Omar Moussa

Diego Francelino

Dominique Tarlet

Patrizio Massoli

Jérôme Bellettre

Jerome Bellettre
email: jerome.bellettre@univ-nantes.fr

Jerome Bellettre

Insight of a w/o emulsion drop under leidenfrost heating using laser-induced fluorescence optical diagnostics

Keywords: atomization, biofuel, emulsion, droplet, micro-explosion, LIF, fluorescence, image treatment Interface tension N.m -1 λ Wavelength m µ Viscosity Pa.s 𝜌 Density kg.m -3

D

Diameter m HLB Hydrophilic-lipophilic balance -

Oh

Ohnesorge number -T Temperature (°C) 1. INTRODUCTION In the last decades, the international scientific community is facing the challenge of the century: the energy independence. Currently, the principal source of energy in the world comes from fossil fuel combustion. Energy overconsumption and the effects induced by the fossil fuel combustion (change of the atmosphere composition with the greenhouse gases associated emissions) led to serious damages to our health and planet (Baker et al., 2007;[START_REF] Solomon | Climate Change 2007-the Physical Science Basis: Working Group I Contribution to the Fourth Assessment Report of the IPCC[END_REF].

Interest has been growing in using alternative fuels, like emulsified fuels, as it was demonstrated that adding water in hydrocarbon fuels can reduce the exhaust emissions.

According to some authors, the use of these emulsified fuels or water-in-oil (W/O) emulsions can lead to the reduction of NOx, PM, CO and soot emissions (Khan et al., 2014a;[START_REF] Kadota | Recent Advances in the Combustion of Water Fuel Emulsion[END_REF][START_REF] Armas | Characterization of Light Duty Diesel Engine Pollutant Emissions Using Water-Emulsified Fuel[END_REF][START_REF] Marchitto | Optical Investigations in a CI Engine Fueled with Water in Diesel Emulsion Produced through Microchannels[END_REF][START_REF] Hagos | Water-in-Diesel Emulsion and Its Micro-Explosion Phenomenon-Review[END_REF][START_REF] Mura | Contribution à l'étude de la Micro-Explosion d'une Goutte d'émulsion d'eau dans l'huile : Impact de la Granulométrie de la Phase Dispersée[END_REF]. Indeed, presence of water inside the oil phase can trigger the phenomenon called "micro-explosion". It can be defined as the secondary atomization of the W/O emulsion drop under strong heating, caused by the phase change of water droplets (liquid water into steam). Microexplosion strongly relies on the boiling points difference of oil (200-300 °C) and water (100 °C).

The emulsion drop atomization permits a cleaner and complete combustion thanks to the emulsion drop break up, which leads to a better air-fuel mixing [START_REF] Crookes | Systematic Assessment of Combustion Characteristics of Biofuels and Emulsions with Water for Use as Diesel Engine Fuels[END_REF][START_REF] Matiello | Experimental Evidences for Micro-Explosion in Water/Fuel Oil Emulsion Flames Inferred by Laser Light Scattering[END_REF][START_REF] Nazha | Effect of Water Content on Pollutant Formation in a Burning Spray of Water-in-Diesel Fuel Emulsion[END_REF][START_REF] Mizutani | In Situ Observation of Micro-Explosion of Emulsion Droplets in Spray Flames[END_REF][START_REF] Fuchihata | The Effect of Water Content Diameter on the Structure of Light Oil-Water Emulsion Spray Flames[END_REF][START_REF] Geng | Effects of Alternative Fuels on the Combustion Characteristics and Emission Products from Diesel Engines: A Review[END_REF][START_REF] Hagos | Effect of Emulsification and Blending on the Oxygenation and Substitution of Diesel Fuel for Compression Ignition Engine[END_REF].

Micro-explosion is also characterized by its random aspect: in certain cases, the water embedded droplets phase change is not powerful enough to break the oil phase, leading to a partial atomization called "puffing" [START_REF] Shinjo | Physics of Puffing and Micro-Explosion of Emulsion Fuel Droplets[END_REF]Watanabe et al., 2009). Thus, the phenomenon can be analyzed by introducing a statistical parameter called "occurrence of microexplosion", defined as the ratio of number of optimal atomization and number of emulsion drops tested [START_REF] Moussa | Parametric Study of the Micro-Explosion Occurrence of W/O Emulsions[END_REF]. Quantitative and qualitative works about parameters influencing micro-explosion showed a great correlation between coalescence (even partial) of water embedded droplets and micro-explosion occurrence [START_REF] Moussa | Parametric Study of the Micro-Explosion Occurrence of W/O Emulsions[END_REF][START_REF] Califano | Experimental Evaluation of the Effect of Emulsion Stability on Micro-Explosion Phenomena for Water-in-Oil Emulsions[END_REF][START_REF] Suzuki | Visualization of Aggregation Process of Dispersed Water Droplets and the Effect of Aggregation on Secondary Atomization of Emulsified Fuel Droplets[END_REF][START_REF] Khan | Puffing and Micro-Explosion Behavior of Water-in-Pure Diesel Emulsion Droplets during Leidenfrost Effect[END_REF][START_REF] Mura | Effect of Dispersed Water Droplet Size in Micro-Explosion Phenomenon for Water in Oil Emulsion[END_REF][START_REF] Mura | Study of the micro-explosion temperature of water in oil emulsion droplets during the Leidenfrost effect[END_REF][START_REF] Jarvis | Bubble Nucleation Mechanisms of Liquid Droplets Superheated in Other Liquids[END_REF]Volkov and Strizhak., 2018;[START_REF] Rashid | Experimental Study on Influence of Surfactant Dosage on Micro Explosion Occurrence in Water in Diesel Emulsion[END_REF][START_REF] Nam | An Experimental Investigation of Micro-explosion in Emulsified Vegetable-Methanol Blend[END_REF]Khan et al., 2014b;[START_REF] Tarlet | Comparison between Unique and Coalesced Water[END_REF]Avidisan and Fatehi, 1988;[START_REF] Morozumi | Characteristics of Auto-Ignition and Micro-Explosion Behavior of a Single Droplet of Water-in-Fuel[END_REF]Khan et al., 2018). Coalescence is the process by which two droplets merge, which will inevitably tend to increase the average size of dispersed droplets [START_REF] Palermo | Le Phénomène de Coalescence. Etude Bibliographique[END_REF].

The present work reports the experimental analysis of the heating of water-in-tetradecane emulsion droplets in Leidenfrost regime. Taking into account the space and time scales of both heating and phase change processes, diagnostics based on optical methods are the best solution thanks to their high frequency acquisition and the non-intrusive aspect. Laser Induced Fluorescence (LIF) is an optical technique widely used in fluid mechanics and combustion processes allowing imaging, temperature and concentration measurements. It is based on the excitation/emission of light by molecules present in the fluid to be studied or by specific compounds, called dyes or tracers, previously dissolved in it. An experimental test bench, involving high-speed cameras and continuous laser for LIF visualization, has been developed in order to measure the size evolution of the water droplets, and to identify the phenomena occurring inside the emulsion drops.

BACKGROUND

Secondary Atomization Due to Micro-Explosion

This phenomenon, typical of an emulsified fuel, is due to an abrupt phase change of dispersed droplets, embedded in the continuous phase (100°C at atmospheric pressure in the case of water).

