1. Department of Energy, Environmental and Chemical Engineering, Washington University in St. Louis, MO 63130, USA 2. State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Chengdu University of Technology, Chengdu 610059, Sichuan,
China 3. Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education, Institute of Nuclear and New Energy Technology,
Tsinghua University, Beijing 100084, China † Huang Zhang and Jianxin Li contributed equally to this work. Abstract
Experiment study of a droplet impacting on a static hemispherical liquid film was conducted. The static hemispherical liquid film was formed by a first droplet impacting on a dry solid surface, and the diameter, impact velocity, and liquid properties of the second droplet were the
same with the first one. A high-speed camera was used to capture the deformation process of the impacting droplet at a shooting speed of 4000 frames per second. The effects of droplet Weber number and Reynolds number on the spread factor and flatness factor were analyzed
quantitatively. The result shows that as increasing of droplet Weber number, the phenomena of spread, formation of liquid crown, and splashing occurred subsequently after the droplet impacted on the liquid film. The maximum spread factor of the liquid film after droplet
impacting on the static hemispherical liquid film is higher comparing to the case of droplet impacting on the dry solid surface under the same impacting condition. Further, with the increase of droplet Weber number, the maximum spread factor of the liquid film increases. With
the decrease of droplet Reynolds number, the maximum spread factor of the liquid film decreases and formation of the liquid crown is inhabited.
The phenomena of drop impingement extensively exist in daily life and industrial applications, such as coffee ring, rain drops, fuel droplets inside of an internal combustion engine, inkjet printing, and spray cooling (Liang and Mudawar, 2016). Regarding to the nuclear energy engineering, the droplet–wall impact phenomenon plays a critical role in the two-phase flows in moisture separators (Green and Hetsroni, 1995; Li et al., 2019; Shen et al., 2019). The phenomenon of droplet–wall impact is affected by many factors, like liquid properties, surface properties, environmental factors (Yarin, 2006). Due to the complexity of this phenomenon, the underlying mechanism is still attracting the interest of many researchers (Josserand and Thoroddsen, 2016).
The research on the droplet–wall impaction phenomenon
has been more than 100 years since Worthington’s first study on the impact of liquid film on the wall was published in 1876 (Worthington, 1877). With the development of high-speed camera technology and the related experimental techniques, the understanding of this phenomenon has improved a lot (Thoroddsen et al., 2008). Depending on the conditions of the initial falling droplet, the outcomes of the impaction result in many ways. The impaction of a droplet on a dry surface is classified into different categories, which are bounce, spread, crown-formation, and splash (Rioboo et al., 2001). For the case that a single droplet impacts the dry wall, both the physical properties of the droplet and the wall (roughness, wettability, etc.) have obvious influence on the impaction process and outcome. Šikalo et al. (2002) found that when the Weber number and Reynolds number of the droplet are small, the wettability of the wall has a great influence on the droplet spreading behavior through their experiment. As
eD equivalence diameter of a droplet fD diameter of a liquid film hD horizontal diameter of a droplet vD vertical diameter of a droplet fH height of a liquid film
Re Reynolds number of a droplet t real time T non-dimensional characteristic time
0V impacting velocity of a droplet
We Webber number of a droplet β spreading factor
maxβ maximum spreading factor δ flatness factor
maxδ maximum flatness factor ρ droplet/liquid density σ droplet/liquid surface tension coefficient μ droplet/liquid viscosity
the droplet Weber number and Reynolds number increase, the influence on the spreading of the droplet caused by the surface wettability is reduced. As the hydrophobicity of the wall increases, the droplets can obtain higher surface energy during the spreading process, thus achieving a larger spreading diameter. Vander Wal et al. (2006) found through experiments that the increase of droplet viscosity promotes the generation of splash when the droplet falls on a dry surface, and the increase of droplet viscosity inhibits the generation of splash when the droplet falls on the wet wall. Bird et al. (2009) studied the problem of tangential velocity when the droplet impacts on the wall by applying a horizontal displacement to the wall surface. The experimental results show that in the presence of the impact tangential velocity, the droplet will undergo asymmetric spreading or splashing, and the tangential direction of motion Splash phenomenon will be suppressed. Tsai et al. (2009) found that when a droplet impacts on a superhydrophobic surface with mirco and nano-structures, in particular, phenomena like bounce and jet appear. Antonini et al. (2012) found that, as 20 < Weber number < 200, the surface wettability has significant effect on the maximum spreading diameter of impaction droplet and the characteristic spreading time. Aboud and Kiezig (2015) explored the phenomenon that droplet impacts on different kind of wall surfaces with different wettability under high Webber number, and found that for highly hydrophobic walls, the droplets have a lower critical value for splashing. On an inclined and smooth wall, the splash is asymmetrical, and when the wall has a microscopic appearance, even if the wall is inclined, the splash still exhibits high symmetry. Tang et al. (2017) investigated the effect of wall roughness on the dynamic behavior of the droplet impacting on the dry solid wall by high-speed camera. The experimental results show that the droplet diameter decreases slightly with the increase of wall roughness. It is more prone to splashing, and for droplets with low surface tension, the shrinkage after spreading is not obvious.
