Combined techniques of secondary atomization of multi-component droplets

Chemical Engineering Science 209 (2019) 115199

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Combined techniques of secondary atomization of multi-component droplets G.V. Kuznetsov, N.E. Shlegel, Ya. Solomatin, P.A. Strizhak ⇑ National Research Tomsk Polytechnic University, 30, Lenin Avenue, Tomsk 634050, Russia

h i g h l i g h t s

g r a p h i c a l a b s t r a c t


Combined techniques provide an over

10–15-fold decrease in droplets sizes.
Free liquid surface area can be

increased 40–50 times.
Homogeneous drops are intensively

crushed during collisions with walls and drops.
Micro-explosive atomization is more effective for multi-component droplets.
Experimental results are generalized using two initial droplets and an aerosol.

a r t i c l e

i n f o

Article history: Received 18 May 2019 Received in revised form 17 August 2019 Accepted 2 September 2019 Available online 3 September 2019 Keywords: Secondary droplet atomization Droplet collision Wall impact Incoming gas jet Micro-explosive breakup Combined atomization schemes

a b s t r a c t In this paper, we present the experimental results of a secondary droplet atomization study by combining four schemes: droplet collisions with each other, with a solid surface, with a gas flow, as well as microexplosive breakup of highly inhomogeneous liquid exposed to extensive heating. For each of the four schemes, we show the droplets sizes reduction range, atomization time, and the measured growth of liquid surface area. The latter parameter describes the intensity of the heat exchange and phase transitions at the liquid – gas interface. The experiments are conducted for water and water-based slurries and emulsions, including high-potential fuels. Basing on the experimental results for isolated droplets, we propose a technique for the experimental study of aerosol flows. We determine the droplets sizes that does not lead to its drastic increase due to coalescence or decrease due to disruption during aerosol cloud intermixing. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction 1.1. Contemporary secondary droplet atomization systems ⇑ Corresponding author. E-mail address: [email protected] (P.A. Strizhak). URL: http://hmtslab.tpu.ru (P.A. Strizhak). https://doi.org/10.1016/j.ces.2019.115199 0009-2509/Ó 2019 Elsevier Ltd. All rights reserved.

The atomization of liquid droplets in several stages is implemented in a number of applications, including fuel injection in boiler furnaces, cooling systems, internal combustion engines,

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Nomenclature b B Dl Ds G0 KEc KEe

distance between droplets’ centers of mass, m dimensionless linear droplet interaction parameter diameter of large droplet, m diameter of small droplet, m nozzle output, l/s initial kinetic energy of the interacting domains, Nm kinetic energy of the flows caused by surface tension, Nm KEes kinetic energy of stretching separation, Nm KEi, KEii, KEni, KEsii, KEdii, KEsni, KErni kinetic energies of stretching separation, Nm KEre energy of reflexive separation, Nm KEs kinetic energy of stretching flows, Nm n total number of all child droplets N number of child droplets with a stable average size rd Oh Ohnesorge number Q heat flux supplied to the wall, kW/m2 Qc heat flux supplied to the droplet, kW/m2 Rd droplet radius, m Rd1, Rd2 radii of the colliding (first and second) droplets, m rd radius of child droplets, m average radius of child droplets, m rad RE rotation energy, Nm Rl radius of large droplet, m Rs radius of small droplet, m S area of spherical particle, m2 S0 total area of droplets before atomization, m2 S1 total area of child droplets, m2 SEin initial energy of surface tension, Nm SElig surface tension energy of the ligament, Nm SEmd surface tension energy at the moment of maximum deformation, Nm

firefighting system, as well as heat-exchange equipment. The first atomization stage (primary atomization) involves injection nozzles. The second stage (secondary atomization) can be approached in several ways. The choice of the approach is based on the required fineness of the droplet aerosol. In this regard, a thorough study of the secondary droplet atomization is crucial for the development of highly efficient atomization technologies. The four most common secondary atomization techniques (Cen et al., 2018; Pasandideh-Fard et al., 2001; Cossali et al., 2005; Tang et al., 2017; Zhang et al., 2016; Biance et al., 2006; Cao et al., 2007; Lee and Reitz, 2000; Zhang et al., 2018; Avulapati et al., 2016; Jung et al., 2011; Planchette et al., 2010) are as follows: droplet disruption due to the impact with a solid surface (collision with a wall or substrate), due to droplets colliding with each other, due to micro-explosive breakup from overheating, and due to the impact with an incoming air flow (gas jet). The more components the droplet consists of and the more different their surface tension, density, and viscosity, the greater the difference in the integral characteristics of droplet fragmentation (Komrakova et al., 2015; Davanlou et al., 2015; Kékesi et al., 2016). When a droplet interacts with a solid surface, it deforms rapidly and then breaks up (short-term or long-term fragmentation) (Cen et al., 2018). Breakup characteristics (time, number, and size of resulting fragments – child droplets) are heavily dependent on two parameters: Weber number, which describes the relation of the two main forces (inertia and surface tension), and surface temperature (Cen et al., 2018; Pasandideh-Fard et al., 2001). The authors of (Cossali et al., 2005; Tang et al., 2017) also studied the secondary droplet atomization caused by their interaction with a solid sur-

t Td Ud Ud1, Ud2

time of droplet atomization, s initial droplet temperature, °C velocity of the droplet, m/s velocities of the colliding (first and second) droplets, m/s Urel resulting velocity of the droplets, m/s air flow velocity, m/s Ug Ul velocity of the larger droplet accounting for Urel, m/s Us velocity of the smaller droplet accounting for Urel, m/s VDE dissipation energy, Nm VDEsii, VDEdii, VDEsni, VDErni dissipation energy during stretching separation, Nm Vl volume of the large droplet, m3 Vli volume of the interaction zone of the large droplet, m3 Vs volume of the smaller droplet, m3 Vsi volume of the interaction zone of the smaller droplet, m3 We Weber number Greek symbols a total dissipation factor during collision a1, a2, a3, a4, a5 dissipation factors ad impact angle, ° b dimensionless angular interaction parameter h angle between the droplet velocity vectors and the line connecting their centers of mass, ° m dynamic viscosity, Pas q density, kg/m3 r surface tension, N/m D droplet size ratio

face, but unlike in (Cen et al., 2018; Pasandideh-Fard et al., 2001), those experiments were conducted for heated surfaces of different roughness. They explored the effect of the solid wall roughness and viscosity variation of the heated liquid on the atomization characteristics (Cossali et al., 2005; Tang et al., 2017). The experiments (Cossali et al., 2005; Tang et al., 2017) were conducted for water and water-glycerol solution. The initially generated droplets were 1.8–4.6 mm in diameter and their impact velocity varied from 1 m/s to 6 m/s. The child droplets diameters were ranged from 5.5 lm to several millimeters in study (Cossali et al., 2005; Tang et al., 2017). The secondary droplets sizes demonstrated almost a linear dependence on the initial droplets sizes and velocities. Zhang et al. (2016) presented the results of an experimental study and numerical simulation of droplet collision with a solid surface. They uncovered the defining effect of liquid properties on droplet spreading and bounce (Zhang et al., 2016). The dynamic viscosity coefficient appeared to have a greater effect than surface tension. Experiments have revealed that a large droplet generates much more secondary fragments than a micro-droplet, i.e., a significant atomization can be provided for a larger initial liquid particle. In study (Biance et al., 2006), the experiments focused on droplet interaction with a steel plate heated to a temperature of 20 °C to 300 °C. Experiments (Biance et al., 2006) revealed that the maximum radius of each secondary droplet generated by the disruption of the initial one is a function of the Weber number. Thus, the experimental results of (Cen et al., 2018; Pasandideh-Fard et al., 2001; Cossali et al., 2005; Tang et al., 2017; Zhang et al., 2016; Biance et al., 2006) show, that droplet interaction with a solid surface of widely different properties can lead to a substantial