It consists in the mechanical fragmentation of the emulsified droplet in a very short time (1 ms) [START_REF] Mura | Effect of Dispersed Water Droplet Size in Micro-Explosion Phenomenon for Water in Oil Emulsion[END_REF]. The released phase change energy is capable to break up the continuous phase (oil) around the water droplet, causing its fragmentation into child droplets. The reduced size of oil droplet in the flame will contribute for an efficient air-fuel mixing, allowing a complete combustion [START_REF] Matiello | Experimental Evidences for Micro-Explosion in Water/Fuel Oil Emulsion Flames Inferred by Laser Light Scattering[END_REF].

During the heating process of a W/O emulsion, the droplet temperature will increase and, as a function of several parameters (vaporization temperature, pressure, water content), the water can overpass the saturation temperature without changing the phase thus attaining a metastable state [START_REF] Mura | Contribution à l'étude de la Micro-Explosion d'une Goutte d'émulsion d'eau dans l'huile : Impact de la Granulométrie de la Phase Dispersée[END_REF]. The rupture of this state generates a violent expansion of the vapor phase, as schematically depicted in Fig. 1.

Occurrence of Micro-Explosion

Several authors have shown that the micro-explosion phenomena is governed by different parameters as heating temperature [START_REF] Moussa | Parametric Study of the Micro-Explosion Occurrence of W/O Emulsions[END_REF][START_REF] Mura | Study of the micro-explosion temperature of water in oil emulsion droplets during the Leidenfrost effect[END_REF], quantity of surfactant or emulsifier [START_REF] Moussa | Parametric Study of the Micro-Explosion Occurrence of W/O Emulsions[END_REF][START_REF] Califano | Experimental Evaluation of the Effect of Emulsion Stability on Micro-Explosion Phenomena for Water-in-Oil Emulsions[END_REF][START_REF] Rashid | Experimental Study on Influence of Surfactant Dosage on Micro Explosion Occurrence in Water in Diesel Emulsion[END_REF], or size distribution of water [START_REF] Moussa | Parametric Study of the Micro-Explosion Occurrence of W/O Emulsions[END_REF][START_REF] Califano | Experimental Evaluation of the Effect of Emulsion Stability on Micro-Explosion Phenomena for Water-in-Oil Emulsions[END_REF][START_REF] Nam | An Experimental Investigation of Micro-explosion in Emulsified Vegetable-Methanol Blend[END_REF]Khan et al., 2014b). Rashid et al., (2016) and Khan et al. (2014b) performed experiments in order to determine the effects of some parameters like surfactant quantity on the occurrence of micro-explosion. It is well known that increasing the surfactant quantity leads to increasing the emulsion droplet stability. Three W/O emulsions are performed with respectively 0.5, 1 and 1.5% of surfactant (adapted by Khan et al. 2014). In fact, the main effect of surfactant is to reduce the surface tension between the two phases. Thus, it was observed that the aggregation and coalescence rates slowed down and, due to embedded droplet's small size and their inability to coalesce, dispersed droplets vaporize without breaking the oil mother-drop (puffing).

More recently, [START_REF] Moussa | Parametric Study of the Micro-Explosion Occurrence of W/O Emulsions[END_REF] carried out a parametrical study where microexplosion occurrence of W/O emulsions was investigated by considering the emulsions physical properties. One of the most interesting results is the evolution of the micro-explosion occurrence with the "internal" Ohnesorge number Oh, which relates the viscous forces to inertial and surface tension forces and its expression is:

𝑂ℎ = (µ𝑐) � 𝛾 𝑊/𝑂 ×𝜌 𝑤 × 𝐷 (1)
Where µc is the continuous phase viscosity, γ 𝑊/𝑂 is the interface tension between water and oil, 𝜌 𝑤 the water density and D the water droplet average size. We can clearly see, from Fig. 2, that the micro-explosion rate is decreasing with Oh. This can highlight the influence of the continuous phase and interface tension.

The configuration where Oh is small (low viscosity, high interface tension and size), offers the highest micro-explosion occurrence (between 40-60%). This is caused by an easier motion of the dispersed droplets through the continuous oil, enhancing water coalescence.

Whereas bigger values of Oh (high viscosity, low inertia) prevent the dispersed droplets from moving through the oil, leading to a decreased micro-explosion rate. Generally speaking, a lower viscosity of the continuous phase triggers a successful micro-explosion more easily within industrial applications.

MATERIALS AND METHODS

Emulsion Preparation

Emulsions are, by definition, the mixture of two non-miscible fluids. This diphasic system presents an interface at its lowest energy level. However, the process of emulsification, which consists of adding mechanical energy, permits the dispersion of one fluid (dispersed phase) in the other (continuous phase) (Fig. 3).

In the present study, the dispersed phase is demineralized water. It is favored over tap water because of its relative purity: indeed, tap water may contain impurities that trigger the bubbling too soon during the heating, which can lead to an early puffing [START_REF] Moussa | Parametric Study of the Micro-Explosion Occurrence of W/O Emulsions[END_REF].

Concerning the continuous phase, n-tetradecane (C 14 H 30 ) is chosen for two reasons: it has almost the same physical properties than diesel oil but, unlike it, n-tetradecane is a pure hydrocarbon that can be excited only in the UV band. Thus, it won't affect the LIF visualization based on visible light excitation (λ=532 nm in our set up).

Non-ionic surfactant (Span 83) is added in order to prevent an early phase separation between water and oil, by reducing the interface tension and thus enhancing the emulsion stability. Surfactants are characterized by the Hydrophile-Lipophile Balance (HLB) value that should be between 3 and 6 for W/O emulsions [START_REF] Belkadi | Étude Expérimentale du Fractionnement Liquide-Liquide en Micro-Canaux pour la Production en Continu de Biodiesels Emulsionnés[END_REF]. As we can see in Table 1, HLB value of Span 83 is 3.7.

The emulsion preparation is performed using a mechanical stirrer at 1500 rpm during 10 minutes, at room temperature in order not to affect the surfactant efficiency and ensure a uniform distribution.

Experimental Apparatus

The Fig. 4 represents the experimental set up for the study of the heating of W/O emulsion droplets by means of LIF.

Heating Device

Leidenfrost levitation was adopted to suspend and heat the droplets. Fig. 5 presents the geometrical shape of the heat plate and its main components. The droplet holder is made in aluminum and was conceived in circular convex geometry (6 mm diameter) to trap the droplet during heating process, avoiding at maximum the lateral displacement and, eventually, the droplet fall. A resistive wire is fixed around the droplet holder, and is connected to a power generator. A 80µm K-type thermocouple is placed at the bottom of the drop holder (measurement error of ± 1.5°C), and is connected to a PID controller, which allows to measure and regulate the heating temperature. The heat plate temperature is fixed according to previous results presented by [START_REF] Moussa | Parametric Study of the Micro-Explosion Occurrence of W/O Emulsions[END_REF]. Indeed the authors found out that the higher the heating temperature is, the higher the micro-explosion rate is (for the same heating configuration). Thus, the temperature is fixed at 500°C, because it is the highest temperature achievable with the used heating device.

Optical Acquisition

As it was previously stated, LIF method is used for the visualization of water embedded droplets. LIF (or PLIF, Planar Laser Induced Fluorescence, being the laser beam reduced to a sheet) is an optical, non-intrusive technique allowing the measurements of different properties (species concentration, fluid temperature distribution, imaging…). It involves the dissolution of a fluorescence dye or tracer in a gas or liquid phase and is based on a two-step process: first, the absorption of an incident laser photon at a defined wavelength that leads the tracer molecule to a higher energetic state. Such state is unstable and thus, it results in a photon emission at a different wavelength, moving from an excited to a lower energy state.

