Sage Journals: Discover world-class research

Abstract

An experimental investigation is performed into the behavior of ethanol droplets impacting on a vibrating stainless steel surface. In characterizing the impact behavior, the dimensionless kinetic energy of the droplet prior to its impact on the surface is represented by the original Weber number (We). Meanwhile, the dimensionless relative impact kinetic energy of the droplet as it impacts the vibrating surface, and thus undergoes a change in its relative impact speed, is represented by the relative Weber number (We_r). Impact experiments are performed for various values of the original Weber number We and vibration frequency f. The impact behavior in each case is classified as either post-spreading deposition or crown splashing. It is shown that for a static (non-vibrating) surface, the critical Weber number for the generation of splashing is We_c = 400. Furthermore, for a given impact speed and vibration frequency, if no splashing occurs without vibration but splashing takes place after vibration, the difference between the original Weber number (We) and the critical Weber number (We_c) is proportional to the additional impact Weber number provided by the vibrating surface, that is, (We_r − We_c). For a given relative impact speed, a higher vibration frequency ƒ results in a greater relative impact distance during splashing and a larger effective impact energy. Overall, the experimental results show that the relation between We and We_r for the generation of splashing is given as $We = (- cf / (1 - cf)) W e_{r} + (1 / (1 - cf)) W e_{c}$ , where $c = 3.45 \times 10^{- 4}$ .

Keywords

Droplet impact vibrating surface splashing deposition Weber number

Introduction

The impact of liquid droplets on a solid surface is of practical interest in many engineering and agricultural applications. According to Rein,¹ droplets impacting on a dry solid surface may exhibit three different behaviors, namely spreading, splashing, or bouncing. Lesser and Field² reported that the spreading of droplets impinging on a solid surface comprises three stages, namely (1) propagation of an internal shock immediately after impact; (2) generation of spreading lamella, during which the backside drop shape remains unchanged since the spreading speed is higher than the collision speed; and (3) drop deformation into a pancake shape. To explain the observed phenomena, many researchers assumed a velocity profile in the spreading process and derived expressions for the maximal spread diameter based on a force or energy balance.^3,4

To determine the effects of surface tension, a few experimental studies, such as Pasandideh-Fard et al.,⁵ conducted an experimental investigation into the effect of surfactant-induced surface tension on the impact behavior of water droplets on solid surfaces and found that while the surfactant had no effect on the shape of the impacted droplet, it increased the maximum spreading diameter and reduced the bouncing height. Zhang and Basaran⁶ showed that an accumulation of surfactants on the impacted solid surface reduced the surface tension and increased the spreading diameter. However, an uneven surfactant distribution increased the Marangoni stress, and hence suppressed the droplet spread.

In addition to the liquid properties and droplet kinematics, the physical characteristics of the target surface, for example, its wettability, roughness, temperature, and inclination, also have a significant effect on the impact outcome. Fukai et al.⁷ quantified the effect of the surface wettability on the ability of a liquid to spread in a known gaseous surrounding by means of static contact angle measurements. Ford and Furmidge⁸ found that a reduced static contact angle resulted in a greater spreading diameter. Karl et al.⁹ examined the spreading of liquid drops from the perspectives of dynamic energy, surface energy, and potential energy conservation, respectively. Mao et al.¹⁰ used the static contact angle and maximum spreading diameter to predict the critical value of bouncing and verified the predicted value by means of extensive experimental data.

