Splashing of a Drop Impacting on a Thin Liquid Film

Transcription

1 ILASS Americas 27th Annual Conference on Liquid Atomization and Spray Systems, Raleigh, NC, May 2015 Splashing of a Drop Impacting on a Thin Liquid Film S. Rajendran, M.A. Jog*, and R.M. Manglik Thermal-Fluids and Thermal Processing Laboratory Department of Mechanical and Materials Engineering College of Engineering and Applied Science, University of Cincinnati, Cincinnati, OH USA Abstract When a drop impinges on a thin layer of liquid, there are one of three outcomes: a prompt splash, or a delayed splash, or deposition on the liquid film. Prompt splash occurs at the instant of drop impact, whereas delayed splash occurs with the breakup of the liquid film of the crown at or beyond the maximum expansion of the crown. An experimental and analytical investigation on the onset of delayed splash is reported in this paper. Experiments are carried out with varying drop sizes ranging from 3.5 mm to 5.2 mm and altering the impact velocity from 1 m/s to 3 m/s. Four different liquids are used to study the effect of liquid properties on the phenomena of splashing. A high speed digital camera Hi-D cam II version 3.0 (NAC Image technology) is used to capture the phenomena of splashing. The threshold of splashing is found to be related to drop size, impact velocity, liquid properties and thin film thickness. Experimental analysis shows the significance of inertial, viscous and capillary forces in determining the splash/no-splash (or deposition) boundary. The effects of liquid properties and flow parameters on demarcating splash/no-splash regimes are discussed in the paper. * Corresponding Author: Milind.Jog@uc.edu

2 Introduction The significance of drop impact and its subsequent splashing was recognized in studies as early as 1876 by Worthington [1]. Since then, various components of this process have been examined in a number of experimental, numerical and analytical studies. Spray impingement is a common tool used in a multitude of industries to enhance heat and mass transfer. Workers and operators in such industries, that involve spray coating, metal annealing and fertilizer sprays, are in constant danger of contact and/or inhalation of these small drops of toxic chemicals. A means to predict and control the splash occurring, while maintaining the functionality of the process, becomes crucial. Due to the inherent complexities in the drop post impact behavior, understanding of the subject in its entirety, is far from complete. With the exception of a few applications, most spray impingement occurs on a thin film accumulated after impact from previous droplets. The interaction of a liquid drop impinging on a layer of thin film is addressed in the present work. When a drop impinges on a thin liquid film, it leads to different regimes of liquid movement that can broadly be classified under deposition or splashing. Illustrations of these regimes are provided in Table 1. Deposition, post impact of a drop, involves the drop merging with the liquid film without forming secondary drops. Deposition may or may not include capillary surface waves that form a crown of liquid, before merging with the liquid film. Splashing happens when secondary drops are formed as the drop impacts the thin film. At high Weber numbers (We) and high Reynolds numbers (Re), on impact, an ejected jet is formed at the neck (small region between the drop and the thin film). The ejected jet, spreads out and tilts upwards, forming a crown whose rims are unstable and breakup into secondary drops before merging into the thin film. This was termed crown splashing by Deegan et al. [2] and by Josserand and Zaleski [3]. Table 1. Images showing (a) deposition (no splash), (b) prompt splash and (c) crown (delayed) splash along with respective properties. (a) Liquid: 50% by volume Propylene Glycol (b) Liquid: Water (c) Liquid: 50% by volume Propylene Glycol Re = 1899 Re = Re = We = We = We = Prompt splash is a supplementary phenomenon that could occur when secondary drops are formed at the instant of drop impact on the thin film. Deegan et al. [2] studied the complexities of splashing and found that during a prompt splash, the ejected jet shot out from underneath the drop parallel to the fluid layer. Their study delineated the different regimes of drop impact based on two parameters: We and Re. They present a correlation to demarcate occurrence of prompt splash from crown splash. Delayed splash or crown splash, occurs when the liquid crown breaks up at or beyond the expansion of the crown. Another extensive review of drop impact dynamics was provided by Yarin [4]. Drop impact dynamics depends on a number of parameters: drop size and impact velocity, drop as well as film liquid properties (density, viscosity, rheology), interfacial tension, surface properties (roughness, contact angle, wettability), and thermal properties. Both experimental and analytical methods have been used to find the splashing threshold. Yarin and Weiss [5] experimentally defined a velocity threshold for drop splashing based on the frequency of falling drops. Cossali et al. [6] tested the splashing threshold by analyzing drop impact experiments that involved a wide range of liquids on different target surface conditions. They proposed a correlation to estimate splashing limit; Oh -0.4 We = K L, where K L depends on the non-dimensional film thickness to predict the deposition-splashing limit. The nondimensional film thickness is defined as H* = H/d. Their experiments were carried out for film thickness of H* 1. Mundo et al. [7] investigated a new model that was based on liquid properties, drop diameter and impingement kinetics to develop a predicting correlation for the onset of splashing. Their correlation was also based on non-dimensional parameters of Weber number and Ohnesorge number. Wang et al. (2000) proposed a new method to produce thin film less than 1 mm in thickness with good reliability. Their experiments found that a critical Weber number determined splashing threshold. This critical Weber number was found to be dependent on surface characteristics and on liquid viscosity. The liquid thickness was maintained at H* 0.1. Different liquids and impact conditions were tested experimentally by Rioboo et al. [8]. They defined two limits, crown-splash and deposition-crown limits, based on their experimental evidence. They note that for impacts on liquid films of thickness of H* 0.03, the two limits converge. Their correlation is based on that provided by Cossali et al. [6] and defines new methods of defining the parameter K L. Vander Wal et al. [9] conducted a number of studies to investigate the onset of splashing based on the surface character-