The major point is the choice of the proper fluorescent dye. In the present case, Fluorescein was dissolved in the dispersed phase (water). It was chosen over other classical dyes for its very low solubility in oil phases and a complete solubility in water. Indeed, the LIF technique is used in this study in order to create a visual contrast between water and oil phases allowing us to identify water droplets embedded in oil. Fig. 6a shows absorption and emission spectrum of Fluorescein.

The W/O emulsion droplet, previously generated with a syringe and put on the heating device, is excited by a λ=532 nm laser beam (Nd-YAG 2 nd harmonic, Spectra Physics). The 4 Watts laser beam is transformed to a planar sheet (100-200 µm) by means of a pair of convex lenses (Fig. 6b). The fluorescent emitted light is then filtered with a 550±10 nm band pass filter and recorded by a Photron V4 Fastcam high speed camera mounted perpendicularly to the beam.

It allows the capture of pictures up to 12000 fps with maximum resolution of 1080 x 1024 pixels (Fig. 7). In order to ensure the same water droplets size distribution for all the drops tested after emulsification and before heating, the emulsion is continuously stirred. This way, there is no waiting time between the emulsification and the heating, and thus no emulsion stability breakdown.

Regarding the Fluorescein solubility properties, the fluorescent emitted light comes essentially from the tracer dissolved in water, meaning that water droplets should appear as bright circular shapes in a dark background that represents the oil phase. The frame rate adopted is between 2000 and 5000 Hz with an exposure time between 0.08 and 0.125 ms. The frame rate could have been higher, but the chosen parameters ensure a good compromise between number of images to process and their quality.

Image Processing

The frames recorded by the high speed camera permits the identification of the water droplets as bright circular shapes. However, in many cases, image treatment is needed in order to ensure the viability of the measurements. The image (a) of the fig. 8 is the original picture recorded. The image (b) corresponds the original image with contrast and brightness adjustments and a background subtraction.

In order to identify and measure water droplets size, an algorithm is built using the Image Processing Toolbox of Matlab. It is based on the Circle Hough Transform (CHT), a reliable technique used for the detection of circles in images where noise, occlusion and varying illumination are occurring. Despite the possible quality improvements using such techniques, occasionally, some unworkable images can be captured. These correspond to a droplet high motion or even to a water phase change, as we can see in the Fig. 9.

RESULTS

The Results section is divided in three parts: the sizing procedure validation, a description of the common behavior observed during the heating of the emulsion drop, and finally, a statistical investigation. This later aims to identify a physical criteria that would explain why an emulsion drop can undergo micro-explosion while another drop from the same emulsion may be subject to puffing.

(b) (c)

Sizing Procedure Validation

The heating of a typically observed W/O emulsion drop is recorded at 2000 fps and with an exposure time of 0.125 ms. The emulsion is composed of 7% v of water and 0.1% of surfactant.

The emulsion drop undergoes an optimal micro-explosion at the end of a heating duration of 950 ms. The water droplets average size is measured for each frame using the procedure described previously (Fig. 10)

In order to assess the reliability of the measurements, the results given by the algorithm are compared to manual measurements (orange curve) representing the reference measurements.

These measurements basically consists on manually identify bright circular shapes representing water droplets and measure their size. It is found that for 95% of the frames, the estimated error e between manual (D ref ) and automatic (D auto ) measurements of average diameter (Eq.2) is less than 10%, endorsing the use of such a technique in the study. The error comes mainly from the low quality of some frames (Fig. 9) and/or the presence of steam within the emulsion drop. We can notice that the average trend of the size evolution is increasing and this is mainly due to the coalescence of water droplets, as it is outlined by the Fig. 11. Moreover, the temperature rise is accompanied by the oil phase viscosity decrease that leads to an easier motion of the dispersed droplets and, therefore, their coalescence rate.

𝑒 = 100 × �𝐷 𝑟𝑟𝑟 -𝐷 𝑎𝑎𝑎𝑎 � 𝐷 𝑟𝑟𝑟 (2)
Despite the general increase of the water droplets average size, one can notice local decreases of the size evolution, giving the curve an oscillating shape. If the local increase can be explained by coalescence, the fell in the average size can be generated by intermediate puffings represented by black circles in the Fig. 10. Some water droplets undergo a phase change to steam without affecting the emulsion drop lifetime (Fig. 12).

It is also important to underline that the images recorded are a 2D-projection of the emulsion drop heating and the phenomena happening inside. By analyzing the movies, it appears that some droplets tend to disappear from the field of view, and reappear few ms later, which can justify the oscillating trend. This can be explained by two factors: first, as it was mentioned, the heating plate has a convex shape in order to maintain the droplet. In this case, the lower area is not visible by the camera (Fig. 13). The second explanation concerns the water droplets that are subject to internal convection motions caused by the temperature gradient within the emulsion drop. When the water droplet is not crossing the laser sheet area, it cannot be excited and, therefore it will not be visible (Fig. 13).

Concerning multi-disperse droplets size distribution, which is the case for emulsions, the average diameter does not provide a proper measurement of the dispersion, which among other features, are the basis to encourage the coalescence among the dispersed droplets. For these reasons, the evolution of size distribution is investigated in Table 2, between a local minima and maxima. Indeed, coalescence is governed by Laplace Pressure difference between drops. Laplace pressure is inversely related to the size of the drop, which means that droplets of different size are more likely to coalesce than two droplets of same size.

Micro-Explosion Characterization

This section is dedicated to the investigation and the heating of 50 W/O emulsion drops.

Regarding the random and difficult-to-reproduce aspect of the micro-explosion, it seemed necessary to investigate a large number of W/O emulsion drops even if they have the same composition and initial conditions. The emulsion is composed of 5% of water and 0.1% of surfactant is selected, heated at 500°C, with an acquisition frequency of 5000 fps and an exposure time of 0.08 ms. These parameters are fixed in order to ensure a good rate of micro-explosion and a workable image quality.

38 over the 50 cases underwent an optimal atomization (76%) whereas puffings occurred for the 12 remaining drops. Besides, efforts have been undertaken in order to identify the atomization trigger. Nonetheless, in 40% of the cases (optimal and weak atomization combined), it was not possible to identify the trigger, either because of an unworkable image just before the atomization or the simultaneous presence of two or more potential triggers.

Common Behavior during the W/O Emulsion Drop Heating

During the heating of all the emulsion drops, a common behavior is noticed and is depicted by the Fig. 14. The occurrence of swelling and disruptive boiling are clearly identified in all the cases investigated. Intermediate puffings cause the swelling of the emulsion drop, due to the ejection of steam. The spatial temperature gradient created by the strong heating induces a density and surface tension gradient and thus, convective motion of the embedded droplets inside the "mother" drop.

Moreover, the onset of water droplets bubbling is also studied: for each emulsion drop, the time when first bubbles appear is measured. Even if the visualization of steam, using the previously described LIF diagnostic, is not very accurate, occurrence of intermediate puffings and/or emulsion drop swelling can attest the presence of steam inside the emulsion drop. If the reasonable assumption that fluorescein (for a given concentration of 300 mg/L) does not affect water properties is made, then presence of vapor states that temperature inside the emulsion drop achieves at least 100°C. Once the phenomenon was observed for the totality of emulsion drops regardless to the atomization efficiency (micro-explosion or puffing), the curve representing the apparition of the first steam bubble by respect to the heating duration is plotted (Fig. 15).