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(up to several orders) variation in the integral characteristic relating the atomized fragments sizes to the initial droplets sizes. Hence, the ratios of liquid surface areas vary substantially as well. Another significant effect of the secondary atomization is achieved by shearing a droplet with an air flow in the form of a gas jet (Cao et al., 2007; Lee and Reitz, 2000). Experiments in study (Cao et al., 2007) were conducted for water and ethanol. Droplets were disrupted by the air flow at an ambient temperature and pressure. The initial droplet diameter varied from 2 to 6 mm, the velocity from 12 to 90 m/s, and the We number from 10 to 100. Lee and Reitz (2000) studied the disruption of a diesel droplet by an air flow. They discovered that droplet atomization depends on the Weber number. Experiments in studies (Cao et al., 2007; Lee and Reitz, 2000) revealed, that the critical We numbers related to a massive droplet breakup, are 50–70% higher than in solid surface impact experiments, especially comparing to a non-heated surface. One more atomization technique is the overheating of a lowboiling component (Zhang et al., 2018; Avulapati et al., 2016) to a point of internal bubble generation, coalescence, and expansion. Experiments (Zhang et al., 2018) were conducted to study the micro-explosive breakup of water-based ethanol solution droplets about 1.5 mm in diameter. The results demonstrate a critical overheat at approximately 180 °C for an ambient pressure. Avulapati et al. (2016) concentrated on the micro-explosive breakup of fuel droplets. They were placed onto the thermocouple tip with the help of a micropipette. The size of droplets ranged from 1 mm to 1.5 mm. The main result of experiments in studies (Zhang et al., 2018; Avulapati et al., 2016) is that the micro-explosive breakup of the initial droplet generates secondary fragments 80–300 lm in size, that is 5–8 times as small. An increase in the heating temperature can provide a more than 10-fold size reduction (Zhang et al., 2018; Avulapati et al., 2016). It is the micro-explosive breakup of heterogeneous droplet (e.g., slurry, emulsion, solution, immiscible two- or multi-component composition) that demonstrates the smallest size and the largest number of the generated secondary liquid fragments (most commonly in the form of a polydisperse aerosol cloud) (Zhang et al., 2018; Avulapati et al., 2016). But since the micro-explosive breakup is a result of extensive heating, a considerable amount of energy supply is required. Basing on the results of a number of known experiments, including (Zhang et al., 2018; Avulapati et al., 2016), any heating scheme can be advised as an efficient one: convective, conductive, radiative, or combined. Each scheme is characterized by its own threshold heat flux that is necessary and sufficient for a transition from a step-by-step droplet disruption into large fragments to a micro-explosive breakup into a cloud of miniature liquid fragments. The latter are called child droplets. The last common approach to secondary atomization involves droplets colliding with each other. This scheme is considered the easiest one to implement and the least energy-consuming. In study (Jung et al., 2011), a series of experiments were conducted with a water-glycerol solution. Jung et al. (2011) studied the interaction of two spray jets intersecting at different angles to each other in order to research the effect of the impact angle. The droplet velocity ranged from 1 to 6 m/s. A rapid droplet atomization was observed at high flow velocities. The dependence of the collision outcomes on droplets sizes, relative velocity, density, liquid viscosity, and surface tension was studied in Planchette et al. (2010). The experimental results of studies (Jung et al., 2011; Planchette et al., 2010) clearly show that even the simplest secondary atomization scheme of initial droplets colliding with each other can provide a considerable fragmentation. This is especially important for the case of mixing aerosol flows. Experimental results of studies (Jung et al., 2011; Planchette et al., 2010; Komrakova et al., 2015; Davanlou et al., 2015; Kékesi et al., 2016) allow us to conclude, that critical (necessary and sufficient) conditions and typical droplet

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breakup outcomes in case of mutual collisions are dependent not only on the Weber number, but also on a large group of different factors, including liquid viscosity, droplet structure and composition, their geometric shape, etc. That is why the size of the resulting liquid fragments may vary in quite a wide range. 1.2. Combined primary and secondary droplet atomization systems Significant decreasing of droplets sizes can be enhanced by combining primary and secondary atomization schemes (directly in the active zone of chamber, unit, or plant), as well as the above techniques. Primary atomization is implemented via various injection nozzles. Secondary atomization in this case can be provided by crossing the nozzle spray cones, by droplet collision with the chamber wall, or by overheating the liquid fragments to their boiling point. Experiments in study (Ko and Ryou, 2005) were conducted to study the effect of the impact angle and distance on the characteristics of intersecting jets. General spraying shape, droplets sizes and its spatial distribution were taken into consideration. When exiting the nozzle, the droplets had a radius of 4 mm. A four times smaller radius of 1 mm was achieved through secondary droplet atomization. Injection pumps of equal burst frequency were used in study (Wang et al., 2003) to study droplets colliding with each other. Droplet generator settings were tuned to achieve the required impact angle. The initial droplet radius varied from 0.1 to 0.4 mm. Post-collision droplets coalesced and fell in a vertical channel that was combined with a high-temperature oxidizing combustion chamber to create a micro-explosion. After a microexplosive breakup, the average ratio of the resulting to initial droplet diameter reached 0.7–0.8. A series of experiments in study (Zhang et al., 2018) was aimed to study the fuel aerosol collision with a wall at a certain angle. It revealed that the impact angle has a considerable effect on the structure of the atomized aerosol and the characteristics of the resulting film. The experimental setup consisted of an injection system, a high-speed camera, and LED lighting. A single-channel injector was used with a nozzle to generate a fuel droplet of 0.135 mm in diameter. After the impact with an angled wall, a droplet was split into fragments of 0.025–0.1 mm in size. Two highspeed cameras were used for recording. They were positioned frontally and laterally to reliably record the size and number of child droplets, as well as the dimensions of the aerosol cloud the droplets formed. Combining primary and secondary atomization schemes may potentially optimize liquid spraying. This is especially important in the case of highly inhomogeneous droplet aerosols in terms of component composition. In practical applications, integral atomization characteristics depend on the gas medium and droplet flow parameters, since discontinuous phase particles of various sizes may switch to turbulent motion. Droplet interaction in such conditions becomes much more complicated (Solsvik et al., 2016; Arogeti et al., 2019). The secondary atomization of liquid droplets due to their mutual collisions is described in studies (Liu et al., 2018; Chen et al., 2016; Chen, 2007; Pawar et al., 2016; Kohno et al., 2013). Here the authors studied the effect of droplet sizes, velocities, and shapes, as well as component concentration and linear dimensionless interaction parameter on droplet collision behavior: separation, disruption, coalescence, or bounce. Atomizers or liquid pumps with spray nozzles were used as droplet generators. Biodiesel emulsion, water, or ethanol served as liquids under test. The size of the generated droplets ranged from 700 to 1000 lm. In articles (Buck et al., 2018; Luo et al., 2018; Fujimoto et al., 2001; Bertola, 2015; Fujimoto et al., 2010), the authors studied

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the breakup of isolated droplets due to their impact with a solid surface. The studies concentrated on the properties of the resulting liquid fragments after the initial droplet collided with solid surfaces of different sorts. The latter had various roughness and thermophysical characteristics and were heated to different temperatures. The authors went on to explore the effect of droplet impact angle, size, velocity, as well as liquid properties (viscosity, surface tension, density) on the solid surface collision behaviors and outcomes. Luo et al. (2018) also studied droplet fuel aerosols colliding with a solid surface. Almost every study on droplet breakup due to the wall impact mentions a wide range of factors, whose variation can drastically change droplet breakup threshold and characteristics. The main factors here are wall roughness, hydrophobic property, and temperature; droplets sizes, velocities, and impact angle; thermophysical and rheological properties of liquids. Experimental setups for recording droplet deformation and breakup in a gas environment are all based on the same principle. As an example let us consider a setup from study (Flock et al., 2012) where Flock et al. studied the deformation of isolated ethanol droplets injected into a continuous air jet. A generator was used to create droplets. A nozzle and a compressor were used to generate the air flow. The air flow velocity was measured using the PIV technique. In these experiments, the authors recorded the droplet surface transformation rate, its shape, size, transition time from one geometry to another, breakup threshold conditions, and the size and number of resulting fragments. Droplet micro-explosion was explored in studies (Meng et al., 2018; Tarlet et al., 2014, 2016a, 2016b). These studies focused on the breakup and ignition of biodiesel and ethanol droplets. A muffle furnace was used to heat the free falling droplet to eliminate the effect of a holder or a substrate on the droplet disruption. The results of the last 30–50 years of the worldwide study on the micro-explosion effect on the droplet disruption allow us to conclude that experimental setup design is aimed at enhancing one of the heat supply types: convective, conductive, radiative, or combined. That is why it is reasonable to create a setup with one predominant heat exchange mechanism, providing critical (threshold) heat flux to ensure complete disruption of a droplet. 1.3. Contemporary size specifications for homogeneous and inhomogeneous liquid droplet for advanced gas-vapor-droplet applications Droplets sizes and velocities variation in contemporary injection systems may differ in quite a wide range. Droplets sizes have a significant effect on the integral characteristics of heat and mass transfer, phase transitions, and chemical reactions. As an example, study (Boulet et al., 2013) describes the research of heat exchange enhancement for a tubular and fin-type heat exchanger using the air flow containing water droplets. It was determined that the evaporation with a sufficiently fast phase transition rate requires droplets less than 25 lm in diameter, since larger droplets evaporate less intensely. A condenser heat transfer was studied in study (Tissot et al., 2011), considering the air cooling by droplet evaporation in the condenser flow. It was established that the evaporated mass ratio reaches 30–50% when using droplets 25–50 lm in size. Feng et al. (2019) reviewed an advanced spraying technology aimed at minimizing the pollutant concentration (relative to typical average) in wastewater by evaporating pollutants in the flue duct of a thermal power plant. The authors also presented a model of wastewater evaporation in flue gases. When modeling, they used droplets sized 20–100 lm. The droplets sizes range is quite wide for different industrial spray injectors. For instance, it is 10–200 lm for diesel injectors and 250–1000 lm for sprinklers. Atomized droplet velocity may

vary as well, from several centimeters to hundreds of meters per second. The knowledge of the optimal droplets sizes is crucial when designing cooling systems based on heat exchange with atomized liquid flows. Sometimes, droplets in an aerosol can be extremely small. For instance, water atomization for preliminary air cooling at the cooling tower input was researched in studies (Kachhwaha et al., 1998; Alkhedhair et al., 2013; Raoult et al., 2019; Tissot et al., 2012). The required droplets sizes here are less than 20 lm (Alkhedhair et al., 2013; Raoult et al., 2019). For spray to be used as a pre-condenser coolant, the optimal size of the droplet is less than 25 lm (Tissot et al., 2012). Unfortunately, atomizing droplets to 20–100 lm in size directly in the active zone of the chamber, using only spray injectors, is not viable for most of the industrial gas-vapor-droplet technologies. The main reason is that droplets being that small would be entrained by the upcoming heated gas and carried away from the mixing zone, or they will settle on chamber walls during the flow agitation. In this case, primary atomization is highly inefficient, so its exclusive use is not feasible. Additional atomization seems to be reasonable to implement. The purpose of this research is to experimentally establish the efficiency of the secondary atomization techniques combined for multi-component liquid droplets.