3 istics and film thickness. Similar to Wang et al. [10] they found a critical Weber number to be the primary factor determining splashing in a drop impact on thin films. They also established that for thin films (H* ~ 0.1), splashing is enhanced while for thicker films (1 H* 10), splashing is suppressed. The specific effects of surface roughness are analyzed in their work as well. Numerical modeling coupled with analytical methods has been used by some researchers for estimating the onset of splashing. Based on the concept of kinematic discontinuity proposed by Yarin and Weiss [5] a model for propagation of the crown formed during drop impact was proposed by Trujillo et al. [11]. Their solution resulted in a defining time scale beyond which it was found that the crown characteristics were independent of upstream conditions. The model also attempted to resolve effect of surface film characteristics and was validated with experimental data. A 2D flow model was numerically simulated using VOF method by Coppola et al. [12]. Their work concentrated on validating the kinetic discontinuity theory of [5] numerically. In our current work, the onset of this delayed splash is studied experimentally and analyzed. While there are a few studies that outline the onset of splashing, there is a large variability in predictions based on their proposed correlations. In this study, we attempt to understand the underlying reason for this disparity. Experimental Methods Single drop impingement was studied as it impacted a thin film formed from prior impinging drops. The thickness of this thin film formed was maintained at H* ~ 0.1. Fig. 2 provides a sketch of the experimental apparatus used. A container made of acrylic sheets was used as the main observation chamber and also functioned as the reservoir/collecting tank. The container had a raised acrylic platform inside it where the copper target surface was installed. The walls of the container were made to be large enough to avoid interference with the splashing droplets and to provide for a clearing viewing of the phenomena of impingement and splash. Impacting drops were generated at a steady rate from a NEXUS 3000 syringe pump. The flow rate was varied from 0.5 ml/min to 8 ml/min for the different cases tested experimentally. This resulted in a range of velocities from 1 m/s to 3 m/s for drop diameters ranging from 3.5 mm to 5.2 mm. The drops were released from a prescribed height above the target surface, through a stainless steel circular needle. The needle was maintained perpendicular to the target surface using a bubble level. Since the target surface was much larger than the impacting drop, the increase in film thickness with each impacting drop, was found to be negligible. The film thickness (H*) was periodically verified to be ~ 0.1 by capturing images using the high speed camera. The height from which the drop was released, was adjusted while keeping a constant flow rate of liquid from the syringe pump. With change in height, the impacting velocity is dramatically altered. As a single drop impacts the thin liquid film, it may either result in a splash or in deposition of the drop. Figure 1. Sketch of experimental apparatus. To study the phenomena of drop impact, a high speed digital camera (Hi-D cam II version 3.0 NAC Image Technology) was used. The camera system was kept at an appropriate angle to view the impact without causing hindrance to the phenomena. Images were recorded at a shutter speed of 1/2000 s and a frame rate of 500 fps with the camera placed at about 1.5 ft. from the target surface. A single bulb focusing light system (ARRI) with glossy aluminum reflectors was used to obtain clear and high contrast images. The light system was focused on a white screen that was placed parallel to the plane of viewing. The high quality images thus obtained were analyzed using the image processing software, Image- Pro 4.0 (Media Cybernetics). The impacting diameter of the drop is calculated based on the area occupied by the drop, assuming the drop to be spherical and therefore, a circle in the image plane. Drop impact velocity is determined by comparing the position of drops, prior to impact, in successive frames with respect to a fixed point in the frame. The impact velocity is not a constant due to gravitational acceleration and drag force acting on the drop. Therefore, only three appropriate images before impact are considered for calculations. For each set of experiment, images are calibrated using the stainless steel needle diameter. To help understand the influence of liquid properties on the splashing phenomena, different liq-