A very interesting linear trend is observed: the first bubbling appears at 20-25% of the emulsion lifetime. So, it is possible to associate the time between bubble apparition and total heating duration. With one information (bubbling or heating duration) it is conceivable to infer about the other and vice-versa. However, as the nucleation sites is random and due to strong convective motion of the dispersed droplets and coalescence, the experimental observation could not be so precise for predicting the dynamics of the droplets neither the most probable region to observe nucleation sites position. To sum up, the typical phenomena happening during the heating of a W/O emulsion drop are represented in the timeline depicted in the Fig. 16 4

.3 Atomization Trigger

In this section, attention is focused on the water droplet that triggers the micro-explosion of the emulsion droplets (called "trigger droplet" in Fig. 17). In this experimental campaign, 3 parameters are considered as key points in the occurrence of micro-explosion: size of the trigger droplet, its temperature and position. The LIF visualization permits to measure droplets size and determine their position.

As it was stated previously, the trigger droplet is identified in 30 cases overs 50 (60%), corresponding to 28 micro-explosions and 2 puffings. For the emulsion drops that underwent puffings, it is more difficult and less accurate to identify trigger droplets principally due to the presence of steam.

Once the identification is done, size of the trigger droplet and the size of an emulsion drop (at the moment of the atomization) are measured. The ratio R (Eq.3) between the size of the trigger droplet and the emulsion drop is then calculated for each case, allowing us to verify if a size threshold is needed. One may notice that the calculation of this ratio takes into account the emulsion drop size, which may differ from one drop to another:

𝑅 = 𝑇𝑇𝑇𝑇𝑇𝑒𝑇 𝑤𝑤𝑤𝑒𝑇 𝑑𝑇𝑑𝑑 𝑇𝑤𝑑𝑇𝑟𝑟 𝐸𝐸𝑟𝐸𝑟𝑇𝑑𝐸 𝑑𝑇𝑑𝑑 𝑇𝑤𝑑𝑇𝑟𝑟 (3)
The Fig. 18 represents the ratio R distribution for all the identified trigger droplets.

As it can be observed, the size ratio results are heterogeneous. Concerning only the microexplosion cases, one can observe that the results are dispersed [10-58]% with an average ratio of 26.7%, which basically means that the trigger droplets size should be in average a quarter of the emulsion drop. Besides, the micro-explosion #2 occurred with a size ratio of 10% whereas the Puffing#1 took place with a bigger ratio (15%), which also points out the fact that size of the trigger droplet is not a sufficient criteria to determine whether micro-explosion or puffing is occurring. Thereby, another parameter, like temperature of the trigger droplet, affects the release of the water phase change energy, and thus, the atomization efficiency. Indeed, [START_REF] Mura | Effect of Dispersed Water Droplet Size in Micro-Explosion Phenomenon for Water in Oil Emulsion[END_REF] showed that water embedded droplets may achieve a metastable state up to 170-180°C, higher than the boiling point.

Position of the trigger droplet is the other parameter investigated. As [START_REF] Tarlet | Contribution à la Combustion des Emulsions de l'eau dans le Fioul Lourd[END_REF] explained, during phase change of the droplets positioned in the out layer, the water vapor will be ejected together with some quantity of continuous phase, with no ability to disintegrate the emulsion droplet. On the other hand, if the droplet is positioned in the internal layers, the vaporization could induce contact with metastable neighbor droplets inducing a nucleation that causes a complete disintegration.

Coordinates of the trigger droplet center is measured in relation to emulsion droplet center and then, normalized over the emulsion radius. The associated diameter is normalized over the emulsion diameter. Fig. 19 depicts a "model" emulsion drop where are reported size and position of all the identified trigger droplets.

It shows that the most populated region is located in the bottom part of the emulsion drop, matching with sedimentation effects, encouraged by coalescence and density difference of the two phases. However, two of the smallest droplets (R 1 =12%, R 2 =13%) are located at the upper part at the moment of their phase change. This is mainly due to the convection motions that are counteracting the effects of gravity for such small sizes. In agreement with the previous discussion it can be also noted that when puffing and not micro-explosion was the dominant effect, the trigger droplets are located close to the surface of the emulsion droplet.

CONCLUSION

This experimental campaign is motivated to grant additional quantitative data, aiming to better understand the micro-explosion phenomenon. Given the samples small scales of space and time, non-intrusive techniques like optical diagnostics are favored for providing an insight of the W/O emulsion drop heating. The experimental conditions presented in this paper are aiming to study the behavior of one single droplet under Leidenfrost effect. These conditions may differ from real industrial spray applications, but the results of this study can be used for modelling validation and numerical simulations of real combustion of W/O emulsion sprays.

Water embedded droplets size is measured thanks to an experimental method based on LIF visualization. The experimental apparatus capability (high frequency images acquisition) and the homemade algorithms are settled to improve image quality and data extraction in a relative short processing time, leading up to satisfactory results when compared to manual results.

Experimental investigations were also carried out on a large number of samples, in order to better visualize and understand the phenomena happening during the heating of a W/O emulsion drop, but also to identify physical criteria to distinguish between optimal and weak atomization.

In that regard, size and position of trigger droplets were noted. Future work should focus on the temperature measurements of the water embedded droplets, using two color LIF. Indeed this method can be complementary to the sizing procedure described in this paper, and it is based on the temperature dependency of the fluorescent emitted light intensity.

FIG. 5 :

 5 FIG. 1: Micro-explosion process

FIG. 6 :FIG. 9 :FIG. 13 :FIG. 15 :FIG. 18 :FIG

 69131518 FIG. 6: (a)Excitation and emission spectrum of Fluorescein; (b)Planar laser sheet visualization

TABLE 1 :

 1 Drops inMicro-Explosions Scanned by Differential Calorimetry, Int. J. Heat Mass Transf., vol. 95, pp. 689-692, 2016. Volkov, R.S. and Strizhak, P.A., Using Planar Laser Induced Fluorescence to Explore the Mechanism of the Explosive Disintegration of Water Emulsion Droplets Exposed to Intense Heating, Int. J. Thermal Sci., vol. 127, pp. 126-141, 2018. Watanabe, H., Harada, T., Matsushita, Y., Aoki, H., and Miura, T., The Characteristics of Puffing of the Carbonated Emulsified Fuels, Int. J. Heat Mass Transf., vol. 52, pp. 3676-3684, 2009. Physical properties of the fluids used

		𝝁	ρ	Boiling Temp	HLB
		mPa.s	kg.m -3	°C	-
	Tetradecane	2,13	762	254	-
	Span 83	1500	9,4	-	3.7
	Water	1	1000	100	-

TABLE 2 :

 2 Size distribution evolution

ACKNOWLEDGMENT

The authors thank the Region Pays de la Loire (Chaire Connect Talent ODE) for the financial support of this work.

Heat Plate

Non visible area

Visible area

Heat


Nikita Shlegel

Pavel Strizhak
email: pavelspa@tpu.ru.

Dominique Tarlet
email: dominique.tarlet@univ-nantes.fr.