2. Experimental setup and procedure When planning the experimental research, we accounted for the progress made so far by the scientific community in studying the atomization of liquid droplets with various component compositions when using separate and combined secondary atomization methods. As a rule, such research is notable for limitations and challenges that should be taken into account by successive researchers. In particular, we accounted for the recommendations and comments on the methods expressed in papers (Liu et al., 2018; Chen et al., 2016; Chen, 2007; Pawar et al., 2016; Kohno et al., 2013; Buck et al., 2018; Luo et al., 2018; Fujimoto et al., 2001; Bertola, 2015; Fujimoto et al., 2010; Flock et al., 2012; Meng et al., 2018). For instance, Liu et al. (2018) used a video camera similar to the one we used in this research. The video frames were processed using the Photron Fastcam Viewer software package. Liu et al. (2018) studied the head-on collision of droplets using specialized capillaries. Chen et al. (2016) explored the collisions of emulsion and biodiesel droplets. Using automatic generators, they produced liquid droplets 0.7–1 mm in size. The collisions were recorded using a high-speed Phantom video camera. The experiments in (Chen et al., 2016) were conducted under ambient pressure and at ambient temperature. In terms of the size of initial droplets and the processing order of the frames with droplet collisions, this research is in good agreement with the experiments from Chen et al. (2016). Pawar et al. (2016) studied liquid droplets colliding with each other. They were recorded by a high-speed video camera HighSpeedStar (LaVision HS3G). The 105 mm macro-lens Sigma DG used with this camera is similar to the one used in our research. Buck et al. (2018) researched the collisions of liquid droplets with a solid wall similar to the one used in these experiments. The collisions were recorded using a high-speed video camera with a frame rate of 7000 fps. Bertola (2015) analyzed the collision characteristics of liquid droplets with a solid surface. Droplets were generated by a nozzle (21-gauge hypodermic needle 0.495 mm in diameter). In this research, nozzles were made of similar needles. The collisions of liquid droplets were recorded using a high-speed video camera Mikrotron MC1310 with a resolution of 576  576 pix and frame rate of 1000 fps. Meng et al. (2018) used a rotary muffle furnace (like in this research) to provide the conditions for the micro-explosive atomization of

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multi-component droplets. The process was recorded using a highspeed video camera with a frame rate of 250 frames per second. The size of the recording area was 1024  1024. When planning the experiments in this research, we took into account all the features and limitations of droplet atomization recording mentioned in papers (Liu et al., 2018; Chen et al., 2016; Chen, 2007; Pawar et al., 2016; Kohno et al., 2013; Buck et al., 2018; Luo et al., 2018; Fujimoto et al., 2001; Bertola, 2015; Fujimoto et al., 2010; Flock et al., 2012; Meng et al., 2018). 2.1. Droplet atomization setup Prior to designing the experimental setup for the combined secondary atomization techniques, we studied the progress of the scientific community in terms of advanced setup and recording schemes (Lee and Reitz, 2000; Zhang et al., 2018; Avulapati et al., 2016; Jung et al., 2011; Planchette et al., 2010; Komrakova et al., 2015; Davanlou et al., 2015; Kékesi et al., 2016; Ko and Ryou, 2005). For instance, an experimental setup for studying the atomization characteristics is outlined in study (Ko and Ryou, 2005). The setup consisted of water sprayers, a plunger pump controlled by a SV-IG5 digitizer, a TM0038X flowmeter, and an ECO-1 KELLER digital pressure gage. Injector nozzles for those experiments had a round opening 400 lm in diameter. A DualPD system was used to register droplets sizes and velocities. The system featured a laser, a transmitter and a receiver, a band pass filter, and a signal processing unit. Water spraying was also studied in Lee and Reitz (2000). The setup used in study (Lee and Reitz, 2000) consisted of a pressurized spraying chamber, liquid droplet generator, gas nozzle, lighting source, microscope, and a video camera. Droplets interacted with the gas flow at a high relative velocity. The microscopic visual recording system featured a high-intensity light source and a video camera combined with a Questar QM-100 microscope. This kind of systems provides us with high level of reliability when studying the atomization of homogeneous and highly inhomogeneous droplets. In this work, in order to enhance the atomization, we used a setup that allowed us to implement several secondary atomization schemes. This is the scientific novelty of this research. The discovered synergistic effects of the combined secondary atomization techniques demonstrate the practical value of the experimental results for advanced gas-vapor-droplet applications. 2.2. Droplet atomization techniques We used experimental setups (Fig. 1) that allowed us to combine several techniques of initial droplet atomization: mutual collision followed by gas jet disruption, breakup due to solid wall impact, and micro-explosive breakup due to extensive heating. To study the mutual droplet collision, disruption by a gas jet, and by collision with a solid wall, we used a setup shown in Fig. 1a. Droplets were generated by nozzles (8) fixed to a ring holder (6). By changing the fixed position of the nozzle in the ring holder, we changed the impact angle. The liquid was supplied to the nozzle from tank (5) by a submersible water pump with an output of 1.2–1.6 l/min. Controllers (7) are responsible for the variation of the sprayed liquid velocity. After the droplets collide with each other (Fig. 2a), they are further atomized by a gas jet. Gas (air) jet is generated by compressor (16). When a shutter opened in front of nozzle (17), a short burst of the air flow occurred, aimed at the downward droplet and disrupting it (Fig. 2b). Then the droplet fell onto the heated wall (substrate), breaking up by impact (Fig. 2c). To heat the substrate surface, we used lab-grade voltage converters (4) with an output current of 40 A and an output voltage

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of 0–250 V. Tank (3) was installed at the bottom of the setup to collect the atomized liquid. Fig. 1b shows a setup used to study the aerosol droplet disruption by solid surface impact. Two aerosol flows were generated by sprayers (10) with the liquid supplied to them from containers (11). Three interchangeable spray nozzles of different flow rates (0.09, 0.017, 0.025 l/s) were used. After two aerosol flows collided, droplets fell onto heated solid surface (2). To study the micro-explosive droplet breakup, we used a setup shown in Fig. 1c. Droplets from generator (12) went onto the solid substrate (15). The resulting smaller droplets then went down to muffle furnace (13), where the micro-explosive disruption occurred (Fig. 2d).

2.3. Recording the characteristics of the processes under study The interacting liquid droplets were recorded using a highspeed video camera (resolution up to 1152  864, 3000 to 100,000 frames per second). With an increase in the frame rate, the resolution went down. The minimum allowable resolution was chosen depending on the droplet atomization scheme and the size of resulting liquid fragments. Using the Photron Fastcam Viewer software, we determined the droplet velocities before collisions and impact angles between them. For that we used temperature field grid and a scale coefficient, which varied in the experiments when we varied the initial experimental parameters. Fig. 2 shows frames with single liquid droplets being atomized according to each of the schemes under study. The initial dimensions of single droplets can be reliably determined using the Photron Fastcam Viewer software and the scale coefficient. To do that, we need to measure at least four droplet diameters (since droplets are non-spherical) and average the resulting value. This way we can calculate the Rd values. To analyze the frames showing the consecutive droplet atomization by their collision with each other, interaction with a substrate, air jet impact, and microexplosive breakup, we used the Shadow Photography technique (SP) (Kuznetsov et al., 2016), because the recording area contained a large array of objects rather than just one. In this case, it is possible to determine the average size of pre-atomization droplets (Rd) at each stage as well as the average size of newly formed child droplets (rad). To determine the number (N) and size (rd) of child droplets resulting from the atomization of initial droplets, we used the SP technique based on the Actual Flow software system. For all the experiments, we used the manual focus with the help of the Multi-Function Calibration Target (for Low Magnification Systems). This target helped us determine the focal depth of the lens. The target as placed in the recording area and the focus was set manually to the zero mark. Then we measured the distance to the next visible mark on the target. This distance was the focal depth. The scale coefficient was determined in the same way. The grid was chosen so that the scale coefficient was three times as small as the typical droplet size. No less than 3 pix corresponded to the smallest droplets resulting from the micro-explosive breakup of initial droplets. The recording area size was as follows: 25  32 mm to 31  38 mm for droplets colliding with each other, 25  34 mm to 27  36 mm for droplets colliding with a wall, 220  270 mm to 330  274 mm for droplets disrupted by the air flow, and 14  14 mm to 17  17 mm for the micro-explosive breakup of droplets. Scale coefficients: 0.025 mm/px to 0.032 mm/px for droplets colliding with each other, 0.025 mm/px to 0.029 mm/px for droplets colliding with a wall, 0.25 mm/px to 0.31 mm/px for droplets disrupted by the air flow, and 0.018 mm/px to 0.023 mm/px for the micro-explosive breakup of droplets. The initial droplets were at least 0.054 mm in size for all the disruption schemes other than in the experiment involving

