop is released from the needle, with an initial velocity of zero. After the detachment from the needle, the drop is then accelerated by gravity. The impact velocity V is measured from the images. By varying the impact height H, V could be controlled. The uncertainty of V is estimated to be 0.04 m/s. The droplet diameter was calculated by processing the images in image analyzer. The drop diameter D, is yielded from 1=3 , where Dx is the horizontal diameter and Dy is the D ¼ D2x Dy vertical diameter. The typical initial shape of the drop is shown in Fig. 1. We employ the same needle in all the experiments, producing drops with diameters of 2.64 mm, which is considered as a constant in the present study. The maximum standard deviation of drop diameter is found to be 0.04 mm. In this paper, the Weber numbers of drops range from 5 to 630. Considering the uncertainty of drop size and impact velocity, the error of Weber numbers is estimated to be less than 0.2. Each experimental point was performed several times (3 times as a minimum) to test the repeatability. 3. Results and discussion According to many investigations [1,15], the drop impact phenomena on liquid pool are divided into four main categories: Floating, bouncing, coalescence and splashing. When the droplet momentum is not enough to break the air film between the droplet and water surface, the floating or bouncing phenomena occur. With the further increase of Weber number, the coalescence occurs accompanied by the creation of a crater without breakup of the fluid or generation of secondary droplets. When the Weber number becomes large enough, the splashing appears, which can be subdivided into crown splashing, jet splashing and canopy bubble that crown close above the cavity [1]. A sketch of the outcomes resulting from the collision of a drop with the liquid surface is shown in Fig. 2, and the outcomes are described in the following section. First, for very low Weber number impact the floating and bouncing are described; secondly, the analysis of coalescence and splashing is presented; finally, the transition boundary of a regime map is discussed. 3.1. Floating and bouncing A few cases of droplets bouncing and floating upon a restricted liquid surface were observed in the experiment. When the Weber number is small enough, the droplet floats on the liquid surface. For the bouncing case, after several times of rebounds on the gas–liquid interface, the drop also floats on it, sometimes lasting for seconds before coalescence with the bulk liquid. In the paper, we focus more on the bouncing phenomenon.
Fig. 2. Phenomena of drop impact on a restricted liquid surface.
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(a)
(b)
Fig. 3. Bouncing sequence of a drop (D = 2.64 mm, We = 5.29) impact on the liquid surface in tubes of different inner diameter, (a) Dt = 8 mm Dt ¼ 3:03 , (b) Dt = 26 mm Dt ¼ 9:85 .
Fig. 3 shows the time-elapsed images of the impact of a water drop (D = 2.64 mm, We = 5.29) onto the restricted liquid surface in tubes. The inner diameters of tubes are 8 mm and 26 mm respectively. These images show that the droplet bounces on the liquid surface and produces waves. During the first several milliseconds of the impact, a crater can be seen, and the waves are generated. The waves propagate from the impact point, and reflect when they reach the wall. When the reflected waves from the walls arrive at the impact point, it means that a portion of impact energy stored in waves returns to the impact area interacting with the bouncing droplet at the moment. During drop collision with liquid surfaces, the kinetic energy of the drop is fractionally converted to restorable energy supplying
the motion of the drop away from the surface, and is mostly lost due to wave propagation and viscosity dissipation [5]. In order to measure the bouncing energy, a restitution coefficient is defined as e = V0 /V, where V0 is the take-off speed derived by (2gH0 gD)1/2, where H0 is the maximum bouncing height of the drop centroid. Jayaratne and Mason [16] deduced from their experiments that about 95% of kinetic energy was lost for a normal impact of drop (diameter 120–400 lm) on a broad liquid surface, rebound with an effective coefficient of restitution of about 0.2. Furthermore, with the increase of drop size, the coefficient of restitution decreases for the increase of energy loss during drop deformation [5]. Fig. 4 shows the effect of surrounding wall on the coefficient of restitution of drop bounce (D = 2.64 mm,
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50 40
0.4
30 0.2
20
Time after impact (ms)
0.6
The restitution coefficient e
60
e Tb Tw
10 0.0 2
4
6
8
10
Dt* Fig. 4. Effect of surrounding wall on the coefficient of restitution e, bounce time Tb, and converging time of the first wave Tw (We = 5.29).