At present, the experiment on the impact of droplets on the wall surface is mainly directed to the phenomenon that
a single droplet falls on the dry or wet wall. But in the practical industrial process, the phenomenon that a single droplet impacts on the wall hardly occurs. Otherwise, the impingement of multiple droplets continuously impacting on the wall often encounters. For example, in the moisture separator of the secondary circuit of the nuclear power plant, the surface of the inner wall of the moisture separator is initially under dry state. As the nuclear power plant runs, small droplets within the steam flow continuously impact on the wall surface, so that the wall gradually becomes forming a liquid film (Green and Hetsroni, 1995; Li et al., 2019). When a first droplet impacts on the wall surface of moisture separator, it may stick on the wall to form a hemispherical droplet. Then the second droplet may impact on this hemispherical one. Thus, studying the mechanism of a droplet impacting on a static hemispherical liquid film is the primary step to learn the whole process that multi-droplets impacts on the wall continuously. Fujimoto et al. (2001) first carried out an experiment in which a single droplet impacts on a stationary hemispherical liquid film, and the related modeling methods were developed to compare the simulation results with the experimental results. Liang et al. (2014) conducted an experiment on the impact of a single droplet on a droplet placed statically on a spherical wall, and studied the effects of the number of droplets, droplet Reynolds number, and the curvature of the wall. Further, Li et al. (2010) and Castrejón-Pita et al. (2013) investigated the collision and mixing of binary droplet, which could be considered as a droplet impacting on a liquid sphere.
To the best of our knowledge, there are few of experiment researches to study the droplet impact on a stationary hemispherical liquid film. And the factors that may influence the impaction result are seldom discussed. This work intends to investigate the droplet impact on a static liquid film, which are the transition phenomena from a single droplet impacting on the wall surface to continuous droplets impacting on the wall surface. Particularly, this work will reveal the process that the wall is initially dry and becomes wetted because of the continuous impacting droplets.
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2 Experimental setup and methods
The schematic of experimental setup is shown in Fig. 1. In general, this setup consists of two parts, droplet generation system, and image acquisition and processing system. The droplet generation system is mainly composed of a container for testing liquid, a peristaltic pump (model: Lab V1, SHENCHEN), a flat-bottomed needle, and a connecting soft tube. The image acquisition and processing system consists of a high-speed camera (model: Phantom v711, 8G memory, shooting frame rate range of 32–32000 frames/second, macro lens 100 mm), an auxiliary light source, and a computer. The light source is softened by sulfuric acid paper. The images obtained by the high-speed camera are imported into the computer for storage and post-processing.
Droplets are produced by the droplet generation system. For this system, the liquid is pushed into the needle by a peristaltic pump, and when the mass of the droplet suspended from the bottom of the flat-bottomed needle is sufficient to cause the gravity to overcome the surface tension, droplets are disengaged from the needle in a nearly spherical state. Before the start of the experiment, the first droplet is generated and struck against the dry wall surface. After it is completely static (the waiting time is larger than 30 s) to form a hemispherical liquid film, the second droplet is generated under the same conditions to let the droplet impact on the stationary hemisphere. The diameter of the droplets is varied by using needles of different diameters, the speed of which is adjusted by adjusting the height of the needle from the wall surface. The velocity and diameter of the droplets are calculated by pixel analysis of the images. The principle of pixel distance measurement is as followings: the quantitative relation between the unit pixel on the picture and the real length should be first calibrated and knowing the distance in the image to calculate real length by counting the number of pixels. The measurement error of the high-speed camera is one pixel. Due to the need to refocus the focal length of the camera after changing the experimental conditions, the corresponding relationship between the pixel and the actual
Fig. 1 Schematic of the experimental setup.