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Fig. 1. Experimental setup with colliding droplets (a), aerosol flow (b), muffle furnace for micro-explosion (c), and four droplet atomization schemes used (d): 1 – high-speed video camera; 2 – metal surface; 3 – tank for liquid fragments; 4 – laboratory-grade voltage converters; 5 – liquid reservoirs with built-in submersible pumps; 6 – nozzleholder disc; 7 – pump performance control; 8 – nozzles; 9 – protective casing; 10 – aerosol flow generators; 11 – aerosol generator reservoirs; 12 – droplet generator; 13 – muffle furnace; 14 – protective cylinder; 15 – compressor; 16 – nozzle; I – droplet collision; II – oncoming air flow interaction; III – solid surface interaction; IV – microexplosive droplet breakup due to extensive heating.

atomizers, in which the minimum droplet diameter was 0.01 mm. The scale coefficient amounted to 0.0026 mm/px. The operating principle of the SP technique is based on using a set of algorithms and procedures that deserve a detailed comment. The initial video frame of droplet collision was high pass filtered (using High-Pass or Laplace Edge Detection) to determine the outlines recorded on the image of the object. Then we set the binarization threshold to exclude the background noise. After that, droplet

boundaries were the only thing left on the frame. At the next stage, we searched for simply connected domains to determine the droplet positions, number, and size. However, non-spherical objects reduce the accuracy of their size measurement. The software identifies an ellipsoid object as a circle of a certain effective radius, i.e., the more distorted the shape of an object, the lower the accuracy. Therefore, it is important to choose the initial droplet size and conditions of their atomization so that the resulting fragments were

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Fig. 2. Experiment video frames for four droplet (emulsion No 2) atomization schemes: droplet collision (a); oncoming air flow impact (b); solid surface interaction (c); micro-explosive droplet breakup due to extensive heating (d).

near-spherical. In addition, to improve the accuracy, we did not consider the droplets following each other in the recording area. We used the following algorithms: Bubbles Identification to determine the positions and radii of the objects and Instant Void Fraction to calculate the instant local content of the discontinuous phase. Bubbles Identification is applied to image nodes and produces a result in the form of irregular data fields with the locations and radii of the identified objects. Instant Void Fraction is applied to irregular data nodes containing the information on the location

and radii of the objects and produces a result in the form of irregular data fields (grids), whose nodes contain the information on the local content of the discontinuous phase. Using the SP technique, we can automatically calculate the total number of child droplets (n) as well as the number of child droplets (N) in the form of certain groups with the radius rd. The number of such groups can be set at random depending on the need to refine the size distributions of child droplets. The comparative analysis of droplet atomization efficiency can help determine the minimum

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and maximum radius of child droplets or calculate the average size of all the secondary droplets (rad). Since not all the child droplets were in the recording area, we introduced an adjustment coefficient for the number of child droplets to ensure that their total volume equals the volume of the initial droplets before atomization. The number and size of invisible droplets were determined assuming that the post-atomization droplets spread evenly in space. With such an assumption, if the distribution is two-dimensional, one can reliably predict three-dimensional distributions. To adjust the methods of measuring child droplet characteristics, we performed test experiments and calculated the corresponding characteristics to provide an acceptable agreement with the data obtained when using two video cameras. We established that the differences in the average size of child droplets did not exceed 12% and their number differed by no more than 8% when we used two video cameras and one video camera (i.e., 3D and 2D recording, respectively). Video frame processing provided us with data on droplet velocity (Ud) (systematic error 1.6%, random error 2.1%), size (Rd) (systematic error 2.1%, random error 3.4%), impact angle (ad) (systematic error 2.3%, random error 3.1%), collision mode, and the number of the resulting child droplets. In the software used for image processing, we set the binarization threshold that allowed us to detect all droplets, even the smallest ones, given that a droplet image is at least 3 pixels large. We analyzed the number and total volume of the small droplets, for which the 3 pix threshold condition was valid. The total volume of such droplets did not exceed 2% of the initial droplet. The measured parameters served to calculate the following values: Urel=(|Ud1|2+|Ud2|2–2|Ud1||Ud2|cos(ad))0.5, Weber number We = q2RdU2rel/r, Ohnesorge number Oh = m/(qr2Rd)0.5, as well as the interaction parameters: B = b/(Rd1 + Rd2), b = cos(ad). Here Rd is the size of small droplet. Areas of free surfaces of the source droplets and those formed as a result of fragmentation were calculated as S = 4pR2d. Since some drops were out of the focal extent of the lens, the volumes of the two initial drops and the drops formed at interaction were taken equal. Preliminary experiments using a group of high-speed video cameras have shown that the number of small drops outside the focus of registration can be from 7 to 12%. Taking into account that their sizes are very small, this factor will contribute to the change of the total surface area of all liquid fragments by 3–6%. Based on these estimates, the number of produced drops was increased in equal shares to ensure this equality. When droplets of Emulsion No 2 collided with each other and the Weber number approximated 150, the minimum radius of child droplets was about 0.05 mm and the average, about 0.1 mm. This means that there are much more small droplets than large ones. When the scheme of atomization in the air flow was used for this composition with the same Weber number, more fragments were produced with a smaller radius (about 0.039 mm). However, the number of large droplets went down, which reduced the average radius by 0.03 mm. With microexplosive atomization, the minimum size of child droplets was 0.03 mm, and the number of such droplets was at its maximum.

That is why the average radius approximated 0.04 mm. A collision with a wall with We  150 produced the so-called crown, which increased the average radius of child droplets up to 0.17 mm. The smallest newly formed liquid fragments were about 0.09 mm. 2.4. Materials In this research, we focused on typical liquid compositions used in advanced chemical engineering and gas-vapor-droplet applications. We used coal particles to produce slurries, since coal-water slurries (CWS) and coal-water slurries containing petrochemicals (CWSP) are becoming increasingly popular as fuels in many countries, e.g., China, Japan, Russia, Sweden, etc. (Glushkov et al., 2016). Using water-containing fuel based on used oil, oil sludge, and CWSP is a way to decrease the carbon dioxide emission (Glushkov et al., 2016). Transformer oil was chosen for its wide use as part of CWSP fuel. Used transformer oil can also be an alternative fuel for diesel engines (Nabi et al., 2013). Being a petroleum product, transformer oil is a waste-water contaminant as well. Studying this emulsion can help with the improvement of thermal water treatment. Diesel was chosen for its wide use in every industry and for being an automobile fuel (Xu et al., 2018). The characteristics of components are presented in Table 1. 3. Results and discussion 3.1. Preliminary experiments with isolated droplets and aerosol flows for each of the four atomization schemes The data in Figs. 3 and 4 is given for the cases of single initial droplets and the analysis of their atomization dynamics to prevent the possible influence of neighboring droplets. We made this decision to analyze in detail the possible effects of droplet atomization using each of the four schemes separately. Data in Figs. 5–7 is presented for a large array of droplets showing the mutual influence of neighboring droplets. Their role was negligible as compared to the effect of each droplet disruption mechanism. That is why, when evaluating the degree of droplet atomization using various schemes, we can use at a first approximation both the methods with single initial droplets and with a group of droplets. Fig. 3 shows the child droplet distribution in an aerosol cloud after the initial droplet atomization according to each of the four schemes. Micro-explosive breakup clearly provides the largest number of child droplets with the smallest radius (0.05 mm). There are much fewer large droplets and their number decreases drastically with an increase in the radius of child droplets. For droplets colliding with each other or a solid surface, the largest number of resulting smaller fragments is observed for the same radius of the droplet (0.05 mm). For these two schemes, the droplet distribution is similar, with the maximum and minimum observed for similar droplets sizes. In the air jet impact atomization, the largest number of fragments is observed for 0.05 mm and 0.1 mm radii. The number of secondary fragments sized from 0.3 to 0.4 mm is the smallest for all the four schemes.

Table 1 Component concentrations and characteristics. Composition name (volume and mass concentration of additives to water are given)

Initial temperature Td, °C

Density q, kg/m3

Surface tension r, N/m

Dynamic viscosity m, Pas

Water Slurry No 1 (10 wt% coal, 90 wt% water) Slurry No 2 (10 wt% coal, 10 wt% transformer oil, 80 wt% water) Emulsion No 1 (10 vol% transformer oil, 90 vol% water) Emulsion No 2 (90 vol% diesel, 10 vol% water) Heptane-hexadecane compositions 34–66 vol% (Wang et al., 2003). Average density, surface tension, and viscosity are given

20 20 20 20 20 20

998 1046 996 986 878 684

0.0726 0.1091 0.0946 0.0674 0.0151 0.0198

0.0014 0.0017 0.0034 0.0032 0.0013 0.0018

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2=3  KEe ¼ r  p  Dl 2 1 þ D2   1 þ D3 ; h i KEs ¼ 1=2  q  ðV l  V li Þ  U l 2 þ ðV s  V si Þ  U s 2 ; VDE ¼ aKEc :

Fig. 3. Typical droplets sizes distribution in aerosol cloud after atomization by each of the four schemes (We100, emulsion No 2): droplet collision (1); solid surface interaction (2); oncoming air flow impact (3); micro-explosive droplet breakup due to extensive heating (4).