Jérôme Bellettre

Comparing the integral characteristics of secondary droplet atomization under different situations

Keywords: secondary atomization, fragmentation, interaction between droplets, wall and air jet impact, micro-explosion, child-droplets

Comparing the integral characteristics of secondary droplet atomization under different situations

Nikita Shlegel, Pavel Strizhak, Dominique Tarlet, Jérôme Bellettre

Nomenclature n -number of child-droplets; P -power consumed, kW/h; Qc -convective heat flux, kW/m 2 ; Rd -droplet radius, mm; Rd1 -radii of the first droplet, mm; Rd2 -radii of the second droplet, mm; rd -average radius of child-droplets, mm; S0 -total surface area of pre-collision droplets, m 2 ; S1 -total surface area of post-collision droplets, m 2 ;

Introduction

In most technologies, liquid droplet atomization is aimed to increase the interfacial area as well as inter-component interfaces for heterogeneous compositions [START_REF] Vysokomornaya | Breakup of heterogeneous water drop immersed in high-temperature air[END_REF]. It is especially important to increase this parameter when evaporating or burning impurities, as well as in fire suppression systems, heat and mass transfer plants, for liquid fuel injection, etc. As a result, it is possible to minimize power consumption and the duration of corresponding technological stage in the aforementioned applications due to extensive phase transformation, gas-phase and heterogeneous chemical reaction. Another application for surface treatment processes is thermal plasma spraying. In this case, heterogeneous drops made of 10-100 nm solid nanoparticles in a carrier liquid (water or ethanol) undergo fragmentation when surrounded by a hightemperature, high-velocity plasma jet [START_REF] Damiani | A Particle-Tracking-Velocimetry (PTV) Investigation of Liquid Injection in a DC Plasma Jet[END_REF].

Besides the primary atomization of liquid droplets, implemented by various injectors, capillaries, and compressors, quite widespread is a secondary atomization, which is normally based on various physical principles and mechanisms [START_REF] Vysokomornaya | Breakup of heterogeneous water drop immersed in high-temperature air[END_REF]. The first of the typical and most commonly applied schemes is the secondary atomization through droplet collision with a solid surface [START_REF] Zen | Ethanol drop impact on an inclined moving surface[END_REF][START_REF] Liang | Liquid sheet behaviors during a drop impact on wetted cylindrical surfaces[END_REF][START_REF] Liang | Review of mass and momentum interactions during drop impact on a liquid film[END_REF][START_REF] Josserand | Drop Impact on a Solid Surface[END_REF][START_REF] Liang | Review of drop impact on heated walls[END_REF]. It is determined [START_REF] Zen | Ethanol drop impact on an inclined moving surface[END_REF][START_REF] Liang | Liquid sheet behaviors during a drop impact on wetted cylindrical surfaces[END_REF][START_REF] Liang | Review of mass and momentum interactions during drop impact on a liquid film[END_REF][START_REF] Josserand | Drop Impact on a Solid Surface[END_REF][START_REF] Liang | Review of drop impact on heated walls[END_REF] that interaction time of the droplet and the surface depends on the roughness of the latter. When We number is increased to 60, the impact with a solid surface destroys the droplet, generating a large number of smaller liquid fragments. For We number less than 30 the droplet bounces off a surface, and for a range of We from 50 to 80, the droplet impact creates a thin film on the solid surface, which then breaks up into smaller fragments. The level of droplet disruption is heavily dependent on surface characteristics (roughness, thermal and physical characteristics, hydrophilic or hydrophobic properties, etc.) as well as on liquid viscosity, wall temperature, and impact angle. For instance, higher wall temperature will provide a considerable shift in the transition boundary (in terms of critical size or velocity) between three atomization modes [START_REF] Zen | Ethanol drop impact on an inclined moving surface[END_REF][START_REF] Liang | Liquid sheet behaviors during a drop impact on wetted cylindrical surfaces[END_REF][START_REF] Liang | Review of mass and momentum interactions during drop impact on a liquid film[END_REF][START_REF] Josserand | Drop Impact on a Solid Surface[END_REF][START_REF] Liang | Review of drop impact on heated walls[END_REF]: partial fragmentation, explosive disruption, and recurrent bounce followed by breakup. The most rapid breakup occurs in limited heating temperature range of 100 to 300 °С.

As part of secondary atomization schemes, several liquid aerosol sprays are often intermixed under various angles by intersecting injector spray cones, in order to stimulate droplet collisions. In this case, the rate of droplet breakup depends heavily on the impact angle and We number, as well as on the liquid properties (viscosity, density, and surface tension). The most important thing to determine here is the conditions providing the increase in the number of smaller fragments due to collisions of initial droplets and the effect of the above parameters [START_REF] Szakáll | Wind tunnel study on the size distribution of droplets after collision induced breakup of levitating water drops[END_REF][START_REF] Kuan | Study on high-Weber-number droplet collision by a parallel, adaptive interface-tracking method[END_REF].

It is determined [START_REF] Ithnin | An overview of utilizing water-in-diesel emulsion fuel in diesel engine and its potential research study[END_REF] that fuel droplets are heavily deformed and break up due to the divergent aerodynamic forces during the secondary atomization. Droplet relative velocity in a gas environment determines the aerodynamic force of droplet deformation, while viscosity (internal friction) and surface tension are the factors that slow down the transformation. The most important dimensionless numbers influencing the droplet breakup are Weber, Ohnesorge, Laplace, Reynolds, and capillary numbers, as well as density and viscosity ratios of two environments (gas and liquid). Studying these forces and effects provided us with thorough knowledge of how droplets of different homogeneous liquids atomize in a gas flow [START_REF] Ithnin | An overview of utilizing water-in-diesel emulsion fuel in diesel engine and its potential research study[END_REF]. Breakup conditions are defined for droplets rapidly moving in the air flow and for droplets with the air flow incoming on them.

Droplet atomization can also be stimulated by heat due to the overheating of the low-boiling component. This way we can obtain a fine aerosol with a greatly increased evaporation surface area due to micro-explosive breakup [START_REF] Stefanitsis | Numerical investigation of the aerodynamic breakup of Diesel and heavy fuel oil droplets[END_REF][START_REF] Sazhin | A simple model for puffing/micro-explosions in water-fuel emulsion droplets[END_REF][START_REF] Mura | Emulsion droplet micro-explosion: Analysis of two experimental approaches[END_REF][START_REF] Antonov | Influence of solid nontransparent inclusion shape on the breakup time of heterogeneous water drops[END_REF][START_REF] Antonov | Impact of holder materials on the heating and explosive breakup of two-component droplets[END_REF]. This atomization scheme involves supplying significant heat fluxes by conductive, convective, and radiative heating, as well as complex mixed energy supply to a droplet. In the lab, the main applicable schemes are the extensive convective, conductive and radiative heating of liquid droplets. The convective scheme is characterized by medium value of critical heat fluxes required for extensive droplet aerosol atomization [START_REF] Antonov | Impact of holder materials on the heating and explosive breakup of two-component droplets[END_REF], whereas the conductive one is more suited to individual emulsion drop study, providing a shorter micro-explosion delay. An important condition of massive droplet micro-explosive breakup is at least two components in the droplet composition with considerably different boiling temperatures and phase transition heat. The most common composition uses water as a low-boiling component, mixed with combustible liquids, fuels, solid particles, waste. Multi-component compositions of the above are also common [START_REF] Antonov | Impact of holder materials on the heating and explosive breakup of two-component droplets[END_REF]. Concerning laboratory experiments using a single emulsion drop, waterin-oil emulsion drops are used in studies [START_REF] Mura | Effect of dispersed water droplet size in microexplosion phenomenon for water in oil emulsion[END_REF][START_REF] Watanabe | The characteristics of puffing of the carbonated emulsified fuel[END_REF].