distance changes, and the corresponding error is between 0.048 and 0.060 mm. The impact velocity of the droplet, V0, is obtained by dividing the distance between the center points of the droplet in the two frames by the time interval 0.25 ms of the two frame pictures. The size of a droplet is represented by its equivalence diameter, eD , which is defined as (Stow and Hadfield, 1981):
2 1/ 3e h v( )D D D= (1)
where hD and vD are the horizontal and vertical diameter of a droplet respectively, which are shown in Fig. 2. In order to quantitatively describe the deformation process of the droplet, it is necessary to measure the diameter ( fD ) and the height ( fH ) of the liquid film formed during the droplet impact process. fD and fH are shown in Fig. 3. Spreading factor β , flatness factor δ , and non-dimensional characteristic time T, are used to describe the formation process of the liquid film. These three parameters are defined as
f
e
DβD
= (2a)
f
e
HδD
= (2b)
0
e
VT tD
= (2c)
where t means real time. Besides, droplet Webber number (We) is used to measure the ratio of droplet inertia to droplet surface tension force, and droplet Reynolds number (Re) is used to measure the ratio of droplet inertia to droplet viscous force, respectively. We and Re are defined as
2
e 0ρD VWeσ
= (3a)
e 0ρD VReμ
= (3b)
where ρ , σ , and μ are droplet density, surface tension coefficient, and viscosity, respectively.
Fig. 2 Definition of droplet horizontal diameter Dh and vertical dimeter Dv. The liquid is deionized liquid.
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Fig. 3 Definition of the spread diameter fD and height of the liquid film fH : (a) time t1, (b) time t2. The liquid is aqueous glycerin (30%) in both Figs. 3(a) and 3(b).
The solid wall surface used in the experiment is a stainless steel plate whose surface is roughened by grinding with metallographic sandpaper. The roughness of the surface is less than 1 μm. The experiment was conducted at normal pressure (1 atm) and room temperature (25 °C). The test liquid used to produce droplet is the mixture of deionized liquid and glycerin, which is shown in Table 1.
3 Results and discussion
3.1 Experimental results
In general, when a single droplet impacts the dry wall at a lower speed, the droplet is continuously compressed and deformed by the inertial force and spreads along the wall. After the droplet reaches the maximum spreading range, the liquid film formed by the droplet retracts under the effect of surface tension, and the height of the liquid film oscillates continuously, eventually forming a stable shape with a nearly hemispherical shape, at which time the total energy carried by the droplets is the lowest (Pasandideh-Fard et al., 1996). So it is seen that the kinetic energy carried by the falling droplets has a great influence on the result of the droplet– wall impaction.
Figure 4 shows a droplet of deionized water impacting on the static hemispherical liquid film under different Webber
Table 1 Properties of the testing liquid
Liquid type Liquid
density ρ (kg/m3)
Liquid surface tension coefficient σ
(N/m)
Liquid viscosity μ
(Pa·s)
Aqueous glycerin (99%) 1255 0.063 0.776
Aqueous glycerin (50%) 1131 0.067 5.0410-3
Aqueous glycerin (30%) 1080 0.072 2.4610-3
Deionized liquid 997 0.073 9.0310-4
numbers. We is changed by the modified impact velocity of the droplet. The static hemispherical liquid film is formed by droplet of the same conditions (droplet diameter, impacting velocity, and physical properties) impacting on the dry wall surface to reach an equilibrium state. The outcomes of the droplet impacting on the static hemispherical liquid film are different from the case where the droplet only impacting on the dry wall. At this time, it is more similar to the case where the droplet impacts on the thin liquid film. But as the hemispherical liquid film has small size, it is deformed on the wall surface after being impacted by the liquid droplet. As shown in Fig. 4(a), when the droplet of We = 23.26 impacts on the static hemispherical liquid film, the newly formed liquid film spreads out on the wall surface. After the droplet contacts the liquid film, they begin to fuse, compress, and deform under the effect of inertia, reaching the maximum spreading diameter at around 4 ms. Then, under the effect of the surface tension of the droplet, the height of the liquid film gradually rises, and the oscillation appears. As droplet We increases (as shown in Fig. 4(b)), the liquid in the liquid film is affected by the impacting droplet near the impact point. As the droplet impacting velocity is large and the edge of the liquid film is stationary, the momentum is discontinuous between the inner and outer layers of the liquid film. A thin layer of coronal liquid is formed between the inner and outer layers (Yarin and Weiss, 1995). Then the liquid crown collapses, and a small spread appears after the wall surface is attached, and the retraction phenomenon also occurs under the effect of the surface tension. As We continues increasing (seen in Fig. 4(c)), in addition to the formation of the liquid crown, the smaller droplets are separated at the edge of the liquid crown due to Plateau-Rayleigh instability (Rieber and Frohn, 1999), which means that a splash occurs.