The initial kinetic energy (KEc) depends on the droplet size and amounts to 40–85% of the resulting kinetic energy of the reflexive separation (KEre). For instance, for the radius Rd approximating 0.2 mm, the KEc value reaches 85% of KEre. This provides stable conditions for the reflexive separation of colliding droplets. The above formula for the VDE shows that it is in direct proportion to the dissipation energy, which contributes 16–42% to the KEc value and also depends on the droplet radius (Rd). When the droplet size is increased to 1 mm, reflexive separation is only possible with the low resulting interaction velocity – no more than 0.5 m/s. At this velocity, the kinetic energy of the stretching flows (KEs) prevails. It increases up to 35% of KEre, which leads to the reflexive separation regime. In turn, the kinetic energy of the superfluous surface flows (KEe) is directly proportional to surface tension (its contribution to the energy balance ranges from 28% to 35% of KEre). Moreover, such energy depends on droplet size but has a much lower impact: when the radius is reduced from 1 mm to 0.2 mm, the contribution of KEe ranges from 2% to 5% of KEre. When the interaction velocity is reduced, however, the KEe contribution may reach 20– 25% of KEre. Based on the models proposed in Ashgriz and Poo (1990), Hu et al. (2017), the reflexive separation occurs when the kinetic energy of reflexive separation exceeds 75% of the surface tension energy, i.e.:


2=3 KEre P 0:75  r  p Dl 3 þ Ds 3 : When stretching separation occurs, the initial kinetic energy includes two constituent parts: the initial kinetic energy of the interaction zone and the initial kinetic energy of the interaction-free zone. The kinetic energy of stretching separation and its constituent parts are given by (Ashgriz and Poo, 1990; Hu et al., 2017): Fig. 4. Resulting fragments sizes compared to initial liquid (emulsion No 2) droplets, for each of the four schemes: I – droplet collision; II – solid surface interaction; III – oncoming air jet impact; IV – micro-explosive droplet breakup due to extensive heating. The minimum power is 220 kW/m2, since stable microexplosive breakup occurred under such conditions with the heterogeneous droplets of all the emulsions and slurries under study.

To clarify the reasons behind liquid droplet atomization in each of the four schemes under study and to find the most effective conditions of reducing the values of the rad/Rd ratio, it is sensible to analyze the main sources of influence with the critical Weber numbers being sufficient for the rapid atomization of initial droplets. Quite a common practice in this case is the analysis of the energy balance in the atomization zone, for instance, as shown in (Ashgriz and Poo, 1990; Hu et al., 2017) for two colliding droplets. When considering the scheme with colliding droplets, separation is usually subdivided into reflexive and stretching separation (Ashgriz and Poo, 1990; Hu et al., 2017) to identify two droplet interaction regimes that are different in their dominating factors. During the reflexive separation of droplets, the kinetic energy in their collision zone and its constituent parts are given by (Ashgriz and Poo, 1990; Hu et al., 2017):

KEre ¼ KEc þ KEe  KEs  VDE;
 KEc ¼ 1=2  q  V li  U l 2 þ V si  U s 2 ;

KEi ¼ KEii þ KEni ¼ KEsii þ KEdii þ KEsni þ KErni ; KEsii ¼ 1=2  q  ½V si  ðU s  sinðhÞÞ þ V li  ðU l  sinðhÞÞ ; 2

2

KEdii ¼ 1=2  q  ½V si  ðU s  cosðhÞÞ2 þ V li  ðU l  cosðhÞÞ2 ; KEsni ¼ 1=2  q  ½ðV s  V si Þ  ðU s  sinðhÞÞ þ ðV l  V li Þ  ðU l  sinðhÞÞ ; 2

2

KErni ¼ 1=2  q  ½ðV s  V si ÞðU s  cosðhÞÞ2 þ ðV l  V li ÞðU l  cosðhÞÞ2 : When droplets collide, the viscous dissipation energy is given by (Ashgriz and Poo, 1990; Hu et al., 2017):

VDE ¼ VDEsii þ VDEdii þ VDEsni þ VDErni ; VDEsii ¼ a2  KEsii ; VDEsni ¼ a3  KEsni ; VDEdii ¼ a4  KEdii ; VDErni ¼ a5  KErni : For stretching separation to occur, the total effective stretching energy must exceed the energy of the surface tension of the ligament (Ashgriz and Poo, 1990; Hu et al., 2017):

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Fig. 5. Maximum liquid (emulsion No 2) surface area ratio, for each of the four schemes: droplet collision (1); solid surface interaction (2); oncoming air flow impact (3); micro-explosive droplet breakup due to extensive heating (4). Weber number varied for schemes 1–3; heat flux towards droplet varied for scheme 4.

Fig. 6. Maximum liquid (emulsion No 2) surface area ratio for combinations (I–IV variants) of several schemes: 1 – droplet collision; 2 – oncoming air flow interaction; 3 – heated solid wall impact; 4 – non-heated solid wall impact; 5 – micro-explosive breakup. The values of S1/S0 for all the atomization schemes applied consecutively are marked with ellipsoids.

KEes ¼ KEi  VDE  RE P SElig ; SElig ¼ ð2  r  ½p  h  ðV si þ V li ÞÞ : 0:5

When the droplet size varied in the range of 0.2 < Rd < 1 mm, the initial kinetic energy of the droplet responsible for stretching along the radial direction (KEsii) varied within 1%. Other constituents of kinetic energy remained practically the same. We can conclude that droplet size has little effect on the stretching separation of droplets. Droplet acceleration can increase the probability of separation occurrence due to droplet stretching but one of the main conditions is Ud1 > Ud2. When this condition holds, the kinetic energy of viscous dissipation (KErni) grows from 5% to 70% of KEi. A larger impact angle causes an increase in the viscous dissipation

energy (KErni) from 50% to 70% and an increase in the droplet stretching energy converting into the energy of surface tension and dissipation (KEsni) from 25% to 35%, depending on the resulting kinetic energy of reflexive separation (KEi). The kinetic energy acting in the radial direction (KEdii) and the initial kinetic energy of the droplet responsible for stretching along the radial direction (KEsii) have a much lesser impact on droplet separation with the total contribution being less than 2% of KEi. This happens because the energy KEdii converts into the viscous dissipation energy and the energy KEsii partially converts into the surface tension energy of the ligament and viscous dissipation energy. The analysis of the research findings from (Ko and Ryou, 2005) indicates that stretching separation resulted in more small

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Fig. 7. Droplets sizes distribution in water aerosol cloud for different nozzles, as well as the nozzle output: 1 – 2.5 mm diameter nozzle; 2 – 2 mm diameter nozzle; 3 – 1 mm diameter nozzle; 4 – collision of aerosol flows generated by nozzle No 1; 5 – collision of aerosol flows generated by nozzle No 2; 6 – collision of aerosol flows generated by nozzle No 3.

droplets than reflexive separation. In this work, we have identified a similar pattern. The child droplets produced from stretching separation were 1.5–2.3 times as many as those from reflexive separation. Using the experimental data, we estimated the number and size of child droplets produced by the collisions of initial emulsion, slurry, and water droplets. Typical size distributions of child droplets for emulsion No 2 are given in Figs. 3 and 4. As an example, we can compare the child droplet size distributions for water, slurry No 1, and emulsion No 2. According to the experimental data, with the same size of initial droplets (for instance, Rd = 0.5– 0.8 mm) and the Weber number of 150–180, parent droplets of slurry No 1 produced 5–10% more child droplets sized under 0.1 mm than emulsion No 2 and almost 50% more than water. The energy balance only accounts for the child droplets produced after the collision of the two initial droplets. When the newly formed fragments of over 0.2 mm move further, stretching forces may cause their secondary atomization. During the reflexive separation of two colliding liquid droplets, the most significant influence on the number of newly formed child droplets came from the kinetic energy of the stretching flows (KEs). For instance, two colliding droplets of slurry No 1 with the initial size of 0.6 mm and the Weber number of about 160 produced 89 satellite droplets under 0.12 mm in size. The KEs contribution to the resulting kinetic energy (KEre) reached 43%. The same-size droplets of emulsion No 2 produced 78 secondary droplets sized under 0.12 mm. KEs was approximately 37% of KEre. In the experiments with water, only

