Experimental Study of Drop Size Distribution in the Bag Breakup Regime

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Experimental Study of Drop Size Distribution in the Bag Breakup Regime Hui Zhao, Hai Feng Liu,* Jian Liang Xu, and Wei Feng Li Key Laboratory of Coal Gasification, Ministry of Education, East China University of Science and Technology, P.O. Box 272, Shanghai 200237, People’s Republic of China ABSTRACT: The situation of a liquid drop exposed to a continuous air jet flow was investigated experimentally. The drop bag breakup of test liquids which included water, ethanol, and various glycerol mixtures was observed using a high-speed camera. The morphological change, such as drop deformation, was observed and analyzed. Mean fragment sizes were obtained, which were in good agreement with those reported in the literature. Big fragments formed from the ring contained the great mass of the initial drop and were studied in detail, and correlations on fragment mean size and number were obtained. Mean size decreased with the Weber number and increased with the Ohnesorge number; fragment number was in contrast to mean size. Fragment size distribution was another useful parameter. Our results showed that fragment size distribution based on the number formed from the ring was a gamma distribution. Fragment size distribution based on the number formed from the whole drop was an exponential distribution. We also investigated fragment size distribution based on the volume formed from the whole drop, which was a RosinRammler distribution.

1. INTRODUCTION The transformation of liquids into sprays is of importance in several industrial processes and has many applications in agriculture, meteorology, and medicine.1 Therefore, the process has been studied extensively both theoretically and experimentally.29 When an initially spherical drop encounters an ambient flow field moving at a velocity relative to it, aerodynamic force causes the drop to deform and (perhaps) break apart into fragments. This process is referred to as secondary atomization.10 In spray combustion and other industrial processes, secondary atomization (or secondary breakup) of liquid drops plays an important role in the increase of surface area and the enhancement of heat and mass transfer between the fuel and the ambient gas. Due to the numerous applications, secondary breakup has received significant attention by, among others, Guildenbecher et al.,10 Pilch and Erdman,11 Faeth et al.,12 and Gel’fand.13 The regimes of secondary breakup are often termed no breakup (or vibrational breakup), bag breakup, multimode breakup, sheet-thinning breakup, and catastrophic breakup. In secondary breakup, the Weber number (We) and the Ohnesorge number (Oh) are important parameters. The Weber number represents the ratio of disruptive hydrodynamic forces to the stabilizing surface tension force: ð1Þ

The study of bag breakup is especially important because it establishes the criteria for the onset of secondary atomization. Some work on the temporal properties of drop bag breakup has been done by Chou and Faeth.14 Fragment size is one of the most important but difficult to measure properties of secondary atomization. Mean fragment diameters such as the Sauter mean diameter (SMD) and the mass median diameter (MMD) were commonly reported.1417 With the help of fragment size distribution data in drop bag breakup, Villermaux and Bossa18 breathed new life into the study of raindrop size distribution. The experimental data of fragment size distribution can also be used to check and improve numerical simulation of atomization. There is abundant literature discussing drop size distribution in sprays; however, so far there are still insufficient data on fragment size distribution of single drop breakup and more work is needed. Motivated by the studies cited above, we performed a further study on drop bag breakup. In the current article, a high-speed digital camera combined with a back illumination method was used to visualize drop deformation and breakup. This research was conducted to study the influence of the Weber number and the Ohnesorge number on drop deformation, big fragment size, and number. Finally, another very important objective of this study was to investigate fragment size distribution after drop bag breakup.

where Fg is the ambient air density, ug is the initial air velocity in the main flow direction, D0 is the initial diameter of a liquid drop, and σ is surface tension. The viscosity effect is highly correlated with the Ohnesorge number:

2. METHODS AND MATERIALS The setup and instrumentation were identical to those in our earlier work,1921 so the test apparatus and instrumentation

We ¼ Fg ug 2 D0 =σ

Oh ¼ μl =ðFl D0 σÞ0:5

ð2Þ

where μl and Fl are the dynamic viscosity and density of the liquid, respectively. r 2011 American Chemical Society