Due to the influence of viscous dissipation, there is energy loss in the process of spreading and shrinking when a single droplet spreading and retracting on the wall. When the kinetic energy is dissipated and only the surface energy that maintains the equilibrium state of the liquid film is left, the liquid film stops moving (Yarin and Weiss, 1995). It is seen that the viscosity has a great influence on the spreading process of the droplet. So Re number is usually used to characterize the relative magnitude of inertial force and viscous force. The smaller the Re number is, the greater the viscous force is.
Figure 5 shows the impaction outcomes in which droplet of 30%, 50%, and 99% aqueous glycerol solutions impacts on the static hemispherical liquid film under the same impact velocity. The Re number gradually decreases as increasing viscosity from Figs. 5(a) to 5(c), and the corresponding We number is 234.56, 242.19, 268.88, respectively. It can be seen that although the Re number in Figs. 5(a) and 5(b) is different, both of them are larger than 1000, and the difference between
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these figures is not obvious, while a crown is formed in both situations first and the liquid film is then collapsed. In Fig. 5(a), since the droplet impacting point is slightly deflected, the formed liquid crown is asymmetrical and inclined toward the left side. However, compared with the case of Fig. 4(c) where Re = 7745.47, although the We number is similar, the edge of the liquid crown is smoother in this figure and there is no instability due to the increase of viscosity. Besides, no secondary droplets are produced. As the Re number is further reduced (Fig. 5(c)), the viscous force is in the same order of magnitude as the inertial force. At this time, after the droplet impacts on the liquid film, the droplet merges with the liquid film, and the degree of deformation is small. After the maximum spreading diameter, there is a small retraction for the liquid film.
3.2 Comparison with dry wall condition
Figure 6 shows the spreading factor and flatness factor between droplet–wall impaction and droplet–liquid film impaction. In the spreading process after the first droplet impacts the dry wall, the spreading factor ( β ) of both increases first and then decreases compared with the process after the second droplet impacts on the static hemispherical liquid film. This is because both of them retract under the effect
of surface tension after reaching the maximum spread. In contrast, the maximum spreading factor max 5.00β = achieved by the droplet impacting on the static hemispherical liquid film is larger than the case where the droplet impacts on the dry wall surface where max 3.82β = , while the non- dimensional characteristic time (T) to reach maxβ is 5.60 which is slightly behind the time T = 2.40 of a droplet impacting on the dry wall. In addition, at the end of the recording time T = 30, the spreading factor ( β ) of the droplet impacting on the static hemisphere is 3.93 which is also larger than the spreading factor 1.64β = of the droplet impinging on the dry wall surface.
As for the curve of the flattening factor ( δ ) (seen in Fig. 6(b)), there is a large difference between the dry wall and liquid film conditions in the range of 0 < T < 5. In the case of dry wall surface, δ reaches a minimum value in a short period of time, and then fluctuates in a range slightly larger than the minimum value. For the case of static hemispherical liquid film, due to the appearance of the crown liquid film, a step value appears in the process of the curve falling, and then δ of the crown collapse continues to decrease with the crown. For the case of dry wall surface, the flattening factor starts to rise at around T = 12.8, and returns to its maximum value max 0.42δ = at the time of T = 17.6. For the case of liquid film, the collapse of the liquid crown brings
Fig. 4 Deformation process after the impact of droplet with different Weber number on the static hemispherical liquid film: (a) We = 23.26, (b) We = 181.00, (c) We = 246.42. The liquid is deionized liquid in Figs. 4(a), 4(b), and 4(c).