11

37 child droplets were formed with a size of less than 0.12 mm, and the KEs contribution was about 31% of KEre. With an increase in the velocity and size of initial droplets (and, therefore, with the growing Weber number), the kinetic energy of the stretching flows went up. This increased the number of child droplets. The number of child droplets was also affected by the initial kinetic energy (KEc). In the above conditions, the contribution of KEc to the resulting kinetic energy (KEre) was as follows: about 57% for slurry No 1, about 55% for emulsion No 2, and about 51% for water. The analysis of the stretching separation regime shows that viscous dissipation energy had the greatest influence on the number and size of child droplets. The collision of two droplets of slurry No 1 with a size of 0.55 mm and the Weber number of 155–175 produced 105 child droplets less than 0.1 mm in size. The KErni contribution was 64% of the resulting kinetic energy. The collision of emulsion No 2 and water droplets with the same parameters produced 89 and 52 satellite droplets, respectively. The KErni contribution was 59% and 42%, respectively. Using the generalized experimental data, we determined the threshold conditions of slurry and emulsion droplet disruption producing at least 10 child droplets. Droplets of slurry No 1 and 2 atomized consistently when their initial size ranged from 0.35 to 0.6 mm with D = 0.8–1, the resulting interaction velocity was above 3.6 m/s and the impact angle was 60–90°. For emulsions No 1 and 2, stable atomization was observed when the droplet size was 0.3 to 0.6 mm with D = 0.8–1, the resulting interaction velocity was at least 3.7 m/s and the impact angle ranged from 60 to 90°. For water, consistent atomization was recorded with droplets sized from 0.4 to 0.8 mm and D = 0.8–1 at the resulting interaction velocity above 3.9 m/s and the impact angle of 60–90°. Thus, slurry atomization required lower threshold kinetic energy of the stretching flows (KEs) (for reflexive separation) and kinetic energy of viscous dissipation (KErni) (for stretching separation) as compared to emulsions and water without additives. With the identical size, velocity, and impact angle of the colliding droplets, the values of KEs/KEre and KErni/KEi are higher for slurries. This provides more child droplets. When the liquid droplets are atomized by the oncoming air flow, this causes a change in the constituent parts of the total kinetic energy of reflexive separation and stretching separation. The total kinetic energy of reflexive separation contains a number of summands including the determining parameters of the two droplets. When the droplets are atomized by the air flow, only one droplet is taken into account, so the constituent parts of the second droplet are eliminated. Other than that, the energy balance is determined in the same way. Since the surface of a droplet exposed to the air flow undergoes transformation, no stretching separation occurs (the corresponding frames were not recorded in the experiments). Therefore, the kinetic stretching energy is minimum. The initial kinetic energy (KEc) of reflexive separation depends on the initial droplet size and makes a major contribution to the stability of the disruption regime – 62% to 70% of KEre. Thus, the dissipation energy is rather high – 28% to 36% of KEre. Unlike droplet collisions with each other, in this interaction regime, the energy of the stretching flows does not have any impact on the atomization of the initial droplet. When droplets collide with a solid surface, the kinetic energy of reflexive separation must account for the liquid layer formed at the surface. This makes it possible to factor in the dissipation energy. The same pattern holds true with stretching separation. The summand in the energy balance typical of the second droplet can be replaced by the summand resulting from the liquid layer at the wall surface. The thickness of this layer does not remain constant: it varies with each of the consecutive droplets hitting the wall. The contribution of energies to reflexive separation is similar, just as under the air flow exposure. If the liquid layer formed at the

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surface is taken into account, this contribution changes: KEc makes up 60–70% of KEre, VDE ranges from 20 to 30% of KEre, and KEe equals 10–15% of KEre. When it comes to the micro-explosive disruption of droplets, the decisive role belongs to the two threshold (necessary and sufficient) conditions also known as droplet fragmentation criteria (Sazhin et al., 2019; Fujimoto et al., 2010; Flock et al., 2012; Meng et al., 2018; Tarlet et al., 2014, 2016a, 2016b). The first criterion is based on the assumption that for the disruption to occur, it is enough to provide that the non-combustible component – water – exceeds its boiling temperature, i.e. 100 °C. The second criterion comes from the assumption that if the bubble being formed in a droplet becomes 2–3 times as large as the initial droplet, this will cause the micro-explosion of the latter. The analysis of data from (Sazhin et al., 2019; Fujimoto et al., 2010; Flock et al., 2012; Meng et al., 2018; Tarlet et al., 2014, 2016a, 2016b) indicates that the first criterion is the reason behind bubble nucleation at the interface between the combustible and non-combustible components within a droplet, and the second criterion characterizes the threshold condition of the complete droplet breakup. The second criterion cannot be fulfilled without the first one. The fulfillment of the first criterion is possible without the second one but only under long-term heating (for 3–10 s) at relatively low temperatures (under 500 °C). Under such conditions, puffing may occur, i.e., partial droplet fragmentation with polysize liquid fragments breaking off. In this research, the heating temperature was much higher (around 1000 °C), since we needed to provide the fast disruption (within 0.2–0.3 s) of moving droplets. The use of both criteria was validated by comparing the experimental and theoretical research findings (Sazhin et al., 2019; Fujimoto et al., 2010; Flock et al., 2012; Meng et al., 2018; Tarlet et al., 2014, 2016a, 2016b). The conclusions in (Sazhin et al., 2019; Fujimoto et al., 2010; Flock et al., 2012; Meng et al., 2018; Tarlet et al., 2014, 2016a, 2016b) indicate that any of the two criteria is enough to predict the conditions sufficient for the active micro-explosive breakup. The fulfillment of these criteria means that the bubble pressure forces in the droplet exceed the forces of the liquid surface tension. In other words, the energy balance shifts towards the forces caused by the increased vapor pressure within a droplet. In this research, we did not use droplet temperature recording equipment. That is why the droplet and bubble size data was the only indicator that the threshold conditions of micro-explosion were fulfilled. It was established that when the droplet size grows 1.8–2.4 times of its initial size due to bubble size increase, the droplet breaks up in the micro-explosion regime. We can conclude that preliminary stages of droplet atomization involving their collisions with each other, with a wall, or with an oncoming air flow promote droplet deformation and swirling. This intensifies the convection in heterogeneous droplets, which reduces the droplet heating time until micro-explosive breakup, as shown in the experiments in Antonov et al. (2019). The conclusions from Antonov et al. (2019) and the atomization scheme sequence considered in this research helped us formulate a hypothesis that this factor led to a 15–25% decrease in the heating time until breakup. Thus, the differences in the number and size of satellite droplets shown in Figs. 3 and 4 as indicators of atomization intensity may be explained by a shift in the energy balance towards the domination of the corresponding forces described above. The key observation of this research is that all the four schemes depend heavily on the correlation of the inertia, viscosity, and surface tension forces. The lower the surface tension, the lower the inertia forces observed during stable droplet atomization (see further for the threshold Weber numbers). The higher the viscous forces to surface tension ratio (for instance, between slurries and emulsions), the larger the child droplets, i.e., the rad/Rd ratio is higher (Figs. 3 and 4). To obtain the minimum rad/Rd values (and, therefore, the maximum

S1/S0 values), the inertial forces must prevail over the surface tension forces and the surface tension must prevail over the viscous forces. When comparing the child droplets obtained in the experiments with slurry, emulsion and water droplets, we observed these trends fully. Further, when considering rad/Rd, we will present the Weber and Ohnesorge numbers for the liquid compositions under study, reflecting the correlation of inertial forces and surface tension forces, as well as viscosity and surface tension. Fig. 4 shows the ratio of resulting fragments sizes and initial droplets sizes calculated from the experimental data for each of the four atomization schemes. The smallest ratio of 7 is demonstrated in the disruption scheme of droplets colliding with each other. For solid surface impact scheme and gas jet impact scheme, the resulting fragment sizes are comparable. But the size ratio is larger for the air jet scheme (10). Maximum pre-disruption to post-disruption size ratio is demonstrated by the micro-explosive breakup scheme. Here the ratio reaches 16. Thus, micro-explosive breakup gave the highest liquid surface area ratio as compared to other atomization schemes (Fig. 5). All schemes demonstrate a considerable increase in the surface area. Again, the micro-explosion breakup scheme shows the maximum growth. This atomization scheme is able to provide up to 100 times increase in the free liquid surface area. The smallest increase in the surface area is shown by the droplet collision scheme and the solid surface impact scheme. For both of these schemes, the free liquid surface growth is similar in nature. Air jet impact increases liquid surface area more than 5–6 times. For the droplets colliding with each other with the Weber number approximating 100, Fig. 4 gives the droplet radius before atomization and the average radius of the newly formed child droplets. With the same Weber number and the same scheme, Fig. 5 shows the ratios of the liquid droplet areas before and after the atomization. The radii of all child droplets were factored in the calculations of such parameters. That is, there are 132 child droplets with a size ranging from 0.05 to 0.3 mm and the average radius equals 0.15 mm. The ratio of the liquid surface areas (S1/S0) equals 3.4 and rad/Rd makes up 0.19. Thus, it is important to account for rad/ Rd and S1/S0 when analyzing all the four atomization schemes. When calculating the total free surface area of child droplets (S1), we account for their size distribution, i.e., a wide variation range of rd. When it comes to calculating the ratio of the precollision droplet size to the size of the newly formed fragments, we use the average radius of child droplets (rad). Since the radii of child droplets (rd) vary in a wide range (often from 0.01 to 0.5 mm), this affects the variation ranges of S1/S0 and rad/Rd. For instance, in the case of water droplets colliding with each other, with the initial radii being around 0.55 mm and We100, 48 child droplets were produced ranging from 0.05 to 0.35 mm. The liquid surface areas before and after the collision were 7.64 mm2 and 19.13 mm2; S1/S0  2.51. At the same time, the ratio of the average radius of the newly formed child droplets to the initial droplet size (rad/Rd) approximates 0.32. Now let us consider the collision of droplets with the same initial dimensions when We  150. 73 child droplets were produced, ranging from 0.05 to 0.3 mm in size. The calculations showed that the area ratio S1/S0  3.13 and the size ratio is about 0.21. Using several atomization schemes (Fig. 6) leads to a several times bigger increase in liquid surface area compared to the application of a single scheme. The experiments show that combining four atomization schemes (droplet collision, air jet impact, heated solid surface impact, and micro-explosive breakup) allows us to increase the liquid surface area several dozens of times. The most drastic increase in the surface area is recorded at the third stage, when previously atomized droplets are disrupted due to the impact with the substrate, especially if the substrate is heated. The same combination of the four schemes, only with a non-