Received: March 29, 2011 Accepted: July 11, 2011 Revised: May 23, 2011 Published: July 22, 2011 9767

dx.doi.org/10.1021/ie200622d | Ind. Eng. Chem. Res. 2011, 50, 9767–9773

Industrial & Engineering Chemistry Research

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Table 1. Summary of Experimental Conditions test liquid

dynamic viscosity (mPa 3 s)

surface tension (mN/m)

density (kg/m3)

test liquid drop diameter (mm) 5.9

water

1.0

70.8

997

ethanol

1.3

24.0

800

4.1

glycerol (75%)

36.5

67.1

1195

5.3

glycerol (85%)

112.9

65.6

1222

5.3

glycerol (90%)

234.6

64.9

1235

5.3

Figure 1. Pictures of drop bag breakup taken by high-speed camera. Air flow direction = right to left.

will be described only briefly. A circular nozzle combined with an air blower was used to form a continuous and uniform air jet flow. The air flow rate was regulated by a high accuracy rotameter. The drop generator included a cylindrical liquid chamber, and a small-diameter tube was fixed at the bottom of the water chamber. Liquid drops dripped from the tip of the tube under the action of gravity and fell into the air jet. The horizontal distance between the initial drop and the nozzle exit was 20 mm. The fragments produced in the bag breakup regime were made visible by back illumination through a diffusive screen.

A high-speed camera (Fastcam APX-RS, Photron Limited, frame rate 3000 images per second in this experiment) was used combined with a continuous 2000 W halogen spot to capture the pictures of the fragments. The resolution of pictures was 1024 1024 pixels. All experimental pictures of drop breakup were from this high-speed camera. Experiments, which were repeated three times, were performed at room temperature and atmospheric pressure. The test liquids were water, ethanol, and various glycerol solutions, whose physical properties are shown in Table 1. In this test, Oh was varied from 0.0018 to 0.36, and We was varied from 9.4 to 23. 9768

dx.doi.org/10.1021/ie200622d |Ind. Eng. Chem. Res. 2011, 50, 9767–9773


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Figure 2. Influence of We on Dmax/D0 for different test liquids.

Figure 4. Drop detection procedure using NIH Image software.

Figure 3. Comparison of measured Dmax/D0 to Dmax/D0 predicted by eq 3.

3. RESULTS AND DISCUSSION 3.1. Drop Deformation. In bag breakup, the drop evolves from its initial spherical shape into an oblate spheroid, the center of the drop gets blown downstream and forms a hollow bag attached to a roughly circular ring as shown in Figure 1c, then the bag bursts forming a large number of small fragments, and finally the ring forms a small number of large fragments. Figure 1 illustrates typical bag breakup. Small fragments are accelerated easily by the motion and breakup of bag film, which leads to the disjointed position and velocity distribution of small fragments. Dmax is the maximum cross stream diameter of the drop at the start of the bag formation as shown in Figure 1b. Figure 2 illustrates the typical behavior of Dmax/D0 with We for different test liquids. Due to the pressure force of air flow, the shape of the drop becomes oblate with increasing We. At higher Oh, the maximum deformation at a given We decreases. This is due to the slowing of the rate of deformation which reduces the relative velocity. Here, we obtain a correlation which includes the effect of Oh:

Dmax ¼ 1 þ 0:20We0:56 ð1 0:48Oh0:49 Þ D0

ð3Þ

Dmax/D0 values calculated using eq 3 are plotted against the measured values in Figure 3. The experimental results of Hsiang and Faeth16 are also shown in Figure 3. When Oh is small, eq 3 is close to the correlating expression of Hsiang and Faeth,16 whose

correlation does not include the effect of Oh. In the literature the experimental correlation of drop deformation only considers the influence of the Weber number. Here, the influence of the Ohnesorge number is also considered in eq 3. 3.2. Drop Detection Algorithm. The resulting digital images are analyzed with NIH Image software following several steps of operation. These steps are illustrated in Figure 4. NIH Image software is often used to analyze digital images of atomization in the literature, such as in the paper by Marmottant and Villermaux.22 The drop detection procedure from raw images is as follows. Figure 4a is the original image (8-bit grayscale), which is obtained by the high-speed camera directly. The Sobel operator is often used in image processing, particularly within edge detection algorithms. With the help of the classical Sobel filters, we can obtain Figure 4b. Then we segment an image into objects of interest and background on the basis of gray level. A grayscale image is converted to binary by defining a grayscale cutoff point. Grayscale values below the cutoff become black and those above become white. Appropriate threshold values are determined based on most of the fragment drops being distinctly identified as shown in Figure 4c. Finally, we count and measure objects in binary images with the help of NIH Image software, and obtain Figure 4d. The equivalent diameter De of the drop is defined from S ¼ πDe 2 =4