Another widely used droplet flow atomization scheme introduces a high-density liquid. For instance, when a lower density liquid flow is moving in a high-density flow, the lighter liquid is affected by a complimentary pressure that leads to atomization or partial fragmentation [START_REF] Gelfand | Droplet breakup phenomena in flows with velocity lag[END_REF]. This scheme is economically inefficient when building industrial facilities, and the probability of complete droplet breakup during atomization is low. The droplet does not necessarily break up. For instance, low velocity droplet flow (We<50) does not overcome the surface tension, and the droplet does not disperse even under heavy surface deformation.

-4 -A droplet atomization scheme with gas flow injection [START_REF] Gelfand | Droplet breakup phenomena in flows with velocity lag[END_REF] is proposed for various fuel combustion devices. The scheme is characterized by high probability of droplet fragmentation, but also by gas (air) oversupply in the combustion chamber, increasing both economic expenses and the generated nitrogen dioxide concentration. It is known [START_REF] Shraiber | Deformation and breakup of drops by aerodynamic forces[END_REF] that high velocity of droplet flow leads to droplet fragmentation due to friction and resistance domination over the surface tension. However, this scheme is economically inefficient because the chambers and heat exchangers need to be pressurized, which increases their cost and wear. In the field of surface coating, a liquid jet is injected into a plasma jet where it undergoes a first fragmentation into liquid drops, which in turn undergo their secondary atomization [START_REF] Damiani | A Particle-Tracking-Velocimetry (PTV) Investigation of Liquid Injection in a DC Plasma Jet[END_REF], also by means of the surrounding gas phase momentum.

An interesting possibility here is to combine several primary and secondary atomization schemes, with a possible decrease in cost and time needed to generate a droplet aerosol of the required fineness.

There is no comparative data yet on the integral characteristics of droplet breakup for different liquid compositions in every known secondary atomization scheme. The main obstacle seems to be the absence of common comparative criteria due to a drastic difference in physical origin of atomization in the above mentioned schemes. As a first step, it is reasonable to compare the integral characteristics of atomization by determining the average and maximum size of liquid fragments generated, their total surface area or total volume occupied. Next, we need to evaluate the amount of energy required to obtain the identical parameters, mentioned above, for each secondary atomization scheme. Another promising objective is to find a combination of several secondary atomization schemes for different liquids. Considering the results of experimental studies [START_REF] Vysokomornaya | Breakup of heterogeneous water drop immersed in high-temperature air[END_REF][START_REF] Negeed | Experimental study on the effect of surface conditions on evaporation of sprayed liquid droplet[END_REF][START_REF] Zen | Ethanol drop impact on an inclined moving surface[END_REF][START_REF] Liang | Liquid sheet behaviors during a drop impact on wetted cylindrical surfaces[END_REF][START_REF] Liang | Review of mass and momentum interactions during drop impact on a liquid film[END_REF][START_REF] Josserand | Drop Impact on a Solid Surface[END_REF][START_REF] Liang | Review of drop impact on heated walls[END_REF][START_REF] Szakáll | Wind tunnel study on the size distribution of droplets after collision induced breakup of levitating water drops[END_REF][START_REF] Kuan | Study on high-Weber-number droplet collision by a parallel, adaptive interface-tracking method[END_REF][START_REF] Ithnin | An overview of utilizing water-in-diesel emulsion fuel in diesel engine and its potential research study[END_REF][START_REF] Stefanitsis | Numerical investigation of the aerodynamic breakup of Diesel and heavy fuel oil droplets[END_REF][START_REF] Sazhin | A simple model for puffing/micro-explosions in water-fuel emulsion droplets[END_REF], we can safely assume that atomization schemes with droplet collisions, collision (impact) with a wall, and incoming air flow are more promising for heterogeneous droplets. Microexplosive breakup by overheating and boiling is important for inhomogeneous droplets.

The aim of this research is to compare the droplet atomization characteristics for different liquids by stimulating droplet collisions, impact with an obstacle (solid surface), droplet acceleration in the air flow (or by intense incoming gas jet), and micro-explosive breakup.

Experimental Procedures

We used several experimental setups and recording techniques for this research. The different schemes of atomization are presented in Fig. 1. Each setup design was based on the phenomenological approach using only isolated droplets as an object under study in the recording area. We have not yet considered the synergy effects of adjacent droplets inside the aerosol flow. To study droplet collisions, we used the setup fitted with a droplet generator and a liquid supply system. The experimental parameters were recorded in the same way as in studies [START_REF] Szakáll | Wind tunnel study on the size distribution of droplets after collision induced breakup of levitating water drops[END_REF][START_REF] Kuan | Study on high-Weber-number droplet collision by a parallel, adaptive interface-tracking method[END_REF]. The liquid supply system consists of a submersible pump with variable performance (1.2 to 1.6 l/min) and two silicone capillaries connected to specially designed nozzles (droplet generators) fixed to a holder ring. Droplet size was varied from 0.3 to 1.5 mm with the help of interchangeable nozzles. Impact angle (αd) was varied from 0 to 90 o by changing their position in the holder ring. By varying the pump performance, we changed the droplets velocities (Ud1, Ud2). To produce the interaction regime maps, we calculated the Weber numbers of the droplets closing in before collision, considering their relative velocity (Urel=(Ud1 2 +Ud2 2 -2|Ud1|•|Ud2|•cos(αd)) 0.5 ) and radius of small

droplet (Rd1): We=2•Rd1•ρ•Urel 2 /σ.
In preliminary tests, we used a pair of high-speed video cameras (resolution 1152x864, frequency 3000 to 100000 fps) to capture the droplet size, velocity, angle, shape, and the number of fragments, as well as to determine the interaction regimes. The observation area was lit by several light screens. The cameras were located at an angle of 90 o relative to each other to reproduce the spatial pattern. Two elements of a lighting system were opposite the cameras to enhance droplets image quality. Each camera was used for 2dimensional recording as shown in Figs. 1 and2. A focus depth was from 5 mm to 15 mm for the cameras.

To determine the focus depth, the Multi-Function Calibration Target (for Low Magnification Systems) was applied. In preliminary experiments, manual focusing was used for the subsequent calculation of scale and correction factors. Methods of measuring the primary droplets size, velocity and impact angles, as well as the number, size, and velocities of the secondary droplets, are based on the processing of videograms, the applying of a coordinate grid (collisions -from 25x32 mm to 31x38 mm; wall impact -from 25x34 mm to 27x36 mm; air jet impact -from 220x270 mm to 330x274 mm; micro-explosive breakup by overheatingfrom 14x14 mm to 17x17 mm) and the scale factors (collisions -from 0.025 mm/px to 0.032 mm/px; wall impact -from 0.025 mm/px to 0.029 mm/px; air jet impact -from 0.25 mm/px to 0.31 mm/px; microexplosive breakup by overheating -from 0.018 mm/px to 0.023 mm/px).

For processing the videograms, the Tema Automotive and FastCam software were applied. The software allowed to analyze the position of droplets, their velocities, accelerations, impact angles and covered distances with a high temporal sampling. The Tema Automotive software used the following functions: scaling/coordinate systems; analysis properties like position, velocity, acceleration, and angle are automatically calculated for all points in the session; automatic tracking; semi-automatic tracking; manual; time panel; time panel; graphs and tables panel. The FastCam software involved the use of the following functions: display scale; angle measurement; measuring distance between the two points; analysis. Markers allowing to track objects were used for the subsequent calculation of velocity, size, and impact angle (Fig. 1).