4 uids with varying properties were used for the experiment. Table 2 presents the properties of the four liquids used. Mixtures of water and propylene glycol by volume, were used as working fluids to obtain a range of liquid properties for the experiment. The values of viscosity and surface tension for these mixtures were found by using the AR 2000 controlled stress/controlled shear rate Rheometer and the SensaDyne QC6000 Tensiometer respectively. Table 2. Properties of the liquids used in the experiment. Liquids Density (kg/m 3 ) Viscosity (Pa.s) Surface Tension (N/m) Water % by volume of Propylene Glycol (25% PG) % by volume of Propylene Glycol (50% PG) % by volume of Propylene Glycol (75% PG) Ethylene Glycol (EG) Table 3. Correlations available in the literature Vander Wal et al. [9] Deegan et al. [2] and Christophe [3] Okawa [13], Cossali [6] and Rioboo [8] Oh. RR = WW = C 1 (1) WW. RR = C 2 (2) Oh 0.4. WW = WW 0.8. RR 0.4 = C 3 (3) Results and Discussion To characterize the splashing behavior of a drop impact on a thin film, controlled experiments were conducted. High-speed photographs taken during the experiment are analyzed to determine their splashing characteristics. Correlations proposed in previous studies (shown in Table 3), for determining the splashing threshold, are compared with the experimental data obtained from this study. These suggested correlations to characterize the splashing threshold are based on parameters that can primarily be reduced into two dimensionless quantities: Weber number (We) and Reynolds number (Re). Fig. 4 compares our experiments along with experiments from past literature, with these suggested correlations. It should be noted that all the data presented here are for H* 0.1. The three correlation presented are unable to predict the splashing limit in good agreement with the experimental data. While correlation (3) is able to limit most splash cases above it, it is an underestimate of the splashing threshold. In contrast, correlation (2) is an overestimate. Correlation (1) was provided by [9] using water as the working fluid. While the correlation is in some agreement with their experimental data, it fails to be in accord with data from other experimental studies where water is used as the working fluid. Studies have attempted to resolve this disparity in predictions by concentrating on finding optimum values of the constants C 1, C 2 and C 3. It can be concluded that, considering only We and Re as the governing parameters could lead to neglecting other important forces that may be significant in the splashing of the drop. To identify the relevant significant elements, the effect of working liquid properties along with parameters of the flow domain are studied. The analysis ensues from the examination of the images captured during experimentation. The impact of water drops on a thin water film is shown in Fig. 3. The occurrence of four different phenomena are captured and presented here. Figs. 3a and 3b show splashing occurring, while Figs. 3c and 3d show deposition. Images are captured for each s. As the drop impacts on the thin film surface, at impact, a splash could occur. This is the prompt splash and is seen to occur in Fig. 3a. The capillary surfaces waves formed on the crown create fingers of the crown that extend upwards. These surface waves could then grow into fingers of the crown that could then breakup into droplets. In Fig. 3a, the drops formed from the prompt splash are still seen at 0.01 s. The fingers of the crown are seen to be growing and these ultimately breakup at 0.14 s, while falling back into the thin film layer. Fig. 3(b) shows the case of a delayed or crown splash, where, at impact, no prompt splash occurs. However, at impact, the formation of capillary waves can be seen on the surface. These propagate to the fingers of the crown that breakup at s. In the crown splash, the droplets formed are noticed to be much larger and uniform in comparison to the prompt splash in Fig. 3(a). Figs. 3(c) and 3(d) present deposition of the drops. In Fig. 3(c) the capillary surface wave formed at impact at s is seen to propagate and form fingers of the crown. These fingers however, do not further breakup