Fig. 5 Deformation process after the impact of droplet with different Reynolds number on the static hemispherical liquid film: (a) Re = 2847.80, (b) Re = 1481.65, (c) Re = 10.09. The liquid is aqueous glycerin (30%) in Fig. 5(a), aqueous glycerin (50%) in Fig. 5(b), andaqueous glycerin (99%) in Fig. 5(c).
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Fig. 6 Comparison between the impact of a deionized water droplet on a dry surface and a static hemispherical liquid film (We = 181.00): (a) spread factor, (b) flatness factor.
about a large randomness to the change of δ , and δ fluctuates around 0.24. Until the time of T = 17.2, δ shows a similar rebound trend with the case of dry wall surface, and rises to its maximum value max 0.42δ = at the time of T = 25.5, which is delayed compared with the dry wall case, but with nonsignificant difference.
3.3 Influence of Webber number (We)
As can be seen in Section 3.1, increasing Webber number from 23.26 to 246.42 results in the phenomena of spreading with merging, crown of liquid film, crown of splash after a droplet impacting on the static hemispherical liquid film. Seeing in Fig. 7(a), the spread factors of three different We are quite different. For the case of We = 23.26, since the kinetic energy carried by the droplet is small, the maximum spreading factor ( maxβ ) equals to 2.45 (marked as ◆ black solid diamond symbol in this figure), and the time to reach
maxβ is the shortest for T = 1.46. As the increase of Webber number, the maximum spreading factor is also increased for the case of We = 181.00, max 5.17β = and We = 246.42,
max 7.31β = . In addition, the time to reach the maximum spreading factor is also delayed for We = 181.00, T = 6.51,
and when We = 246.42, T = 8.25. For the cases of We = 181.00 and 246.42, the droplet impacts on the liquid film causing a crown of liquid film, and in Fig. 7(a), the timing of the formation and collapse of the crown liquid film is marked by two ★ solid pentagram symbols. It can be seen that with the increase of Webber number, the duration of the crown film increases, and both of them reach the maximum spreading factor after the crown collapses. And the liquid film still has the kinetic energy to continue spreading after this collapse.
From Fig. 7(b) that the case of We = 23.26, since there is no crown liquid film, the time when the flattening factor first reaches the minimum value is T = 2.38, which is basically the same moment when its spreading factor reaching the maximum value. The flattening factor then decreases as the liquid film shrinks and then decreases as it spreads. For the case of We = 181.00 and 246.42, the flattening factor decreased rapidly in a very short time after the impaction in a range that T < 1. Then it rebounds due to the appearance of the crown of liquid film at T = 1.93 and T = 1.75 when δmax is 0.64 and 0.88, respectively. At this time, the crown liquid
Fig. 7 Comparison between the impact of a deionized water droplet with different Weber number on a static hemispherical liquid film: (a) spread factor, (b) flatness factor.
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film reaches its maximum height. With the collapse of the crown film, the flattening factor of liquid film oscillates continuously at a later time, but the oscillation does not have a particularly regularity with respect to the case of We = 23.26. The flattening factor at the oscillation equilibrium position of the two is close, but less than the value of the equilibrium position of We = 23.26.