In the splashing of droplets on a dry surface, the liquid drops first form a thin corona ring. Fluctuations then develop around the thin film, and finally surface tension effects lead to fragmentation. The literature contains many investigations into the effects of the drop size, drop density, surface tension, drop viscosity, and impact velocity on the splashing phenomenon, such as Thoroddsen and Sakakibara,¹¹ Bhola and Chandra,¹² Bussmann et al.,¹³ and Mehdizadeh et al.¹⁴ The authors in Mundo et al.,¹⁵ Cossali et al.,¹⁶ and Range and Feuillebois¹⁷ investigated the effects of surface roughness on the splashing behavior of impacting droplets and proposed a critical value for splashing/deposition of K′ = WeOh^−0.4, where We is the Weber number and Oh is the Ohnesorge number (defined as Oh = We^1/2Re, in which Re is the Reynolds number). It was shown that K′ varied as a function of the mean roughness amplitude. Stow and Hadfield¹⁸ investigated the asymmetric spreading of droplet films formed by droplet impact on an oblique smooth surface. Similarly, Šikalo et al.¹⁹ studied the bouncing and deposition phenomena for droplets impinging on a smooth sloping surface. Both studies showed that when droplets impact on an inclined surface, gravitational effects cause splashing to occur around the lower side of the droplet along the inclined plane when the impact kinetic energy exceeds a certain critical value. Kang and Lee²⁰ investigated the dynamic behavior of water drops impacting on dry surfaces with different inclination angles and temperatures. Bussmann et al.²¹ Reznik and Yarin,²² and Lunkad et al.²³ conducted numerical simulations to investigate the capillarity effect for droplets impacting on a dry horizontal surface and the gravitational effect for droplets impacting on a dry inclined surface. Moreover, the authors in Hanchak et al.²⁴ Capizzano and Iuliano,²⁵ and Dyment²⁶ employed different numerical methodologies to simulate the behavior of water droplets impinging on different surfaces. Xu et al.²⁷ investigated the corona splash behavior for liquid droplets impacting on a smooth dry substrate. The results showed that splashing can be completely suppressed by decreasing the pressure of the surrounding gas.

In the studies above, the authors considered single liquid droplets impacting a static horizontal or inclined solid surface. To investigate impact of droplet on high-velocity moving surface (stimulation of water drop’s impacting on turbine blade), Povarov et al.^28,29 utilized wheel-and-jet technology to investigate the impact behavior of a string of drops impacting vertically on a high-speed rotating disc. It was shown that droplet spreading occurred when the air flow above the disc had the form of a laminar boundary layer. Furthermore, in the event of bouncing, the droplets acquired a rotational speed as a result of the dynamic effect of the surrounding air. However, when the disc rotated at a very high speed, the droplets could not impinge directly on the surface of the disc. Chen and Wang³⁰ used three parameters to analyze the spreading adhesion/bouncing behavior of water droplets impacting on a solid rotating surface, namely (1) the peripheral velocity (different centrifugal acceleration), (2) a positive Webber number for positive impacts of the droplet on the surface, and (3) a Webber number associated with the relative speed of the droplet in a direction tangential to the circumferential surface. Courbin et al.³¹ examined the behavior of milk drops impacting on the center of a rotating disc and found that the Weber number associated with splashing reduced as the centrifugal force increased. Zen et al.³² investigated the influence of the gravitational effects induced by different inclination angles and surface movement velocities on the impact behavior of ethyl alcohol drops with diameters ranging from 2.32 to 2.58 mm on inclined rotating silicon wafer discs. The results showed that the critical value of the impact Weber number for the occurrence of side-splash or splash-around of the ethyl drops was approximately W_en = 120. Moreover, it was shown that while gravitational effects contributed to an instability of the downward flow of the liquid film, they enhanced the stability of the upward flow. Therefore, as the downward movement speed of the inclined surface was increased, the downward splashing behavior of the droplet changed to deposition behavior, while the upward deposition behavior changed to upward splashing. In addition, it was shown that given a sufficiently large inclination angle, the deposition area could be enlarged through an appropriate control of the surface movement speed.

The deposition/splashing behavior of droplets impacting on a vibrating solid surface is of practical interest in many engineering applications, for example, the wall vibration of engine fuel systems in operation, secondary droplet generation in fuel atomization systems or spray dyers, spray coating and cooling in vibration environments, and so on. However, the literature contains very few investigations into the related phenomena. Brothier et al.³³ investigated the behaviors of three different types of droplets (water, polyvinyl alcohol/water solution, and uranyl nitrate, diameter: 2–5 mm in every case) impacting at velocities of up to 1.7 m/s on a vibrating hot plate with a temperature of 260°C, a vibration frequency of 0–1 kHz, and an amplitude of several μm to 0.5 cm. No corona splashing was observed under the considered impact conditions. However, fingers were formed on the anterior edge of the spreading droplet as a result of the air film between the droplet and the surface and the vibration of the high-temperature plate.