5 into drops before deposition on the thin liquid film. The drop in fig. 3(d) does not form capillary waves on impact at s. Minor surface undulations are observed at 0.01 s. These undulations however do not form finger like structures before deposition. Accordingly, there can be two types of deposition: fingered and non-fingered. By inspecting Fig. 3(c) with 3(a) and (b), it is noted that both an increase in diameter and an increase in impact velocity affects droplet splashing on a thin film. The diameter of the resulting crown on the thin film is seen be a function of the drop diameter. So, for the same velocity of impact, a smaller drop results is a smaller crown diameter (Fig. 3(a) and 3(c)). Figure 2. Comparing past correlations with experimental data and with data from other studies ([2], [3], [6], [8], [9], and [13]) 0 s s 0.01 s s (a) Time progression of water drop impact on a thin film. r d 2.3 mm V 2.2 m/s Re = We = 305

6 0 s s s s (b) Time progression of water drop impact on a thin film. r d 1.8 mm V 2.5 m/s Re = 8982 We = s s s s (c) Time progression of water drop impact on a thin film. r d 1.8 mm V 2.2 m/s Re =7904 We = s 0.01 s s (d) Time progression of water drop impact on a thin film. r d 2.6 mm V 1.1 m/s Re = 5709 We = 86 To understand the influence of different forces on the phenomena of splashing, the effect of liquid properties is studied in addition to the drop size and drop velocity. As the drop impacts the thin film, the base of the crown has a velocity comparable to the impact velocity. This velocity of increment of the crown base, decrease with crown development until the crown collapses on the thin film. The impact of the drop primarily receives resistance from the thin film. The decrease in velocity of the crown base is therefore based on the resistance offered by the liquid. This resistance is the viscous property of the liquid. The drop impact of EG and 50% PG is shown in Fig. 4. To understand the role of the viscosity of the liquid, drops of two different liquids impacting on a thin film with nearly the same velocity are shown in Fig. 4. The Weber numbers of these two cases shown Figure 3. Time progression of drops of Water in Fig. 4 are about the same. For the EG drop, at s, the rim of the crown is still uniform and no undulations are observed. Instability on the crown rim is not observed till deposition occurs at s. For 50% PG water solution, though the drop diameter is smaller than that of EG in Fig 4(a), minor surface waves are noticed at s. These disturbances grow and ultimately result in a modest splash at s. Though the diameter of the EG drop is higher than the 50% PG drop, the EG drop does not splash. As the viscosity of EG is higher than 50%PG, EG offers more resistance to the growing crown base and thus suppresses splashing by a greater measure than 50% PG solution. Consequently, it can be concluded that viscosity of the liquid affects the spread of the liquid crown layer and restrains the phenomena of drop splash on a thin liquid film. 0 s s 0.01 s s (a) Time progression of EG drop impact on a thin film. r d 2.27 mm V 2.17 m/s Re = We = 491.7