We = 5.29). In our experiments, the restitution coefficient e of the drop impact on the target liquid surface Dt ¼ 2:27 is over 0.45 at the Weber number 5.29, which is at least 4 times than that for drop impact on the liquid surface held in a larger tubes Dt ¼ 9:85 . It is noticeable that when the distance from surrounding walls to impact point is over 6 times of drop radius, after a sharp descent the restitution coefficient e shows stable and is close to the experimental results of drop bouncing on a broad liquid surface [5]. Considering the sharp descent of restitution coefficient e in Fig. 4, one possible physical explanation is the wave effect. After the impact, surface waves produced by the drop impact propagate away from the impact point, until they are reflected back by the tube wall, as shown in Fig. 3. If the reflected waves reach the impact point before the drop rebounces from the liquid surface, the energy stored in the wave will give the drop a higher upward velocity. Therefore the condition for a higher restitution coefficient e should be Tb > Tw, where Tb denotes the time when the bouncing drop leaves the surface and Tw denotes the time when the first reflected wave converges. Tw can be evaluated as Dt/Vw, where Vw is the velocity of the first wave front, which can be measured according to the sequential pictures captured by high speed camera. The
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values of Tb and Tw with different tube diameters are shown in Fig. 4. When Dt is over 4.75, the value of Tw increases to outstrip the valve of Tb. It means the energy stored in reflected waves cannot be timely fed back to the drops to enhancing the bouncing behavior, which is represented by a obvious sudden decrease of the restitution coefficient e for the tube size Dt over 4.54, as shown in Fig. 4. 3.2. Coalescence and splashing Fig. 5 shows the time-elapsed images of the impact of a water drop (D = 2.64, We = 12.5) onto the liquid surface in the tube Dt ¼ 6:44 . These images show that the drop coalesces with the liquid and produces a crater. No jet and secondary droplets are produced during and after impact. As the droplet merges in the target liquid surface, a crater forms and wave is generated. Surface waves expands outward at first, and then is reflected by the wall, concentrating toward the impact point, making the crater bottom rough and ‘‘striped’’ (Fig. 5, 24–38 ms). It is noticeable the second crater occurs after the first one produced by drop impact (Fig. 5, 72 ms). According to our observation, the second crater is always shallower than the first one impacted by the drop. Fig. 6a, shows the sequence images of the impact of a water droplet with the Weber number of 115 onto the liquid surface in the tube Dt ¼ 4:54 . The impact exhibits a different behavior to that shown in the previous sequence of images (Fig. 4) due to the increasing impact velocity. A crater with a higher depth is formed at 13 ms, which then collapses and develops into a jet without bubble entrapment. The jet reaches a maximum height at 50 ms, breaking up and producing one droplet, and then slumps downward. The slumping jet impacts the liquid surface, forming a crater again, which expands to its highest depth at 76 ms. For the first crater generated by drop impact, the top edge of crater expands from the impact point until reaching the tube wall. However, for the second crater almost the whole liquid surface descends except that near the tube wall. The reflected surface wave can be easily observed moving along the crater surface, concentrating toward the crater bottom (Fig. 6a, 66–76 ms). When the bottom of the crater becomes cone shape, a tiny bubble pinches off the bottom of crater due to the focusing reflected wave.
Fig. 5. Coalescence sequence of a drop (D = 2.64 mm, We = 12.5) impact on the liquid surface in the tube of Dt = 17 mm Dt ¼ 6:44 .
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(a)
(b)
Fig. 6. Outcomes of a drop (D = 2.64 mm, We = 115) impact onto the liquid surface in tubes of different inner diameter or broad liquid surface, (a) Dt = 12 mm Dt ¼ 4:54 , (b) Dt = 17 mm Dt ¼ 6:44 , (c) broad surface.