The results presented in Brothier et al.³³ suggest that a positive impact velocity provides momentum for an outward spreading of the film. At the moment of impact, an upward movement of the vibrating surface provides not only a higher positive impact velocity, but also a stress which promotes an upward motion of the anterior edge of the droplet film. By contrast, a downward motion of the plate inhibits the upward movement of the anterior edge of the liquid film, and thus results in a greater thickness of the anterior edge due to inertial forces. A sufficiently large and continuous vibrating disturbance generates fingers on the anterior edge of the droplet film and leads to secondary droplet splashing. Consequently, the vibration frequency (i.e. the action time of the upward–downward motion) and the vibration amplitude (i.e. the speed of the upward–downward movement) both influence the generation of deposition/splashing after impact.

The present study explores the deposition/splashing phenomena for droplets impacting on a vibrating surface with various vibration frequencies. In order to eliminate the effects of surface roughness on the droplet impact behavior, the impact tests were performed using stainless steel reeds polished to a final surface finish of 100 nm. In addition, ethanol was used as the working fluid due to its low surface tension (approximately 0.022 N/m), and hence increased propensity to produce splashing. The experimental results are used to determine a predictive equation for the splashing phenomenon as a function of the vibration frequency. The predictive equation provides a useful practical tool for regulating the vibration frequency in such a way as to control the formation of deposition/splashing and secondary droplets during droplet impacts.

Experimental system

Figure 1 presents a schematic illustration of the experimental setup. As shown, the major items of equipment include a droplet-generating system, a position-adjustment system, an image acquisition system, and a vibrating surface system. The details of each system are described in the following.

Figure 1.

Schematic illustration of experimental setup.

Droplet-generating system

The droplet-generating system consisted of a syringe pump designed to provide the working fluid (ethanol) at a constant flow rate of 1 mL/min and a droplet nozzle in the form of a subcutaneous hypodermic needle tube with a diameter of approximately 0.4 mm. The ethanol drop ejected from the syringe pump accumulated at the tip of the nozzle and then fell freely under its own weight until impact on the vibrating surface. Changes in the needle tube diameter and syringe pump flow rate result in droplets of a different diameter. In the present study, the droplets had a mean measured diameter of approximately 1.9 mm. To avoid the possibility of contamination effects (thereby resulting in a change in the droplet surface tension), each impact test was performed using a new bottle of ethanol.

Position-adjustment system

The position-adjustment system comprised two 3D mobile platforms supporting the droplet-generating system and vibrating surface system, respectively. In performing the experiments, the vertical distance between the droplet nozzle and the vibrating surface was adjusted in order to change the droplet impact velocity (i.e. the Weber number, We), while the horizontal position of the droplet-generating system relative to the vibrating surface was adjusted in order to change the droplet impact point.

Image acquisition system

Experimental images were captured using a Phantom V9.1 high-speed camera (1632 × 1200 pixels at 1016 frames/s) with a maximum frame speed of 153,846 frame/s and a photosensitivity of 2400/ Mono (ISO-12232 Standard). The images were captured with a minimum exposure time of 2 μs using a 500 W halogen lamp as the illumination source. The shade of the lamp was attached to a 3D mobile platform along with a vibrating reed so as to facilitate localization. During the experiments, the halogen lamp was turned on only during image shooting in order to prevent overheating of the reed.