7 0 s s s s (b) Time progression of 50% PG drop impact on a thin film. r d 2.2 mm V 2.18 m/s Re = 1951 We = Figure 4. A comparison of impact behavior of EG and 50% PG drops Fig. 5 illustrates two liquid drops, of 25% PG and of 75% PG, impacting of a thin liquid film of same liquid. The two cases considered have similar velocities but different drop diameter, Re and We. For 25% PG, at s, the impact is seen to generate capillary waves. The formation of capillary waves is not observed at impact for 75% PG. For both the liquids shown, the capillary waves lead to formation of fingers of the crown that eventually breakup to form droplets. For 25% PG (Fig. 4(a)), this breakup occurs more easily than for the 75% PG drop. The number of splash drops formed is more for 25% PG. As the liquid crown is spreading, the instability on the rim leads to crown formation and possible breakup leading to formation of droplets. In addition to this instability driven crown breakup, the crown edges are constantly looking to minimize their surface energy. This surface energy is lower for a unit volume of a drop than for the same unit volume within the crown. As seen in Table 2, the surface tension of 25% PG is higher than that of 75% PG. As surface tension governs the surface energy, the 25% PG drop splashes more violently than the 75% PG. It can thus be concluded that a higher surface tension helps in breaking up the crown rim hence forming splashed droplets. 0 s s s s (a) Time progression of 25% PG drop impact on a thin film. r d 2.25 mm V 2.5 m/s Re = We = s s 0.02 s s (a) Time progression of 75% PG drop impact on a thin film. r d 2.5 mm V 2.45 m/s Re = 1048 We = Figure 5. A comparison of impact behavior of 25% PG and 75% PG drops Conclusions An experimental investigation of liquid drop impact on a thin liquid film is carried out. A range of nozzle diameters and different working liquids are used. The drop splash phenomenon was captured using a high speed camera. The observed modes of impact are described. The current experimental data coupled with data from other studies in the past, are used to estimate the effectiveness of existing correlations. The present study highlights the disparity in existing correlations for determining the splashdeposition limit. An analysis of the phenomena of drop impact is conducted. It is noted that the drop diameter and the impact velocity play an important role governing the outcomes of drop impact. On

8 varying liquid properties, the significance of viscosity and surface tension is also noted. Both these liquid properties are seen to affect the drop impact. Its effects are highlighted by comparing experimental images. The role of viscosity appears to offer resistance to the spreading of the crown. This limits expansion of the crown base. Surface tension plays a role in limiting the surface energy of the expanding crown rim. This therefore, affects the breakup of the rim into droplets. It is seen that Re and We are insufficient in predicting splashing and deposition limits. Further study to identify the governing parameters is required to better characterize the influence of liquid properties and drop dynamics during drop impact splatter. 10. Wang, A. B., and Chen, C. C., Physics of Fluids (1994-present) 12.9: (2000). 11. Trujillo, M. F., and Lee, C. F., Physics of Fluids (1994-present) 13.9: (2001). 12. Coppola, G., Rocco, G., and de Luca, L., Physics of Fluids (1994-present) 23.2: (2011). 13. Okawa, T., Shiraishi, T., and Mori, T. Experiments in fluids 41.6: (2006). 14. Harlow, F. H., and Shannon, J. P., Journal of Applied Physics 38.10: (1967). 15. Liu, J., Vu, H., Yoon, S. S., Jepsen, R. A., and Aguilar, G., Atomization and Sprays 20.4 (2010). Nomenclature d diameter (mm) H height of liquid film (mm) r d drop radius t time V velocity K L, C 1, C 2, C 3 constants Dimensionless quantities RR = ρρρ Reynolds number μ WW = ρv2 d Weber number σ BB = ρρd2 Bond number σ μ Oh = Ohnesorge number ρρρ H = H d dimensionless film height References 1. Worthington, A. M. Proceedings of the royal society of London 25: (1876). 2. Deegan, R. D., Brunet, P., and Eggers, J., Nonlinearity, 21.1:C1 (2008). 3. Josserand, C., and Zaleski, S., Physics of Fluids (1994-present) 15.6: (2003). 4. Yarin, A. L., Annual Review of Fluid Mechanics 38: (2006). 5. Yarin, A. L., and Weiss, D. A., Journal of Fluid Mechanics 283: (1995). 6. Cossali, G. E., Coghe, A., and Marengo, M., Experiments in fluids 22.6: (1997). 7. Mundo, C., Sommerfeld, M., and Tropea, C., Atomization and Sprays 8.6 (1998). 8. Rioboo, R., Bauthier, C., Conti, J., Voue, M., and De Coninck, J., Experiments in fluids 35.6: (2003). 9. Vander Wal, R. L., Berger, G. M., and Mozes, S. D., Experiments in fluids 40.1:53-59 (2006).