To determine the parameters characterizing the droplet fragmentation outcomes, the ratio between the surface areas of the emerged child-droplets and the two initial primary drops (S1/S0) was calculated. The surface area of the initial droplets, e.g., in the experiments with droplets collisions, was calculated using the formula: S0=4•π•(Rd1 2 +Rd2 2 ). When determining the surface area of the child-droplets, the size of all these droplets (rdi) and their number (N) were considered using the formula S1=4•π•∑N•rdi 2 . Since not all newly emerged secondary droplets were in the recording area, a correction factor (0.15-0.76) was introduced for the number of child-droplets. The number of apparent (Nti) and invisible (Ntv) droplets was determined. The latter (Ntv) should be considered to ensure equality of the volumes of the droplets before and after the interaction. The number and size of the invisible droplets were estimated on the basis of the assumption of the spatial homogeneity of the scattering of child-droplets during primary droplets collision. Following this assumption, if there is a two-dimensional distribution, the spatial one can be reliably predicted. The experiments have shown that the number and mean size of the secondary droplets in the case of single camera use and spatial homogeneity assumption differed from the analogous parameters recorded using a pair of cameras by 8-13 %. Considering such insignificant differences, it was decided to use further the results obtained using a single camera.

Systematic error for all of the experiments was: 1.6% for droplet radius measurement, 2.1% for droplet velocity measurement, 3% for air flow velocity measurement, and 2.3% for impact angle measurement. Random error will be shown as a confidence interval in the curves.

To study the droplet collision with a solid surface, we used the setup fitted with a liquid tank and a dispenser (droplet generator). Droplets fell free from the dispenser onto the solid surface -a copper plate also referred to as a wall or an obstacle. The plate was fixed on a holder. The droplet impact angle to the surface was varied by changing the plate position on the holder. Plates of different characteristics (roughness, thermal and physical characteristics, hydrophilic and hydrophobic properties, temperature, etc.) could be fixed on the holder. The experimental parameters were recorded in the same way as in studies [START_REF] Negeed | Experimental study on the effect of surface conditions on evaporation of sprayed liquid droplet[END_REF][START_REF] Zen | Ethanol drop impact on an inclined moving surface[END_REF][START_REF] Liang | Liquid sheet behaviors during a drop impact on wetted cylindrical surfaces[END_REF][START_REF] Liang | Review of mass and momentum interactions during drop impact on a liquid film[END_REF][START_REF] Josserand | Drop Impact on a Solid Surface[END_REF][START_REF] Liang | Review of drop impact on heated walls[END_REF]. The experiments enabled to observe the size and number change of the secondary droplets emerged because of the collision of the primary droplets with a wall during liquid film formation on the wall surface. These issues were well learned within a number of experimental and theoretical studies [START_REF] Zen | Ethanol drop impact on an inclined moving surface[END_REF][START_REF] Liang | Liquid sheet behaviors during a drop impact on wetted cylindrical surfaces[END_REF][START_REF] Liang | Review of mass and momentum interactions during drop impact on a liquid film[END_REF][START_REF] Josserand | Drop Impact on a Solid Surface[END_REF][START_REF] Liang | Review of drop impact on heated walls[END_REF]. Next, the mean amount and size of the secondary droplets detected in the tests with the primary droplets colliding with a wall will be discussed. In this case, a set of the tests, during which the primary droplets successively collided with a wall, forming the liquid film, was implemented. After performing this experiment during one minute, the number and size of the secondary droplets were averaged. In the future, it is planned to learn in detail the effect of these peculiarities on the values of S1/S0.

To study the droplet micro-explosion during high-temperature convective heating, we released a droplet into a vertically positioned rotary muffle furnace (temperature range 20-1200 °С). Dispensers were used to generate droplets of 0.62 to 1.34 mm in size. Furnace temperature was recorded by a system of National Instruments data collection module and fast thermocouples (accuracy ±3 °С, response 0.1 s). The measurement technique is similar to the one used in study [START_REF] Antonov | Impact of holder materials on the heating and explosive breakup of two-component droplets[END_REF]. Mura et al. [START_REF] Mura | Effect of dispersed water droplet size in microexplosion phenomenon for water in oil emulsion[END_REF] studied an individual emulsion drop sliding onto a 5.71 mm-diameter heated plate, by means of the Leidenfrost effect. The heated plate was maintained at the temperature of 363 °С, providing a conductive heat transfer to the emulsion drop. A fast (10 kHz) CMOS camera LAVision High Speed-Star 6 with a 60 mm objective was used to visualize and count the child-droplets issued from the micro-explosion. Watanabe et al. [START_REF] Watanabe | The characteristics of puffing of the carbonated emulsified fuel[END_REF] expose the thermocouple-suspended drop of emulsified fuel to both convective and radiative heating, within an electric furnace where wall temperature is set to 700 °С and air temperature is set to 577 °С. From these three sets of experimental data, we derive the micro-explosion behavior of emulsified fuel drops undergoing the three modes of heat transfer. Generally speaking, convective and radiative heat transfer are more representative of spray combustion applications, whereas conductive heat transfer is used in the lab to closely observe an individual emulsion drop.

To study the isolated droplet interaction with an air jet, we used a setup with an atmospheric pressure liquid tank. The lower part of the tank is connected to a dispenser tip via an elastic tube with a roller clamp.

Opening the roller clamp generated a droplet of required size at the tip of the dispenser. At a 0.4 m distance from the dispenser, a narrow (10 mm) nozzle is mounted. When a shutter opened in front of the nozzle, a short burst of air flow occurred, aimed at the downward droplet. The air flow velocity was recorded by a hot-wire anemometer (accuracy 0.3 m/s, measuring range 0-60 m/s) and varied in the range of 2 to 45 m/s for all of the experiments. The experimental parameters were recorded in the same way as in study [START_REF] Kuan | Study on high-Weber-number droplet collision by a parallel, adaptive interface-tracking method[END_REF].

Damiani et al. [START_REF] Damiani | A Particle-Tracking-Velocimetry (PTV) Investigation of Liquid Injection in a DC Plasma Jet[END_REF] studied the secondary atomization of pure water drops within a high-temperature (up to 13727 °С), high-velocity (1000-3000 m/s) plasma jet issued from a SULZER F4 plasma gun with an anode diameter of 6 mm. A CMOS fast camera PHOTRON Fastcam SA 1.1 was used to record the spray images at the acquisition frequency of 20 kHz. This was necessary to measure the sizes of the drops fragmented by the surrounding plasma jet. The experimental set-up and parameters are fully documented in study [START_REF] Damiani | A Particle-Tracking-Velocimetry (PTV) Investigation of Liquid Injection in a DC Plasma Jet[END_REF].

We researched the compositions (Table 1) that are typical of the practical applications, mentioned in the Introduction Section. Graphite particles were used to compose slurries, because it is the most common ingredient of firefighting compositions. Among the solutions of environmental and energy problems there is an implementation of vegetable oil-based fuel. In countries with temperate climate, rapeseed oil-based fuel is considered the most efficient. Given that, we used rapeseed oil emulsion for our experiments. We chose diesel for our experiments for its wide usage in every industry, especially as internal combustion engine and power plant fuel. The main physical properties of components and liquid compositions are shown in Table 2. It also gives the key characteristics describing the reasons for surface transformation and droplet fragmentation in the reported secondary atomization schemes.