Vibrating surface system

The vibrating surface system had the form of a stainless steel reed with dimensions of 6 cm × 2 cm × 0.1 cm (length × width × thickness). As described above, the reed was polished to a final surface finish of 100 nm in order to eliminate surface roughness effects. The ends of the reed were attached to piezoelectric characteristic plates by means of basal copper plates and screw fasteners. In performing the impact tests, the piezoelectric plates were driven by square-wave voltage signals with different amplitudes (0–12 V) and frequencies (0–2500 Hz). The waves were produced by a TG1010A wave generator and then passed through a PZD350 voltage amplifier. Figure 2(a) shows the sketch of vibrating surface positions. Figure 2(b) shows the displacement of the vibrating surface over time given a driving frequency of 2000 Hz. Note that the displacement of the vibrating surface was determined from experimental images captured at a speed of 10,000 frames/s.

Figure 2.

(a) Sketch of vibrating surface position and (b) variation of vibrating surface position over time (t).

Measurement method and physical model

Surface vibration velocity (V_s)

The droplet impact tests were performed at vibrating surface frequencies in the range of 0–2500 Hz and a maximum amplitude of 0.08 mm. Each vibration cycle was divided uniformly into eight different time points and the position of the vibrating surface at each point was measured directly from the images captured using the high-speed camera. The measured surface positions were plotted (see the “+” symbols in Figure 2(b)) and a curve-fitting technique was then applied to determine the relation between the surface position and time (t). For the example shown in Figure 2(b), the maximum amplitude is 0.065 mm and the cycle time is 0.5 ms (i.e. the vibrating frequency is 2000 Hz). Furthermore, the time reference t = 0 is assigned to the point at which the surface is located at its highest position. From the number of shoots (n) (between the impacting point and the highest point of the surface) and the photographing frequency of the high-speed camera (f), it can be deduced that t = n/f.

Figure 2(b) shows that the position of the vibrating surface varies as a cosine function. In other words, the displacement of the surface can be written as

y = - \frac{L}{2} \cos (2 π f t)

(1)

where L is the amplitude; f is the vibration frequency; t is the time; and the minus sign indicates that the downward direction is taken as the positive direction.

Differentiating equation (1) with respect to time, the velocity of the vibrating surface is obtained as

V_{s} = - \frac{L}{2} \frac{d (\cos (2 π f t))}{d t} = π f L \sin (2 π f t)

(2)

As described above, the experimental images were captured using a high-speed camera at a rate of 10,000 images/s. In other words, the time interval between successive images was just $10^{- 4} s$ and hence, determining the image corresponding to the exact point of droplet impact is relatively easy. Using the neighboring images to determine the impact time t, and knowing the vibration frequency of the vibrating surface f, the velocity V_s of the surface at the moment of impact can be readily derived using equation (2).

Droplet impact velocity

In the experiments, the droplets fell freely under their own weight through a height h. Since the maximum amplitude of the vibration surface is relatively small compared to the drop height, the droplet velocity immediately prior to impact with the stainless steel surface can be approximated simply as

V_{d} = \sqrt{2 g h}

(3)

where g is the gravitational acceleration force and has a value of 9.8 m/s². The instantaneous relative velocity of the droplet as it impacts the vibrating surface is thus obtained as

V_{d s} = V_{d} - V_{s} = \sqrt{2 g h} - π f_{s} L \sin (2 π f t)

(4)

In general, three different outcomes exist for droplets impacting on a dry solid surface, namely spreading, splashing, or bouncing. According to Rein¹ and Zen et al.,³² deposition and splashing can be distinguished by the magnitude of the Weber number, which represents the competition process between the kinetic energy and surface energy of the droplet. The kinetic energy tends to deform the shape of the droplet, whereas the surface energy tries to keep the droplet geometry compact. In the present study, the Weber number of the droplet prior to impact on the stainless steel surface was derived in terms of its falling velocity (equation (3)) as follows

W e = \frac{ρ V_{d}^{2} d}{σ}

(5a)

where ρ is the droplet density, d is the droplet diameter, and σ is the droplet surface tension.

In order to quantify the threshold for splashing of the ethanol droplets on the vibrating surface, the following relative Weber number (We_r) was also derived

W e_{r} = \frac{ρ V_{d s}^{2} d}{σ}

(5b)

where $V_{ds}$ is the instantaneous relative velocity of the droplet as it impacts the vibrating surface (i.e. equation (4)).