ð4Þ

where S corresponds to the projected area of a drop. 3.3. Mean Drop Size. Various definitions of mean drop size are available, of which the most widely used in atomization are the Sauter mean diameter (SMD) and the mass median diameter (MMD). Most previous studies on drop breakup have focused mainly on SMD and MMD. On the basis of the experimental results of a large number of nozzles, Simmons15 finds that the drop size distribution at each instant of time satisfies that MMD/SMD = 1.20, with almost all the points falling within (5% of the mean. In secondary atomization, Hsiang and Faeth16,17 and Chou and Faeth14 find 9769



Figure 5. Influence of We on Dr/D0 for different test liquids.

Figure 6. Comparison of measured Dr/D0 to Dr/D0 predicted by eq 5.

that their results of MMD/SMD = 1.2 for different breakup regimes (bag breakup, multimode breakup, and shear breakup) are very close to the result of Simmons.15 Here, the average value of our experimental result (MMD/SMD = 1.19 ( 0.06) is in good agreement with those reported in the literature. Our experimental result on D10/D0 is equal to about 0.12, where D10 denotes the final average diameter of the fragments, which is close to the measurements of Villermaux and Bossa18 (D10/D0 ≈ 0.19 at D0 < 10 mm), and our experimental result on SMD/D0 is equal to about 0.29, which is close to the measurements of Dai and Faeth23 (SMD/D0 ≈ 0.27 at We = 15). The experimental result of Chou and Faeth14 is SMD/D0 = 0.36. 3.4. Fragments Formed from Ring. The volume fraction of the ring is very large, so it has great influence on the mean fragment size. Many previous studies on drop breakup have also focused on the ring. Lane24 finds that the ring contains at least 70% of the mass of the original drop, which means Vring/ V0 > 0.70, where Vring is the volume of the ring and V0 is the volume of initial drop. The experimental result of Chou and Faeth14 is Vring/V0 = 0.56. Dai and Faeth23 carry out their measurements of bag breakup and mention a determination of Vring/V0 = 0.75 (at We = 15). Our experimental result is Vring/ V0 = 0.85 ( 0.04, which is close to the results of Lane24 and Dai and Faeth.23 The experimental result of Chou and Faeth14 is N = 28.1 and Dr/D0 = 0.30, while our result is N = 34.8 and Dr/D0 = 0.28, where N is the number (including nodes) of fragments formed from the ring and Dr is the mean size of fragments formed from the ring.

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Figure 7. Influence of We on N for different test liquids.

Wert25 proposes a correlation for SMD based on the physics of bag breakup. Actually, that mode is assumed to be governed by the growth of capillary instability waves on the ring. Therefore, it is a correlation for SMDring, where SMDring corresponds to SMD values of fragments formed from the ring. However, the most unstable wavelength chosen in the study of Wert25 is independent of air velocity and liquid viscosity. In atomization, air velocity and liquid viscosity have great influences on the maximum growth rate or most unstable wave,22,26 so further work is needed. In atomization, surface tension tends to pull the liquid into the form of a sphere, since this has the minimum surface energy. Liquid viscosity exerts a stabilizing influence by opposing any change in the system. On the other hand, aerodynamic forces acting on the liquid surface may promote the disruption process by applying an external distorting force to the bulk liquid.1 Therefore, Dr/D0 should decrease with We, and should increase with Oh. Figure 5 illustrates the typical behavior of Dr/D0 with We. The experimental results of Chou and Faeth14 are also shown in Figure 5, whose We is varied from 13 to 20. The results of Chou and Faeth14 were published in 1998, and they only obtained the mean value of Dr/D0. As technology progresses, we can obtain clearer pictures in experiments with the help of new high-speed cameras. More details such as the influence of the Weber number and the Ohnesorge number can be studied today. The state on N in Figure 7 is similar. The best fit correlations for the present measurements are as follows: Dr =D0 ¼ ð4:3 103 Þð1 þ 890Oh0:09 ÞWe0:82