3.4 Influence of Reynolds number (Re)
Figure 8 shows the spread factor and the flattening factor of the 30%, 50%, and 99% aqueous glycerin solution (Re = 2847.87, 1481.62, and 10.09) at the same impact velocity after impacting the static hemispherical liquid film with non-dimensional characteristic time (T). It can be seen from Fig. 8(a) that under the conditions of nearly equal Webber numbers, the curve of the spreading factor of Re = 2847.80 is very close to the curve of Re = 1481.65, but the former case can reach a lager maximum value. The maximum spreading factors reach by the liquid film of two cases where βmax = 4.98 and 4.60, respectively. It can be also seen that the increase of viscosity has an inhibitory effect on the spreading of the droplets after impaction and the growth of crown film. The time to reach the maximum spreading factor under Re = 2847.80 is T = 5.75 that is slightly later than that in the case of Re = 1481.65 when T = 4.29. And the crown of liquid film has collapsed for the former case while it is still in the crown for the latter case. The reason for this phenomenon may be that the viscosity is dissipated due to the increase of viscosity, so that the liquid film consumes most of the kinetic energy in the process of crown formation, and no excess energy is used after the collapse of the crown film to spread on the wall. For the case of Re = 10.06, since the droplet viscosity is much larger than that in the first two cases, the curve of the spreading factor changes with time is also different, and the maximum spreading factor βmax reaches to 2.02 at the time of T = 2.25. And the degree of deformation is not large, then the liquid film has a small retraction. In addition, the time to reach the maximum spreading factor under this condition is also the earliest one. It can be seen that the time for the liquid film to reach the maximum spreading factor is shortened due to the enhancement of the viscous dissipation.
As can be seen from Fig. 8(b), for the cases of Re = 2847.80 and 1481.65, the curves of the flattening factors ( δ ) are substantially the same except for the period from the formation to the collapse of the liquid crown. Due to the enhanced viscous effect, the kinetic energy consumed during the formation of the liquid crown is greater, so the former case can achieve a larger maximum flattening factor. After the liquid crown collapses, the flattening factors show small amplitude oscillations, but they soon become balanced. The
Fig. 8 Comparison between the impact of a droplet with different Reynolds number on a static hemispherical liquid film: (a) spread factor, (b) flatness factor.
flattening factor curve of Re = 10.06 is also quite different from the former two cases. The flattening factor does not decrease after reaching the minimum value δmin = 0.38 at T = 1.69, then it is in a state of slow recovery. Until the end of the recording time, there is still a rising trend.
4 Conclusions
In this work, an experimental study on the phenomenon that a droplet impacts on the static hemispherical liquid film that commonly occurs in practical industrial applications was carried out. The high-speed camera was used to record the droplet impact on the static hemispherical liquid film, and the pixel diameter and the liquid film height were measured by the pixel analysis technique. The experimental results show that as We and Re of the falling droplets are different, different results will occur for the static hemisphere liquid film. The difference of the deformation process after the droplet impacts on the hemispherical liquid film and the dry wall surface was also compared. Besides, the influence
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of We and Re of the droplet on the deformation process of the liquid film was quantitatively discussed.
The specific conclusions are as follows: (1) Compared with the impaction of the droplet under
the same conditions for the dry wall surface (We = 169.88, Re = 6384.82), the droplet impacts on the hemispherical liquid film causing a formation of a liquid crown. The maximum spreading factor ( maxβ ) that can be achieved has increased, and the time to reach maxβ has been delayed. Retraction still occurs after the liquid crown collapses.
(2) As increasing the Webber number (23.26 ≤ We ≤ 246.42), the droplet would appear in the order of spreading, forming a crown and splashing after impacting on the hemispherical liquid film. The maximum spreading factor ( maxβ ) that can be achieved by the liquid film and the height of the formed liquid crown increase with the increase of We. For low We, the oscillation of the flattening factor ( δ ) is stronger after the droplet impacting on the liquid film.
(3) For nearly equal Webber number (234.56 ≤ We ≤ 268.88), as decreasing Re in the range of 10.09 ≤ Re ≤ 2847.80, the formation of the liquid crown is gradually suppressed, and the maximum spreading factor ( maxβ ) that the liquid film can reach is reduced to the maximum. The spread time is advanced and the height of the liquid crown is lowered.
Acknowledgements
This work was supported by Open Fund (PLC20190602) of State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation (Chengdu University of Technology), and Natural Science Foundation of Beijing (Grant Nos. 3194054 and 3184051).
References
Aboud, D. G. K., Kietzig, A. M. 2015. Splashing threshold of oblique droplet impacts on surfaces of various wettability. Langmuir, 31: 10100–10111.
Antonini, C., Amirfazli, A., Marengo, M. 2012. Drop impact and wettability: From hydrophilic to superhydrophobic surfaces. Phys Fluids, 24: 102104.