Experimental method

Experiments were performed to investigate the effects of the impact Weber number and vibration frequency on the post-spreading deposition and post-spreading splashing of the droplet. The working temperature was set at 25°C. Five vibration frequencies were considered, namely 0, 1250, 1560, 2000, and 2500 Hz. For each vibration frequency, the effect of the relative droplet impact velocity on the impact behavior was investigated by varying the impacting point. Finally, the experimental results were used to determine a predictive equation for the splashing phenomenon as a function of the vibration frequency.

The experimental images were captured at a rate of 10,000 images/s. Consequently, the interval between successive images was equal to just $10^{- 4} s$ . Thus, the measurement errors in the present study relate mainly to the subjective decision made regarding the existing of either post-spreading deposition or post-spreading splashing in the related images. To minimize the effects of such errors, 10 times the number of experiments shown in the data points presented in Figures 5 –8 were actually performed, with very similar results obtained in every case.

Experimental results and discussion

Figure 3 presents a sequence of experimental images showing the impact of an ethanol drop on the downward-moving stainless steel surface at a velocity of 2.3 m/s (We = 400, We_r = 286). From Figure 3, it can be seen that the drop hits the surface and spreads a liquid sheet and then deposits on the surface (i.e. t = 0.25–0.5 ms). Note that the surface has a vibration frequency of 2000 Hz and an amplitude of 0.08 mm. Since the surface is moving in the downward direction at the moment of impact, the instantaneous relative velocity of the droplet impacting on the vibrating surface reduces. Deposition happens in low-energy impacts or impacts with a lower relative Weber number. Consequently, no crown splashing occurs. However, fingers are generated after spreading. Figure 4 shows the impact of an ethanol droplet on an upward-moving stainless steel surface at a velocity of 2.3 m/s (We = 400, We_r = 533). Since the surface is moving in the upward direction at the moment of impact, the instantaneous relative velocity of the droplet impacting on the vibrating surface increases. The high relative velocity stretches the drop into a thinner but longer sheet. If the elongation is sufficient, the instability of the disc edge increases to encourage the occurrence of splashing (i.e. t = 0.25–0.5 ms). Consequently, splashing occurs in addition to the fingers generated after spreading. Moreover, it can be seen that the ethanol drop broke into a lot of smaller drops both in Figures 3 and 4 at t = 5 ms. This phenomenon shows the completion of impact and then surface vibration dominates.

Figure 3.

Photographic images showing impact of ethyl alcohol droplet on downward-moving stainless steel surface with velocity of 2.3 m/s (post-spreading deposition, f = 2000 Hz, We = 400, We_r = 286).

Figure 4.

Photographic images showing impact of ethyl alcohol droplet on upward-moving stainless steel surface with velocity of 2.3 m/s (splashing, f = 2000 Hz, We = 400, We_r = 533).

In a series of preliminary experiments using a static surface (i.e. no vibration), the critical Weber number for splashing generation was found to be We_c = 400. This value was subsequently taken as a benchmark in exploring the impact behavior (i.e. post-spreading deposition or crown splashing) of the ethanol droplets given different values of the surface vibration frequency. Figures 5 –8 present the experimental results obtained for the ethanol droplet impact behavior given original impact Weber numbers in the range of We = 300–550 and surface vibration frequencies of 1250, 1560, 2000, and 2500 Hz, respectively. Note that the droplet diameter is 1.9 ± 0.1 mm in every case and the vibration amplitude ranges from 0 to 0.08 mm. Note also that the solid symbols (e.g. ■, ●, ▲) represent post-spreading deposition, while the hollow symbols (e.g. □, ◯, △) represent post-spreading splashing. (The exact definitions of each symbol used in the four figures are indicated in Table 1.) Taking the critical splashing Weber number of We_c = 400 for a static surface as a benchmark, it is seen that for a droplet with an original impact Weber number We greater than 400, the value of We_r for splashing generation reduces as We increases. Conversely, for a droplet with an original impact Weber number We less than 400, the value of We_r associated with the generation of splashing increases as We decreases.

Figure 5.