ð5Þ

Dr/D0 values calculated using eq 5 are plotted against the measured values in Figure 6. Ng et al.27 study the bag breakup of nonturbulent liquid jets in air crossflow, whose test liquids include water and ethanol (low viscosity, so the effect of Oh is neglected). The best fit correlation for their measurements is SMDring =dj ¼ 4:8We1:0

ð6Þ

where dj is the liquid jet exit diameter. The effect of We in eq 5 is in good agreement with eq 6. Figure 7 illustrates the typical behavior of N with We. The experimental results of Chou and Faeth14 are also shown in Figure 7, whose We is varied from 13 to 20. N increases with We and decreases with Oh. 9770



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Figure 8. Comparison of measured N to N predicted by eq 7.

Figure 10. Fragment size distribution of the whole drop based on number.

fragment probability density function is a single-parameter gamma distribution, which is given by Pðx ¼ D=Dr Þ ¼

Figure 9. Fragment size distribution of ring based on number.

The best fit correlations for the present measurements are as follows: N ¼ 0:99ð1 þ 6:26Oh

0:26 1

Þ We

1:72

ð7Þ

N values calculated using eq 7 are plotted against the measured values in Figure 8. 3.5. Fragment Size Distribution. The fragment size distribution in drop breakup receives only cursory attention, even though it plays a key role in many practical processes. Komabayasi et al.28 report that the fragment size distribution for water drops undergoing bag breakup is bimodal, having two peaks. A large number of small fragments are produced when the rim of the bag disintegrates, whereas only a few large fragments are produced when the rim decomposes. Chou and Faeth14 argue that no bimodal behavior for drop size distribution and explain that undersampling of the small drops formed from the bag would tend to support the findings of bimodal distribution. Villermaux, Marmottant, and Duplat29 and Marmottant and Villermaux22 find that this gamma distribution closely fits the experimental fragment distribution after ligament breakup in primary atomization. Then, the work of Bremond, Clanet, and Villermaux30 shows that in sheet breakup a ligament structure appears first, and fragment size distribution is also a gamma distribution in sheet breakup. The ring in drop bag breakup can be considered as a kind of ligament. Our experimental result also shows that the fragment distribution of the ring is a gamma distribution. This indicates that the mechanisms of ligament breakup in both primary atomization and secondary atomization are similar. The experimental

nn n 1 nx x e ΓðnÞ

ð8Þ

where n = 3.68, P is the quantitative distribution, D is the diameter of ring fragment, and Dr is the average fragment size of the ring; Δx = 0.5. Figure 9 shows the fragment distribution after ring breakup in bag breakup. The sheet thickness is unchanged in the study of Bremond, Clanet, and Villermaux;30 however, the film thickness from bag to ring in bag breakup is changing. Therefore, all fragment size distribution of the initial big drop in bag breakup should be different from a single-parameter gamma distribution. The work of Villermaux and Bossa18 indicates that it can be considered to be the MarshallPalmer exponential distribution. The best fit of exponential distribution as shown in Figure 10 is given by Pðx ¼ D=D10 Þ ¼ ex

ð9Þ

where D is the diameter of fragment and D10 denotes the final average diameter of all fragments; Δx = 1. The experimental results of Villermaux and Bossa18 are also shown in Figure 10. Note that the thickness of the bag is limited, the fragments are not infinitesimal, and the fragments are also not infinite. Therefore, there should be a boundary of validity of exponential distribution (eq 9). The test of Villermaux and Bossa18 only contains one kind of liquid: water. Here we choose five kinds of liquids. Therefore we believe the scope of application of our experimental results is wider, and it is very useful in a lot of industrial processes. In order to obtain the cumulative volume distribution, eq 9 can become Z x x3 ex dx 0 Q ðx ¼ D=D10 Þ ¼ Z ∞ x3 ex dx 0 x

¼ 1e

1 1 1 þ x þ x2 þ x3 2 6

ð10Þ

where Q is the fraction of the total volume contained in drops of diameter less than D. At present the most widely used expression 9771



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used to describe the fragment size cumulative volume distribution of the whole drop. The format of the RosinRammler distribution could be widely used in industrial applications.