Bird, J. C., Tsai, S. S. H., Stone, H. A. 2009. Inclined to splash: Triggering and inhibiting a splash with tangential velocity. New J Phys, 11: 063017.
Castrejón-Pita, J. R., Kubiak, K. J., Castrejón-Pita, A. A., Wilson, M. C. T., Hutchings, I. M. 2013. Mixing and internal dynamics of droplets impacting and coalescing on a solid surface. Phys Rev E, 88: 023023.
Fujimoto, H., Ogino, T., Takuda, H., Hatta, N. 2001. Collision of a droplet with a hemispherical static droplet on a solid. Int J Multiphase Flow, 27: 1227–1245.
Green, S. J., Hetsroni, G. 1995. PWR steam generators. Int J Multiphase Flow, 21: 1–97.
Josserand, C., Thoroddsen, S. T. 2016. Drop impact on a solid surface. Ann Rev Fluid Mech, 48: 365–391.
Li, J., Zhang, H., Liu, Q. 2019. Characteristics of secondary droplets produced by a single drop impacting on a static liquid film. Int J Multiphase Flow, 119: 42–55.
Li, R., Ashgriz, N., Chandra, S., Andrews, J. R., Drappel, S. 2010. Coalescence of two droplets impacting a solid surface. Exp Fluids, 48: 1025–1035.
Liang, G., Guo, Y., Shen, S. 2014. Dynamic behaviors during a single liquid drop impact on a static drop located on spheres. Exp Therm Fluid Sci, 53: 244–250.
Liang, G., Mudawar, I. 2016. Review of mass and momentum interactions during drop impact on a liquid film. Int J Heat Mass Tran, 101: 577–599.
Pasandideh-Fard, M., Qiao, Y. M., Chandra, S., Mostaghimi, J. 1996. Capillary effects during droplet impact on a solid surface. Phys Fluids, 8: 650–659.
Rieber, M., Frohn, A. 1999. A numerical study on the mechanism of splashing. Int J Heat Fluid Fl, 20: 455–461.
Rioboo, R., Tropea, C., Marengo, M. 2001. Outcomes from a drop impact on solid surfaces. Atomization Spray, 11: 12.
Shen, X., Miwa, S., Xiao, Y., Han, X., Hibiki, T. 2019. Local measurements of upward air-water two-phase flows in a vertical 6×6 rod bundle. Exp Comput Multiphase Flow, 1: 186–200.
Šikalo, Š., Marengo, M., Tropea, C., Ganić, E. 2002. Analysis of impact of droplets on horizontal surfaces. Exp Therm Fluid Sci, 25: 503–510.
Stow, C. D., Hadfield, M. G. 1981. An experimental investigation of fluid flow resulting from the impact of a water drop with an unyielding dry surface. P Roy Soc A-Math Phy, 373: 419–441.
Tang, C., Qin, M., Weng, X., Zhang, X., Zhang, P., Li, J., Huang, Z. 2017. Dynamics of droplet impact on solid surface with different roughness. Int J Multiphase Flow, 96: 56–69.
Thoroddsen, S. T., Etoh, T. G., Takehara, K. 2008. High-speed imaging of drops and bubbles. Ann Rev Fluid Mech, 40: 257–285.
Tsai, P., Pacheco, S., Pirat, C., Lefferts, L., Lohse, D. 2009. Drop impact upon micro- and nanostructured superhydrophobic surfaces. Langmuir, 25: 12293–12298.
Vander Wal, R. L.,, Berger, G. M., Mozes, S. D. 2006. The splash/ non-splash boundary upon a dry surface and thin fluid film. Exp Fluids, 40: 53–59.
Worthington, A. M. 1877. XXVIII. On the forms assumed by drops of liquids falling vertically on a horizontal plate. P R Soc London, 25, 171–178.
Yarin, A. L. 2006. DROP IMPACT DYNAMICS: Splashing, spreading, receding, bouncing…. Ann Rev Fluid Mech, 38: 159–192.
Yarin, A. L., Weiss, D. A. 1995. Impact of drops on solid surfaces: Self-similar capillary waves, and splashing as a new type of kinematic discontinuity. J Fluid Mech, 283: 141–173.