Deposition/splashing impact phenomena for original impact Weber number We and corresponding relative impact Weber number We_r given vibration frequency of 1250 Hz.

Figure 6.

Deposition/splashing impact phenomena for original impact Weber number We and corresponding relative impact Weber number We_r given vibration frequency of 1560 Hz.

Figure 7.

Deposition/splashing impact phenomena for original impact Weber number We and corresponding relative impact Weber number We_r given vibration frequency of 2000 Hz.

Figure 8.

Deposition/splashing impact phenomena for original impact Weber number We and corresponding relative impact Weber number We_r given vibration frequency of 2500 Hz.

Table 1.

Definition of symbols in Figures 5 –8.

Symbols	Vibration amplitude
■ and □	0.02 mm
▲ and △	0.03 mm
● and ◯	0.04 mm
▼ and ▽	0.05 mm
◆ and ◇	0.06 mm
★ and ☆	0.08 mm

In Figures 5 –8, the boundaries between the solid and hollow symbols (i.e. between the deposition and splashing domains) have a linear characteristic in every case. Thus, the following relation intuitively holds

(W e_{c} - W e) \propto (W e_{r} - W e_{c})

(6)

Equation (6) suggests that in the impact of droplets on a vibrating surface, the original impact Weber number We does not always dominate during the acting time of splashing. For example, in the case of $We < W e_{c}$ , the difference between the critical Weber number and the original Weber number $(W e_{c} - We)$ is proportional to the additional Weber number required by surface vibration to generate splashing $(W e_{r} - W e_{c})$ . In other words, if the original Weber number of the impacting droplet is insufficient to generate splashing in the case of a static surface, the additional Weber number required to produce splashing can be obtained by applying surface vibration.

Regarding the influence of the vibration frequency, the formation of splashing arising from droplet impact on the surface is completed within a single vibration cycle (approximately 0.5 ms, as shown in Figure 2). Therefore, the effective Weber number of the droplet impact is associated with the surface vibration frequency f. For a given relative Weber number, We_r, the relative impact distance and effective impact Weber number both increase as the vibration frequency increases. Figures 5 –8 indicate that the slope of the splashing critical line increases with increasing f, that is, $(W e_{c} - We) \propto f (W e_{r} - W e_{c})$ .

In Figure 5, corresponding to a vibration frequency of ƒ = 1250 Hz, the slope of the splashing critical line is equal to −0.757. In other words, the splashing critical line for ƒ = 1250 Hz can be predicted as

W e = - 0.757 W e_{r} + 1.757 W e_{c} for f = 1250 Hz

(7)

Similarly, in Figure 6, corresponding to a vibration frequency of ƒ = 1560 Hz, the splashing critical line has a slope of −1.15. In other words, the splashing critical line for ƒ = 1560 Hz can be predicted as

W e = - 1.15 W e_{r} + 2.15 W e_{c} for f = 1560 Hz

(8)

In Figure 7, the splashing critical line has a slope of −2.22. Thus, for a vibration frequency of f = 2000 Hz, the splashing critical line can be predicted as

W e = - 2.22 W e_{r} + 3.22 W e_{c} for f = 2000 Hz

(9)

Finally, in Figure 8, corresponding to a vibration frequency of ƒ = 2500 Hz, the slope of the splashing critical line is −6.25. Consequently, the splashing critical line can be predicted as

W e = - 6.25 W e_{r} + 7.25 W e_{c} for f = 2500 Hz

(10)

Based on the four relational expressions given in equations (7)–(10), and the condition that “We = We_c when f = 0,” the relation between We and We_r for predicting the generation of splashing can be obtained via curve-fitting as

We = \frac{- cf}{(1 - cf)} W e_{r} + \frac{1}{(1 - cf)} W e_{c} where W e_{c} = 400, c = 3.45 \times 10^{- 4}

(11)

for $0 \leq f \leq 2500 Hz$ , and $0 \leq L \leq 0.16 mm$ .