Comparing with primary bubble entrapment, the bubble size in Fig. 6a is similar, but the time of its appearance is delayed to be after the collapse of second crater. This special phenomenon of bubble entrapment was not reported in previous literatures of drop
impact on liquid surface. Primary bubble entrainment is believed to be caused by capillary waves converging along the cavity wall, whose timing has a delicate balance with the rebounding of the cavity bottom [17,18]. In the case of bubble entrapment in
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(c)
Fig. 6 (continued)
1.0
0.8
Dr (mm)
Fig. 6a, called the delayed bubble entrapment, the wave can be found, while the bubble appears just together with the contracting of cavity bottom (Fig. 6a, 76–83 ms). Therefore, the formation mechanism of delayed bubble is similar to primary bubble. However, delayed bubble entrapment also has some special features. There is no high-speed jet observed after the delayed bubble entrapment, while primary bubble entrapment always appears together with one. This absence implies that the converging of surface wave, which is perhaps the reflected wave from the wall, is weaker at cavity bottom. The appearance of delayed bubble is sensitive to the tube diam eter Dt , only observed with tube diameter of 12 mm Dt ¼ 4:54 in the experiments. Fig. 6b shows the behavior of drop impacting on the liquid surface in the tube Dt ¼ 6:44 with the same Weber number as Fig. 6a. After the concentration of the surface wave, the phenomenon of high-speed jet break appears (Fig. 6b, 93 ms) instead of bubble entrapment (Fig. 6a, 83 ms). The case of broad liquid surface is also given in Fig. 6c for comparison, where no phenomenon is observed after the first jet break. Fig. 7 shows how the diameter Dr of delayed bubbles varies with the impact Weber number of drops. At the initial stage the bubble size increases with the impact Weber number. When the impact Weber number of drop is over 130, the data show a decline trend. Fig. 8 shows time elapsed images of the impact of a drop with the Weber number of 267 onto the liquid surface in the tube Dt ¼ 4:54 . With the increase of Weber number, a very thin crown rises around the impact point during an early stage of the impact (Fig. 8, 1 ms). Small droplets are ejected from the top edge of the crown and splash to the tube wall. At 29 ms, a bubble is formed during the cavity collapses, which is a primary bubble entrapment. Then a jet rises from the center of the cavity. After that the second crater develops and collapses, but there is no occurrence of both bubble (Fig. 6a, 83 ms) and jet (Fig. 6b, 93 ms).
0.6
0.4
0.2
0.0
80
100
120
140
160
180
200
220
We Fig. 7. Sizes of the delayed bubbles (Dt = 12 mm, Dt ¼ 4:54).
Fig. 9a shows time elapsed images of a drop of We = 490 impact on the liquid surface in the tube Dt ¼ 4:54 . Unlike the previous two cases (Figs. 6a and 8), an obvious crown rises around the impact point. The crater looks more like a hemisphere during its expansion compared to those in Figs. 6a and 8. At 16 ms, it almost occupied the whole tube in radial direction. At the same time, the expansion of the impact crater causes a continual rise of liquid surface in the tube. Finally, the rising crown collapses toward impact point and closes above the cavity, forming a canopy bubble. Its formation mechanism is different from the bubbles formed in Figs. 6a and 8, which are both due to the pinch-off of the cavity, while the canopy bubble is formed by the crown collapsing inward. As shown in Fig. 9b, no canopy forms under the same condition
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Fig. 8. Crown splash sequence of a drop (D = 2.64 mm, We = 267) onto the liquid surface in tubes, Dt = 12 mm Dt ¼ 4:54 .
(D = 2.64 mm, We = 490) if the liquid surface is not restricted. The canopy phenomenon is seldom observed during drop impact on a broad liquid surface, which happens only for the drops close to the terminal velocity [19,20]. But it can be observed frequently for the drop impact on the liquid surface in tubes, especially in smaller tubes. An explanation can be based on the restricting effect of the wall. The wall is a radial restriction to the cavity, so it makes the radial expansion of both the cavity and the crown stop soon. At the same time, because of the expansion of cavity the liquid near tube wall is squeezed upward, sending more liquid into the crown. The two effects speed up the crown to collapse inward, favoring the occurrence of canopy bubble.
3.3. Transition boundaries of regimes The outcomes of drop impact on liquid surfaces have been mapped by many researchers based on most relevant non-dimensional parameters or the combination of them. In the paper, the impact outcomes have been compared with those of Liow [21], Huang and Zhang [22], and Okawa et al. [23] which show the transition between different boundaries for a normal impact. Liow [21] suggested that the transitions between bounce and coalescence should occur at We = 8. Huang and Zhang [22] suggested that the transitions between jet formation and coalescence should occur at K0 = 28 and that the transition between jet formation and splashing occurs at K0 = 70. Okawa et al. [23] suggested that the splashing limit occurs at K = 2100.