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heated substrate at the third stage, shows slightly less increase in the surface area. The least increase in the liquid surface area is demonstrated by a combination of the three schemes: droplet collision, solid surface impact, and a micro-explosive breakup as the third stage. Using the heated substrate at the second stage of the above combination leads to a 1.4 times more growth of the surface area than if using the cold substrate. In general, from Fig. 6 we can conclude that the most important role in combined atomization techniques is played by the impact with a heated solid surface, if preceded by droplet breakup due to their collisions with each other and with the oncoming air jet. A similarly drastic increase in the liquid surface area is observed when the micro-explosive breakup atomization is applied as the last step of the combined scheme. Fig. 7 shows the size distributions of droplets in an aerosol cloud when we used the atomizer nozzles 1 mm, 2 mm, and 2.5 mm in diameter. It is established that with the largest atomizer nozzle, water consumption is 1.5–2.5 times as high as with other atomizers. This leads to the formation of 2–6 times as many small droplets as with other atomizers. Quite a narrow range of droplet dimensions in a spray cone is explained by the high pressure of the spraying device, which leads to droplet separation at the outlet of the nozzle. When aerosol flows coming from the same size nozzles collide with each other, the size of small droplets remains the same (clearly visible in Fig. 7). At the same time, the number of large droplets (over 0.05 mm) goes down because they collide with neighboring droplets and break up. As a result, the number of droplets smaller than 0.05 mm increases by almost 10% for all the atomizer sizes. The main conclusion from Fig. 7 is that with the initial droplet size under 0.1 mm, the droplets are difficult to atomize even with high liquid consumption, i.e., with the high relative concentration of droplets in a flow. The experiments show that with varying impact angle and Weber number in a wide range (0–90° and 50 < We < 200), the distributions of newly formed child droplets differ from the initial ones by no more than 15% in both their number (N) and average radius (rad). A significant atomization is only possible when the initial droplet size exceeds 0.1 mm. For instance, with droplets of about 0.5 mm, it is possible to vary N and rad several-fold by varying the liquid consumption, impact angle, and, therefore, the Weber number.

Fig. 8. Ratios of free surface areas of liquid droplets for the consecutive application of four atomization schemes (droplet collision, oncoming air jet impact, solid surface interaction, micro-explosive droplet breakup): 1 – water (without microexplosive droplet breakup); 2 – emulsion No 1; 3 – emulsion No 2.

3.2. Efficient combinations of secondary droplet atomization schemes

Fig. 9. Ratios of free surface areas of slurry droplets for the consecutive application of four atomization schemes (droplet collision, oncoming air jet impact, solid surface interaction, micro-explosive droplet breakup): 1 – water (without microexplosive droplet breakup); 2 – slurry No 1; 3 – slurry No 2.

From Fig. 8 we can observe that the S1/S0 ratio varies significantly (several-fold) in the range of the relatively small Weber number (We < 100), where droplets may interact in different regimes: coalescence, bounce, separation, and disruption. In the case of bounce and separation, the S1/S0 ratio does not change. Coalescence stimulates a slight variation in S1/S0, and in the disruption regime (also called fragmentation) this ratio may vary considerably, depending on the collision dynamics. The lower the droplets sizes and velocities, the smaller the number of liquid fragments (child droplets) resulting from disruption. Maximum S1/S0 is observed when We ranges from 100 to 125 for the three compositions and remains virtually constant in this range. Efficient atomization in this range of We can be observed for emulsion No 2, because the S1/S0 ratio is significantly higher than that of water in the same conditions. In the case of highly inhomogeneous (multicomponent) droplet atomization, for all the three compositions the droplets sizes variation interval is similar across the whole We number range, i.e. a monotone increase of S1/S0 is observed (Fig. 9). For We from 100 to 125, the maximum S1/S0 was observed reaching 200–250. Notably, the S1/S0 for slurries is significantly higher than for water. It is

250

S 1/S0

200

1 2 3

150

100

50

0

0

50

100

150

200

We

explained by the solid component in the slurry droplet that stimulates the surface transformation due to agglomeration. The analysis of Figs. 8 and 9 can help reveal a distinctive feature of slurry atomization. The atomization of slurries containing coal particles does not provide the same ratios of the free surface areas before and after atomization as emulsions do, since the size of the solid fraction in slurries is limited to about 100 lm. A slurry droplet cannot be atomized to be smaller than the solid particles therein, unlike an emulsion droplet. Nonetheless, the differences of rad/Rd and S1/S0 between emulsions and slurries did not exceed 15%. The difference was this small because the concentration of solid particles in the slurries was not high. Fig. 10 shows the curves for the ratio of the average child droplets sizes to the initial droplets sizes for the combined atomization scheme: droplet collision, gas jet impact, solid surface impact, and micro-explosive breakup. We compare these results with the data from (Wang et al., 2003) obtained for the combined atomization scheme as well. A 30–40% difference in the atomization fineness is observed. It is explained by the different combination sequence

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Fig. 10. Fragments sizes variation of emulsion No 2 for a combined secondary atomization scheme (droplet collision, gas jet impact, heated surface impact, and micro-explosive breakup) (curve 1) compared to the data for 34–66 vol% heptanehexadecane compositions (Wang et al., 2003) (curve 2). The surface tension of emulsion No 2 is 26% lower, density is 28% higher, and viscosity is 27% higher than that of water.

– droplet collision followed by micro-explosive breakup. This combination leads to a longer droplet disruption time, which is a crucial parameter for the practical application of the scheme in industrial combustion chambers. From the analysis of Fig. 11 we can conclude that viscosity and surface tension make a significant contribution to the stability of the atomization regime. In particular, we can see, that diesel emulsion No 2 can be disrupted at 30–60% smaller We number than water. Suspended solid particles contained in the slurry provided almost 40–50% decrease in the threshold We number for the transition to the disruption regime. The experimental results provided us with important knowledge on the generation of child droplets from initial droplets of different viscosity and surface tension. In particular, we discovered that the higher the surface tension, the stronger aerodynamic force and heat flux is needed for active

atomization. This effect is in line with the known concepts and is explained by the balance between viscous friction, surface tension, and inertia, all affecting the droplet. Changing the initial liquid viscosity led to a significant difference in the child droplet generation rate. The higher the viscosity, the faster the child droplet cloud appeared with the droplets sizes remaining constant until the next atomization technique in the sequence. Thus, for the fast atomization of the initial droplet, we should choose a highly viscous liquid with low surface tension. However, the higher the liquid viscosity, the larger the average size of child droplets, so the contribution of liquid viscosity and surface tension should be accounted for simultaneously. If the role of surface tension dominates over that of viscosity, the atomization is more intense. Therefore, many slurries and emulsions usually break up into more child droplets than water. This is why Fig. 11 shows lower rad/Rd and higher S1/S0 for all the emulsions and slurries than for water. By combining the known atomization techniques, we can achieve a several hundred-fold increase in the liquid surface area in a matter of seconds. The comparison of the data for slurry No 1 and No 2 shows that rad/Rd is 7–54% lower and S1/S0 6–9% higher for the slurry with the lower Oh. When analyzing the properties of these slurries (Table), we found that surface tension differs 1.15 times and viscosity, almost two times. The surface tension variation range is in good agreement with the S1/S0 variation range and the viscosity variation range corresponds to the rad/Rd variation range in Fig. 11. When comparing the properties of the emulsions used (Table), we found that surface tension differs 4.4 times and viscosity, 2.5 times. The rad/Rd ratio is 4–6% lower and S1/S0 5–7% higher for the emulsion with the higher Oh. This is because the viscosity and surface tension of emulsion No 1 are much higher than those of emulsion No 2. Data in Fig. 11 can be conveniently used to outline the combination of inertia, viscosity, and surface tension for different liquid compositions that provides the steady secondary atomization by droplet collision, solid wall impact, or gas jet impact. After one or several of these three atomization schemes, thermal microexplosion can be implemented in addition. However, as our experiments show, it is necessary to estimate the possible variation

Fig. 11. Threshold Weber number values in the disruption regime (for three secondary atomization schemes: I – droplet collision; II – gas jet disruption; III – heated surface impact). The ratio of the mean size of child droplets to the ratios of the initial droplet is shown in a square. The ratio of the liquid surface area after disruption to the initial one is shown in a circle. For each liquid, the value of the Ohnesorge number is determined for a certain droplet size to illustrate the correlation of viscosity and surface tension.