From equation (4), it is known that the instantaneous relative velocity depends on the impact position and is difficult to control. However, since $- 1 \leq \sin (2 π ft) \leq 1$ , it can be seen that the maximum instantaneous relative velocity can be derived as

V_{ds, max} = \sqrt{2 gh} + π f_{s} L

(12)

The corresponding maximum relative Weber number can also be derived as

W e_{r, \max} = \frac{ρ V_{ds, \max}^{2} d}{σ}

(13)

Substituting equation (13) into equation (11), a minimum We for inducing splashing can be derived as

W e_{m i n} = \frac{- 3.45 \times 10^{- 4} f}{(1 - 3.45 \times 10^{- 4} f)} W e_{r, m a x} + \frac{400}{(1 - 3.45 \times 10^{- 4} f)}

(14)

Equation (14) represents that if the Weber number of the droplet (i.e. calculate from equations (3) and (5a)) lower than the corresponding We_min (i.e. calculate from equation (14)), splashing will never occur. In other words, for given the vibration frequency f and amplitude L, engineers may use a Weber which lowers than the corresponding We_min to ensure that splashing will not occur.

Conclusion

This study has performed an experimental investigation into the formation mechanisms of deposition/splashing during the impact of ethyl alcohol droplets on a vibrating surface. The study has focused particularly on the effects of the Weber number of the droplet impact and the frequency of the vibrating surface on the impact behavior of the droplet. The experimental results support the following main conclusions:

For a static surface, the critical Weber number for the generation of splashing is We_c = 400.

For a vibrating surface, the difference between the original Weber number and the critical Weber number, that is, (We_c − We), is proportional to the additional relative impact Weber number provided by the surface vibration, that is, (We_r − We_c).

For a given relative impact velocity, the relative impact distance and effective impact energy both increase as the vibration frequency f increases.

Under the surface temperatures at 25°C and the surrounding pressure at atmospheric pressure, the generation of splashing can be predicted as a function of the vibration frequency as follows: $We = (- cf / (1 - cf)) W e_{r} + (1 / (1 - cf)) W e_{c}, c = 3.45 \times 10^{- 4}$ .

For a droplet with a Weber number which lowers than the corresponding We_min, splashing will never occur.

Footnotes

Appendix 1

Handling Editor: Xiao-Jun Yang

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study was financially supported by the Ministry of Science and Technology (MOST) of Taiwan under grant number MOST 103-2221-E-415-007.

References

Rein

. Phenomena of liquid drop impact on solid and liquid surfaces. Fluid Dyn Res 1993; 12: 61–93.

Lesser

Field

. The impact of compressible liquids. Annu Rev Fluid Mec 1983; 15: 97–122.

Asai

Shiova

Hirasawa

et al . Impact of an ink drop on paper. J Imaging Sci Techn 1993; 37: 205–207.

Scheller

Bousfield

. Newtonian drop impact with a solid surface. AIChE J 1995; 41: 1357–1367.

Pasandideh-Fard

Qiao

Chandra

et al . Capillary effects during droplet impact on a solid surface. Phys Fluids 1996; 8: 650.

Zhang

Basaran

. Dynamic surface tension effect in impact of a drop with a solid surface. J Colloid Interf Sci 1997; 187: 166–178.

Fukai

Shiiba

Yamamoto

et al . Wetting effects on the spreading of a liquid droplet colliding with a flat surface: experiments and modeling. Phys Fluids 1995; 7: 236–247.

Ford

Furmidge

CGL

. Impact and spreading of spray drops on foliar surfaces. Wetting Soc Chem Ind Monogr 1967; 25: 417–432.

Karl

Anders

Frohn

. Experimental investigation of droplet deformation during wall collision by image analysis: experimental and numerical flow visualization. ASME FED 1993; 172: 135–141.

10.

Mao

Kuhn

DCS

Tran

. Spread and rebound of liquid droplets upon impact on flat surfaces. AIChE J 1997; 43: 2169–2179.

11.

Thoroddsen

Sakakibara

. Evolution of the fingering pattern of an impacting drop. Phys Fluids 1998; 10: 1359.

12.