The different impact behaviors are presented in Fig. 10 according to the impact Weber number and tube diameter. An alternative representation using K0 and K is shown in Figs. 11 and 12. The notation of infinity represents cases of drops impacting on broad liquid surface, whose results are similar to large tubes Dt ¼ 9:85 . The We Dt map can be divided into four regions: bounce, coalescence/jet, splash and canopy, as shown in Fig. 10. Generally speaking, canopy occurs in small tubes with high Weber numbers, while the other three kinds of outcomes appear in order when the Weber number increases. Fig. 10 shows that the Weber number boundaries of the bounce, coalescence/jet and splash regions are independent from Dt . The explanation could be that the deviation of these three regions is determined by a rapid process after the impact. The tube wall makes little effect on the early stages of the impacting process, so the kinetic energy of the drop is the major factor to distinguish bounce, coalescence and splash. On the other hand, the value of Dt does play an important role in the development of the cavity forming after the impact. That is the reason of the complex outcomes inside the coalescence/jet region, where the formation of jet and the following phenomena are very dependent on the dynamics of the cavity. According to our experimental results (Fig. 10), coalescence occurs at a low Weber number for the impact on liquid surfaces in tubes of five different diameters. By comparing the impact outcomes with Liow’s thresholds [21], the coalescence threshold seems to fit with his results (We = 8). As shown in Fig. 11, Huang and Zhang [22] suggested that the transitions between coalescence and jet formation for drop impact
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(a)
(b)
Fig. 9. Sequence of a drop (D = 2.64 mm, We = 490) impact onto a) the liquid surface in the tube of Dt = 12 mm Dt ¼ 4:54 , b) broad liquid surface.
on the broad liquid surface should occur at K0 = 28. For the case of drop impact on restricted liquid surface in tubes, as shown in Fig. 11, the transition threshold of K0 increases as a function of the tube diameter from Dt ¼ 3:03 to 6:44. Except for the smallest tube size Dt ¼ 3:03 , all the critical value for coalescence to jet
formation is above the results suggested by Huang and Zhang. Moreover, the tube wall gives birth to a special phenomenon of delayed bubble entrapment only appearing in the tube of Dt ¼ 6:44, whose region is below the limit of crown splash and coincidence with the phenomenon of jet break at the first impact.
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Fig. 10. Distribution of the impact regimes obtained in this work on a We Dt map.
Fig. 11. Distribution of the impact regimes obtained in this work on a K 0 Dt map.
Fig. 12. Distribution of the impact regimes obtained in this work on a K Dt map.
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As the impact Weber number increases further than the region of jet break, the crown splashing occurs. As shown in Fig. 10, for larger tubes Dt ¼ 4:54; 6:44 and 9:85 , the crown splashing threshold is around We = 225 for drops with diameter of 2.64 mm, which is independent of the distance from surrounding walls to the impact point. In the smaller tubes Dt ¼ 2:27 and 3:03 , the phenomenon of crown splashing is not observed. As shown in Fig. 11, splashing appears around the line of K0 = 70, fitting well with the results of Huang and Zhang [22]. Okawa et al. [23] suggested K = 2100 as a threshold for splashing. In Fig. 12, our experimental results shows that splashing occurs around K = 2600, higher than the line suggested by Okawa et al. The canopy phenomenon is seldom observed during drop impact on a broad liquid surface. However because of the restricted effect of surrounding walls, the required velocities for the occurrence of canopy decrease sharply with the reduction of the tube size. As shown in Fig. 10, the critical impact Weber number of canopy is only 192 for the drop impact on the liquid surface in the tube of inner diameter 8 mm Dt ¼ 3:03 , but is out of regulating range of our experimental setup (the maximum of impact Weber number = 630) for the case of the drop impact on the li quid surface in the tubes of inner diameter 17 mm Dt ¼ 6:44 and 26 mm Dt ¼ 9:85 . With the present experimental results, the lower limit of the canopy region is estimated to be We ¼ 173Dt 321:8 .
4. Conclusions An experimental study was conducted for water droplet impact on restricted liquid surfaces held in tubes. The droplet impact Weber number was varied between 5 and 630, the tube diameter was changed between 6 mm and 26 mm. By analyzing images of the drop impact, the behavior of the impact process for the range of conditions studied was extracted. In addition, information relating to the coefficient of restitution for drop bounce and the size of delayed bubble entrapment was discussed. The critical Weber numbers for the coalescence to crown splash seem independent of the distance of surrounding walls to impact point under the range of studied here. However, decreasing the distance causes difference in impact outcome, especially for the canopy bubble formation, whose critical velocity decrease sharply to a value easier to reach. Moreover, decreasing distance can reduce the travelling time of the reflected wave, making drop bounce higher. It is interesting that, within a certain distance range, the second crater is observed, perhaps followed by delayed bubble entrapment or jet formation. The impact Weber number of the drop also appears to influence the size of the delayed bubble entrapped.