’ AUTHOR INFORMATION Corresponding Author

*Tel.: +86-21-64251418. Fax: +86-21-6425-1312. E-mail: hfliu@ ecust.edu.cn.

Figure 11. Fragment size cumulative volume distribution of the whole drop.

for drop volume distribution was originally developed for powders by Rosin and Rammler.31 The cumulative distribution function may be expressed in the form " # x k Q ðx ¼ D=D10 Þ ¼ 1 exp ð11Þ λ where λ and k are constants. λ, which is a representative diameter of some kind, is given by the value of D for which 1 Q = e1. Solution of this equation yields the result that Q = 0.632; that is, λ is the drop diameter such that 63.2% of the total volume is in drops of smaller diameter, then λ is made non-dimensional using the characteristic diameter D10. The exponent k provides a measure of the spread of drop sizes. The higher the value of k, the more uniform is the spray. If k is infinite, the drops in the spray are all the same size. For most sprays the value of k lies between 1.5 and 4.1 For the range of parameters studied a value of k equal to 1.99 is found to agree favorably with experimental data as shown in Figure 11.

4. CONCLUSIONS Investigations on the secondary breakup of liquid drops in the bag regime by a continuous, uniform cross-flow air jet were performed. The drop breakup of test liquids, including water, ethanol, and various glycerol mixtures was observed using a highspeed camera. Test conditions included Weber numbers of 9.423 and Ohnesorge numbers of 0.00180.36. The main conclusions can be summarized as follows (1) The influence of the Weber number and the Ohnesorge number on drop deformation was studied; the maximum deformation increased with Weber number and decreased with Ohnesorge number. An empirical correlation was also obtained. (2) Fragment mean diameter and number of ring were researched. Mean size decreased with Weber number and increased with Ohnesorge number; the fragment number was in contrast to mean size. The empirical correlations were also obtained. (3) Fragment size distribution based on number formed from the ring was found to be very well represented by a singleparameter gamma distribution. Fragment size distribution based on number formed from the whole drop was consistent with the MarshallPalmer exponential distribution. Finally, the RosinRammler distribution was

’ ACKNOWLEDGMENT This study was supported by the National Natural Science Foundation of China (20906024), the National Development Programming of Key Fundamental Researches of China (2010CB227005), the PetroChina Innovation Foundation (2009D-5006-04-05), and the New Century Excellent Talents in University (NCET-08-0775) by the Ministry of Education of China. ’ REFERENCES (1) Lefebvre, A. H. Atomization and Sprays; Hemisphere Publishing Corp.: New York, 1989. (2) Liu, H. F.; Gong, X.; Li, W. F.; Wang, F. C.; Yu, Z. H. Prediction of droplet size distribution in sprays of prefilming air-blast atomizers. Chem. Eng. Sci. 2006, 61, 1741–1747. (3) Villermaux, E. Fragmentation. Annu. Rev. Fluid Mech. 2007, 39, 419–446. (4) Wang, Y. J.; Kyoung, S. I.; Kamel, F. Similarity between the primary and secondary air-assisted liquid jet breakup mechanism. Phys. Rev. Lett. 2008, 100, 154502. (5) Eggers, J.; Villermaux, E. Physics of liquid jets. Rep. Prog. Phys. 2008, 71, 036601. (6) Caputo, G.; Adami, R.; Reverchon, E. Analysis of dissolved-gas atomization: supercritical CO2 dissolved in water. Ind. Eng. Chem. Res. 2010, 49 (19), 9454–9461. (7) Reverchon, E.; Adami, R.; Scognamiglio, M.; Fortunato, G.; Della, P. G. Beclomethasone microparticles for wet inhalation, produced by supercritical assisted atomization. Ind. Eng. Chem. Res. 2010, 49 (24), 12747–12755. (8) Rezvanpour, A.; Attia, A. B. E.; Wang, C. H. Enhancement of particle collection efficiency in electrohydrodynamic atomization process for pharmaceutical particle fabrication. Ind. Eng. Chem. Res. 2010, 49 (24), 12620–12631. (9) Theofanous, T. G. Aerobreakup of Newtonian and viscoelastic liquids. Annu. Rev. Fluid Mech. 2011, 43, 661–690. (10) Guildenbecher, D. R.; Lopez-Rivera, C.; Sojka, P. E. Secondary atomization. Exp. Fluids 2009, 6, 371–402. (11) Pilch, M.; Erdman, C. Use of breakup time data and velocity history data to predict the maximum size of stable fragments for acceleration-induced breakup of a liquid drop. Int. J. Multiphase Flow 1987, 13, 741–757. (12) Faeth, G. M.; Hsiang, L. P.; Wu, P. K. Structure and breakup properties of sprays. Int. J. Multiphase Flow 1995, 21, 99–127. (13) Gel’fand, B. E. Droplet breakup phenomena in flows with velocity lag. Prog. Energy Combust. Sci. 1996, 22, 201–265. (14) Chou, W. H.; Faeth, G. M. Temporal properties of secondary drop breakup in the bag breakup regime. Int. J. Multiphase Flow 1998, 24, 889–912. (15) Simmons, H. C. The correlation of drop-size distributions in fuel nozzle sprays. J. Eng. Power 1977, 99, 309–319. (16) Hsiang, L. P.; Faeth, G. M. Near-limit drop deformation and secondary breakup. Int. J. Multiphase Flow 1992, 18, 635–652. (17) Hsiang, L. P.; Faeth, G. M. Drop properties after secondary breakup. Int. J. Multiphase Flow 1993, 19, 721–735. 9772