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interval of the droplets sizes and liquid surface area. When combining several atomization schemes, it is practical to evaluate power and time consumption as well as the possible scale of droplet atomization. For instance, when spraying highly inhomogeneous droplets, especially those containing solid particles, it is advisable to use large channels and relatively low pressure to counter the effects of corrosion and adhesion. Due to these limitations, primary spraying can only provide a coarse droplet aerosol. Further atomization can be provided by one or several secondary atomization schemes. Depending on the properties of a particular chamber or unit, different sequences of atomization steps can be implemented. This research describes the most practical and efficient sequences and combinations. 3.3. Promising avenues for the development of combined atomization schemes Consecutive implementation of several secondary droplet atomization schemes leads to a significant increase in the free liquid surface area. This type of parent-droplet disruption technique is quite effective for water decontamination from solid and liquid anthropogenic pollutants. A usual source of a large amount of contaminated industrial and waste water are the chemical, petrochemical, metal, and energy industry plants. The situation with the large volume of wastewater is exacerbated by the massive amount of energy needed even for the efficient cutting-edge water treatment. This is why most of the large plants have a dedicated subdivision in the form of a foundry, laboratory, or boiler station producing utility vapor and hot water. Every steam or hot water boiler operates with high-temperature flue gas generation, which is considered waste heat. It can be used for the thermal treatment of industrial and waste water. In this case, it is possible, with minimum technological expenses, to create a water-treatment unit using combined droplet atomization schemes. These will provide the exact droplets sizes needed to evaporate all the liquid, separate the vapor, and condense the treated liquid. Solid impurities will deposit, and liquid ones will burn out. For instance, at nonferrous metal industry plants the flue gases from the furnace have a temperature of over 1000 °C. This heat can be efficiently used to heat up the evaporation chamber walls and the air inside. It will provide the required conditions for additional atomization through micro-explosive breakup and heated wall impact. From the experimental results we know that, for the efficient use of these two atomization schemes, it is enough to heat the walls up to 400– 500 °C. With this temperature of the surface (first stage), droplets (second stage), and gas (third stage), water slurry and emulsion treatment from solid and liquid anthropogenic pollutants will only take only several seconds after the initial aerosol spraying. It is important to adjust the technology to the initial wastewater droplets sizes and the capabilities of the heating chamber. Since solid surface impact and micro-explosion of droplets contribute the most to the atomization process, the optimal course of development is to decrease the cost of these steps. If we place the heater, furnace, and high-power chamber next to the solid surface involved in droplet disruption, this will eliminate the need in additional heaters meant to maintain the wall temperature. For example, heat from the furnace and heating chamber, where microexplosive disruption is taking place, can be fed to the surfaces involved in atomization. A reasonable conclusion would be that the development of reliable and adequate physical and mathematical prediction models is of utmost importance for advancing the secondary droplet atomization technology in relation to multi-component liquids: emulsion and slurry fuels, fire-extinguishing agents, and other chemical technology compounds. The experiments described in this work show that the characteristics of child droplets are diffi-

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cult to determine for each of the compositions tested. A lot of time is needed for video frame processing to establish and confirm the size and number of child droplets for each atomization scheme. Existing models often require the average empirically obtained child droplets sizes as initial parameters. The results of our experiments can serve as this empirical evaluation to advance the model development (Sazhin et al., 2019; Antonov et al., 2019; Ko and Ryou, 2005; Focke et al., 2013; Moqaddam et al., 2016; Liu and Bothe, 2016). Consolidated results across the range of liquids of different viscosity, density, and surface tension allow us to predict child droplet characteristics for different initial component compositions. Reliable models of the researched processes may help develop efficient standardized technologies of secondary droplet atomization that would provide the required fineness. Ko et al. (Sazhin et al., 2019) developed a model to predict the number and size of new liquid fragments resulting from droplet collision in the disruption regime. They also calculated the ratio of satellite droplet diameters to the initial droplet diameter. In this study, we calculated a similar parameter but this time we accounted for all the newly formed child droplets, that is, the main fragments corresponding to the two initial droplets were also factored in the calculations, unlike in study (Ko and Ryou, 2005). Using the results from Ko and Ryou (2005), we evaluated the ratios of the average size of satellite droplets to the initial size of precollision droplets. The values of this parameter are given in Fig. 11 for our experiments. In study (Ko and Ryou, 2005), the diameter ratio reached 0.4. In this research, it was 0.12 when a droplet was disrupted by air and 0.35 when droplets collided with each other. This indicates the satisfactory agreement of data in Fig. 11 and (Ko and Ryou, 2005). Thus, the atomization schemes proposed in this research can be used for various component compositions of droplets including those used in study (Ko and Ryou, 2005). Ko and Ryou (2005) determined the critical Weber numbers for stretching separation and reflexive separation, which approximated 20. In this research, however, we identified the disruption regime and did not divide it into further types. We show that the minimum Weber number for the disruption induced by colliding droplets is about 25. Hu et al. (2017) modeled the collision of aluminum oxide droplets (this compound is a slurry). Therefore, the experimental data from Hu et al. (2017) can be compared with the atomization characteristics of slurry No 1 and slurry No 2 studied in this research. Overall, the critical conditions of full droplet breakup appeared to be quite close in the scheme of droplets colliding with each other. Since the micro-explosive atomization of slurries and emulsions can be intensified, it seems promising to further study the micro-explosive fragmentation of aluminum oxide droplets. Sazhin et al. (2019) created a model of microexplosive atomization in water-fuel emulsion droplets. The minimum diameter of child droplets was found to approximate 0.05 mm. In this research, the micro-explosive atomization produced the minimum droplet diameter of 0.054 mm. This result indicates the adequacy of the research methods and high accuracy of determining the number and size of child droplets. Moreover, it shows the possibility to use any combination of the four approaches (Fig. 6) to secondary atomization of high-potential fuel-water droplets (Sazhin et al., 2019). 4. Conclusion (i) We have established that droplets colliding with each other decrease in size 7–8-fold, i.e., the average values of (rad/Rd)1 are in this range. Such conditions are typical, for instance, of the colliding diesel emulsion droplets with Rd = 0.8–1.1 mm and the Weber number of 140–180. The radii of newly formed child droplets rd range from 0.1 to 0.4 mm. The

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S1/S0 ratio reaches 4–5. The sizes of secondary fragments after solid surface impact and air jet impact are similar; initial to secondary droplets size ratio for the air jet impact disruption is 10. For droplets with Rd = 0.8–1.1 mm collide with a wall with the Weber number being 160–180, the rd values make up 0.05–0.3 mm, and S1/S0 varies in the range of 30– 43. In the experiments with the oncoming air flow, the rd ranges from 0.1 to 0.3 mm with the initial values of Rd = 0.7–1 mm and the Weber number of 170–180. The experiments show that the maximum pre-disruption to post-disruption droplet size ratio is demonstrated by the micro-explosive droplet breakup through overheating. Here, the parent droplet size to child droplets size ratio can be over 15. For the micro-explosive breakup of emulsion and slurry droplets heated in a gas at a temperature of about 1000 °C, the rd makes up 0.01–0.05 mm, and S1/S0 ranges from 100 to 120. With the Weber number above 180, none of the four schemes provides a significant change in rad/Rd or S1/S0. Therefore, the rad/Rd and S1/S0 values given above can be considered threshold ones if each of the four schemes is used individually. (ii) A more significant increase in S1/S0 and decrease in rad/Rd is possible if a combination of two, three, or four atomization schemes is used. Experimental research has shown that the best possible atomization of both homogeneous and inhomogeneous liquid droplets can be provided if all the four atomization schemes are combined. The following scheme sequence is recommended for maximum efficiency: droplet collision; air flow impact (as a gas jet pulse); heated solid surface impact; micro-explosive breakup by heating in specialized chambers or furnaces. This particular combination provides the 40–50-fold growth of the free liquid surface area (i.e., increase in the S1/S0 ratio). The experiments show that if all the four schemes of emulsion droplet atomization are used consecutively and We = 100–150, the S1/S0 ratio may reach 200–230. For slurry droplets, these values will be somewhat lower, namely 170–190, under identical atomization conditions. For water without additives, such high S1/S0 ratios cannot be achieved since the microexplosive breakup of homogeneous water droplets is impossible (solid or liquid additives are needed for that). (iii) Using the experimental data, we have singled out the threshold Weber number ranges for all the compositions under study in each atomization scheme: We = 43–80 for droplets colliding with each other, We = 27–46 for the air flow impact, and We = 60–105 for the solid wall impact. When the We numbers exceed these values, the parent droplet breaks up to form a cloud of small fragments. The experimental research helped us identify the greatest deviations of the threshold Weber number for water, emulsions, and slurries. For instance, for droplets colliding with each other, the critical Weber number for water is 60% higher than for emulsion No 1 and 65% higher than for slurry No 1. When droplets are atomized by the air flow, the critical Weber number for water is 40% higher than for emulsion No 1 and 45% higher than for slurry No 1. For droplets colliding with a wall, the threshold Weber number for water is 45% higher than for emulsion No 1 and 40% higher than for slurry No 1. Thus, we can conclude that for the atomization of heterogeneous droplets (it is typical for emulsions and slurries), lower velocities, dimensions, and Weber numbers are required than for water without any additives. Thus, in chemical technologies based on multi-component slurries and emulsions, it is expedient to use the combined droplet atomization schemes considered in this research.

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