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Acknowledgments This work is supported by the National Natural Science Foundation for Excellent Youth Scholars of China (No. 51222501), the Science Fund for Creative Research Groups of the National Natural Science Foundation of China (No. 51221004). References [1] M. Rein, Phenomena of liquid drop impact on solid and liquid surfaces, Fluid Dyn. Res. 12 (1993) 61–93. [2] A.L. Yarin, Drop impact dynamics: splashing, spreading, receding, bouncing, Annu. Rev. Fluid Mech. 38 (2006) 159–192. [3] M. Hsiao, S. Lichter, L.G. Quintero, The critical Weber number for vortex and jet formation for drops impinging on a liquid pool, Phys. Fluids 31 (1988) 3560– 3562. [4] Q. Deng, A.V. Anilkumar, T.G. Wang, The role of viscosity and surface tension in bubble entrapment during drop impact onto a deep liquid pool, J. Fluid Mech. 578 (2007) 119–138. [5] J. Zou, P.F. Wang, T.R. Zhang, X. Fu, X.D. Ruan, Experimental study of a drop bouncing on a liquid surface, Phys. Fluids 23 (2011) 044101. [6] J. Shin, T.A. McMahon, The tuning of a splash, Phys. Fluids A 2 (1990) 1312– 1317. [7] A.B. Wang, C.C. Chen, Splashing impact of a single drop onto very thin liquid films, Phys. Fluids 12 (2000) 2155–2158. [8] G.E. Cossali, M. Marengo, A. Coghe, S. Zhdanow, The role of time in single drop splash on thin film, Exp. Fluids 36 (2004) 888–900. [9] S. Mukherjee, J. Abraham, Crown behavior in drop impact on wet walls, Phys. Fluids 19 (2007) 052103. [10] J. Zou, C. Ji, B.G. Yuan, Y.L. Ren, X.D. Ruan, X. Fu, Large bubble entrapment during drop impacts on a restricted liquid surface, Phys. Fluids 24 (2012) 057101. [11] V. Mironov, T. Boland, T. Trusk, G. Forgacs, R.R. Markwald, Organ printing: computer-aided jet-based 3D tissue engineering, Trends Biotechnol. 21 (2003) 157–161. [12] C.M. Weickgenannt, Y.Y. Zhang, S. Sinha-Ray, I.V. Roisman, T. GambaryanRoisman, C. Tropea, A.L. Yarin, Inverse-Leidenfrost phenomenon on nanofiber mats on hot surfaces, Phys. Rev. E 83 (2011) 036310. [13] A.N. Lembach, H.B. Tan, I.V. Roisman, T. Gambaryan-Roisman, Y.Y. Zhang, C. Tropea, A.L. Yarin, Drop impact, spreading, splashing, and penetration into electrospun nanofiber mats, Langmuir 26 (2010) 9516–9523. [14] S. Sinha-Ray, Y. Zhang, A.L. Yarin, Thorny devil nanotextured fibers: the way to cooling rates on the order of 1 kW/cm2, Langmuir 27 (2011) 215–226. [15] S.K. Alghoul, C.N. Eastwick, D.B. Hann, Normal droplet impact on horizontal moving films: an investigation of impact behavior and regimes, Exp. Fluids 50 (2011) 1305–1316. [16] O.W. Jayaratne, B.J. Mason, The coalescence and bouncing of water drops at an air/water interface, Proc. R. Soc. Lond. A 280 (1964) 545–565. [17] H.C. Pumphrey, P.A. Elmore, The entrainment of bubbles by drop impacts, J. Fluid Mech. 220 (1990) 539–567. [18] H.N. Oguz, A. Prosperetti, Bubble entrainment by the impact of drops on liquid surfaces, J. Fluid Mech. 219 (1990) 143–179. [19] G.J. Franz, Splashes as sources of sound in liquids, J. Acoust. Soc. Am. 31 (1959) 1080–1096. [20] O.G. Engel, Crater depth in fluid impacts, J. Appl. Phys. 37 (1966) 1798–1808. [21] J.L. Liow, Splash formation by spherical drops, J. Fluid Mech. 427 (2001) 73– 105. [22] Q. Huang, H. Zhang, A study of different fluid droplets impacting on a liquid film, Pet. Sci. 5 (2008) 62–66. [23] T. Okawa, T. Shiraishi, T. Mori, Production of secondary drops during the single water drop impact onto a plane water surface, Exp. Fluids 41 (2006) 965–974.