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(18) Villermaux, E.; Bossa, B. Single-drop fragmentation determines size distribution of raindrops. Nat. Phys. 2009, 5, 697–702. (19) Cao, X. K.; Sun, Z. G.; Li, W. F.; Liu, H. F.; Yu, Z. H. A new breakup regime for liquid drops identified in a continuous and uniform air jet flow. Phys. Fluids 2007, 19, 057103. (20) Zhao, H.; Liu, H. F.; Cao, X. K.; Li, W. F.; Xu, J. L. Breakup characteristics of liquid drops in bag regime by a continuous and uniform air jet flow. Int. J. Multiphase Flow 2011, 37, 530–534. (21) Zhao, H.; Liu, H. F.; Li, W. F.; Xu, J. L. Morphological classification of low viscosity drop bag breakup in a continuous air jet stream. Phys. Fluids 2010, 22, 114103. (22) Marmottant, P.; Villermaux, E. On spray formation. J. Fluid Mech. 2004, 498, 73–111. (23) Dai, Z.; Faeth, G. M. Temporal properties of secondary drop breakup in the multimode breakup regime. Int. J. Multiphase Flow 2001, 27, 217–236. (24) Lane, W. R. Shatter of drops in streams of air. Ind. Eng. Chem. 1951, 43, 1312–1317. (25) Wert, K. L. A rationally-based correlation of mean fragment size for drop secondary breakup. Int. J. Multiphase Flow 1995, 21, 1063–1071. (26) Varga, C. M.; Lasheras, J. C.; Hopfinger, E. J. Initial breakup of a small-diameter liquid jet by a high-speed gas stream. J. Fluid Mech. 2003, 497, 405–434. (27) Ng, C.-L.; Sankarakrishnan, R.; Sallam, K. A. Bag breakup of nonturbulent liquid jets in crossflow. Int. J. Multiphase Flow 2008, 34, 241–259. (28) Komabayasi, M.; Gonda, T.; Isono, K. Lifetime of water drops before breaking and size distribution of fragment droplets. J. Meteorol. Soc. Jpn. 1964, 42, 330–340. (29) Villermaux, E.; Marmottant, P.; Duplat, J. Ligament-Mediated Spray Formation. Phys. Rev. Lett. 2004, 92, 074501. (30) Bremond, N.; Clanet, C.; Villermaux, E. Atomization of undulating liquid sheets. J. Fluid Mech. 2007, 585, 421–456. (31) Rosin, P.; Rammler, E. The laws governing the fineness of powdered coal. J. Inst. Fuel 1933, 7, 29–36.

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Experimental Study of Drop Size Distribution in the Bag Breakup Regime

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