Bhola

Chandra

. Parameters controlling solidification of molten wax droplets falling on a solid surface. J Mater Sci 1999; 34: 4883–4894.

13.

Bussmann

Chandra

Mostaghimi

. Modeling the splash of a droplet impacting a solid surface. Phys Fluids 2000; 12: 3121.

14.

Mehdizadeh

Chandra

Mostaghimi

. Formation of fingers around the edges of a drop hitting a metal plate with high velocity. J Fluid Mech 2004; 510: 353–373.

15.

Mundo

Sommerfeld

Tropea

. Droplet-wall collisions: experimental studies of the deformation and breakup process. Int J Multiphas Flow 1995; 21: 151–173.

16.

Cossali

Coghe

Marengo

. The impact of a single drop on a wetted solid surface. Exp Fluids 1997; 22: 463–472.

17.

Range

Feuillebois

. Influence of surface roughness on liquid drop impact. J Colloid Interf Sci 1998; 203: 16–30.

18.

Stow

Hadfield

. 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 1981; 373: 419–441.

19.

Šikalo

Tropea

Ganić

. Impact of droplets onto inclined surfaces. J Colloid Interf Sci 2005; 286: 661–669.

20.

Kang

Lee

. On the dynamic behavior of a liquid droplet impacting upon an inclined heated surface. Exp Fluids 2000; 29: 380–387.

21.

Bussmann

Mostaghimi

Chandra

. On a three-dimensional volume tracking model of droplet impact. Phys Fluids 1999; 11: 1406–1417.

22.

Reznik

Yarin

. Spreading of a viscous drop due to gravity and capillarity on a horizontal or an inclined dry wall. Phys Fluids 2002; 14: 118–132.

23.

Lunkad

Buwa

Nigam

KDP

. Numerical simulations of drop impact and spreading on horizontal and inclined surfaces. Chem Eng Sci 2007; 62: 7214–7224.

24.

Hanchak

Byrd

Briones

et al . Model of droplet impingement based on least-squares solution of proper orthogonal decomposition basis matrices. J Fluid Eng: T ASME 2012; 134: 041301.

25.

Capizzano

Iuliano

. A Eulerian method for water droplet impingement by means of an immersed boundary technique. J Fluid Eng: T ASME 2014; 136: 040906.

26.

Dyment

. Compressible liquid impact against a rigid body. J Fluid Eng: T ASME 2014; 137: 031102.

27.

Zhang

Nagel

. Drop splashing on a dry smooth surface. Phys Rev Lett 2005; 94: 184505.

28.

Povarov

Nazarov

Igant’evskaya

et al . Interaction of drops with boundary layer on rotating surface. J Eng Phys 1976; 31: 1453–1456.

29.

Povarov

Shal’nev

Nazarov

et al . Collision of droplet with a moving plane surface. Sov Phys Dokl 1976; 20: 782–783.

30.

Chen

Wang

. Effects of tangential speed on low-normal-speed liquid drop impact on a non-wettable solid surface. Exp Fluids 2005; 39: 754–760.

31.

Courbin

Bird

Stone

. Black hole nucleation in a splash of milk. Phys Fluids 2008; 20: 091106.

32.

Zen

Chou

. Ethanol drop impact on an inclined moving surface. Int Commun Heat Mass 2010; 37: 1025–1030.

33.

Brothier

Moulinier

Bertaux

. Drop impact on a vibrated, heated surface: towards a potential new way of elaborating nuclear fuel from gel microspheres. Int J Chem Mol Nucl Mater Metall Eng 2012; 6: 238–246.

Experimental investigation into deposition/splashing behavior of droplets impacting vibrating surface

Abstract

Keywords

Introduction

Experimental system

Droplet-generating system

Position-adjustment system

Image acquisition system

Vibrating surface system

Measurement method and physical model

Surface vibration velocity (Vs)

Droplet impact velocity

Experimental method

Experimental results and discussion

Conclusion

Footnotes

Appendix 1

Declaration of conflicting interests

Funding

References

Surface vibration velocity (V_s)