Results and Discussion

General patterns and aspects of droplet breakup modes

Figs. 2 and3 demonstrate typical experimental video frames to illustrate general and particular modes of droplet breakup during each of the used secondary atomization schemes, and data from study [START_REF] Mura | Effect of dispersed water droplet size in microexplosion phenomenon for water in oil emulsion[END_REF]. In terms of the shape sequence of breaking droplets, we can distinguish three types. The first one is characterized by considerable droplet surface deformation while maintaining its integrity, the growth of its maximum size due to the aerodynamic force, and the following breakup into a small number of relatively large fragments. In the second one, fragments separate from a dispersing droplet (referred to as partial fragmentation). The third one is the complete droplet breakup to form a fine aerosol. The higher the inertia, the more often the third scenario of droplet breakup occurs. The third type is the most desirable for the practical applications since it provides droplet fragments that are significantly smaller than the original droplets (Fig. 2) formed by a spray nozzle, dispenser, compressor or sprinkler. Fragmentation by means of the surrounding plasma jet (photos shown in Fig. 4 of study [START_REF] Damiani | A Particle-Tracking-Velocimetry (PTV) Investigation of Liquid Injection in a DC Plasma Jet[END_REF]) is also an example of the third shape sequence of break-up, referred to as "sheet stripping" fragmentation regime (fifth secondary atomization scheme) in the Weber number interval 100≤We≤350.

All schemes of droplet interaction are characterized by the significant transformation and increased size of the droplet and thinner near-surface layers prior to the imminent breakup. Each of used approaches has different physical reasons, factors and mechanisms leading to the droplet size increase prior to the breakup. For instance, in the case of micro-explosive breakup, the droplet size increases due to inner vapor bubbles. The pressure growth in the bubbles leads to the thinning of the liquid surface film, and the droplet breaks up when the critical pressure is reached. In the case of droplet collisions, impact with a wall or with a gas jet, a shift in droplet layers is observed, with considerable distortion of its spherical shape. This leads to droplet surface instability due to the increasing aerodynamic forces. In particular, the shape of distorted droplets was near-elliptical, or even disc-like. The drag coefficient of these shapes is 30-50% higher than that of a sphere. Therefore, the lifetime of these droplets for the same Weber number (i.e., velocity and size) is shorter than that of a sphere. Molecular bonds in the droplet are affected considerably by acceleration and heating. This is why we observed variations in the decrement of the relative size of droplet fragments and increment of the total surface area for the same We numbers or durations (Figs. 4 and5).

The inhomogeneous droplet micro-explosive breakup characteristics are dependent not only on temperature, but also on the velocity of heating gases. The latter is the definitive factor of heat flux calculation. That is why in the comparative analysis of atomization characteristics in Figs. 4 and5 there are curves of rd/Rd and S1/S0 versus We and Qc as functions of droplet velocity in a gas environment. The chosen threshold heat fluxes were to ensure the stable disruption mode. A partial droplet fragmentation scenario was typical of Qc lower than those presented in this work. It demonstrated a long-lasting process of droplet disruption (2-3 to 15-20 seconds) resulting in quite large liquid fragments, often polydisperse ones. This atomization mode is deemed inapplicable for it demands longer droplet heating. Experiments [START_REF] Stefanitsis | Numerical investigation of the aerodynamic breakup of Diesel and heavy fuel oil droplets[END_REF][START_REF] Sazhin | A simple model for puffing/micro-explosions in water-fuel emulsion droplets[END_REF][START_REF] Mura | Emulsion droplet micro-explosion: Analysis of two experimental approaches[END_REF][START_REF] Antonov | Influence of solid nontransparent inclusion shape on the breakup time of heterogeneous water drops[END_REF][START_REF] Antonov | Impact of holder materials on the heating and explosive breakup of two-component droplets[END_REF] demonstrate principal differences in droplet disruption characteristics between partial fragmentation and micro-explosive breakup scenarios. Basing on these results, at a high concentration of droplets in the gas environment, their partial fragmentation will not have any significant effect on aerosol particle size distribution due to coalescence, bounce, and separation of generated fragments. Only with the low concentration of initial droplets in aerosol and longer droplet travel time, the S1/S0 can be increased up to 3-5 times by partial fragmentation. There are some rare cases when these conditions may occur. For example, in firefighting, the droplet aerosol travel time from the drop zone to the surface of thermally decomposing materials is several minutes. The concentration of atomized droplets remains low due to smaller droplets being entrained by up going high-temperature combustion product flow.

Figs. 4 and5 show that micro-explosive breakup can be ensured in a wide range of both temperature or heat flux, and duration. At relatively low heat fluxes, the duration of initial droplet disruption can be 10 -9 -times longer than in the three impact schemes of atomization. Figs. 4 and5 show that in terms of atomization time, as well as rd/Rd and S1/S0, at higher (over 1000 °С) heating temperature, the micro-explosive breakup scheme becomes the most desirable one. It is the two components with different boiling temperature that become the definitive factor of breakup stimulation. The higher this difference, the greater the breakup stimulation even at relatively low incoming heat flux [START_REF] Antonov | Impact of holder materials on the heating and explosive breakup of two-component droplets[END_REF]. Among the three other schemes -droplet interaction with the wall, with the adjacent droplet, or with the air flow -for equal Weber numbers, wall impact takes the shortest time. Comparative analysis shows that the higher the density and viscosity of liquid, the smaller the difference between droplet breakup duration for droplet collisions and wall impact.

Friction and inertia will have a close effect, especially considering the interaction of hundreds of droplets with the wall. In this case, every droplet impact creates a thin film on the wall surface that will run off. The conditions of impact scenario are close to those of the droplet collision scheme, especially at high velocity and impact angle of 60-90°. That is why relatively close breakup duration, minimum fragment size, and total surface area were recorded under the convective mode of heat transfer (Figs. 4 and5). The conductive mode of heat transfer to the emulsion drop (Mura et al. [START_REF] Mura | Effect of dispersed water droplet size in microexplosion phenomenon for water in oil emulsion[END_REF]) enables a faster atomization of the emulsion drop (within less than 0.03 s). This reported decrease of diameter is actually the average of the same experiment repeated 4 times. It illustrates the case of an optimized micro-explosion, concerning an emulsion drop having a doubled diameter compared to results (1,2,3,4) under convective heat. After a longer heating time as long as 1 s, Watanabe et al. [START_REF] Watanabe | The characteristics of puffing of the carbonated emulsified fuel[END_REF] observe a disintegration of the 0.7-1.3 mm diameter emulsion drop over a duration of 0.5 s., in an electric furnace providing most of its heat as radiation. Fig. 5 clearly shows that at We>100 we can achieve quite high S1/S0 by hitting the droplet with an air jet. Unlike in the droplet collision or impact schemes, there is no counter flowing liquid that would lead to a possibility of coalescence, increasing the fragment size rd, and decreasing the total surface area S. Even at high velocities, the layers of colliding droplets due to high viscosity will produce large fragments when intermixing, especially in the case of coaxial collisions or droplet-to-wall interactions. Air jet impact on the droplet distends the latter, creating a number of liquid arrays, which afterwards are torn into a large amount of smaller fragments. No coagulation was recorded due to the unidirectional motion, hence the higher S1/S0 (Fig. 5). Under the blow of a plasma jet [START_REF] Damiani | A Particle-Tracking-Velocimetry (PTV) Investigation of Liquid Injection in a DC Plasma Jet[END_REF], the "sheet stripping" fragmentation regime in the Weber number interval 100≤We≤350 is interestingly in the same order of magnitude than the other reported results of micro-explosion and air jet impact.

For each droplet interaction scheme (droplet collision, wall impact, and air jet impact), certain conditions are determined when S1/S0 as a function of We reaches an asymptote (Fig. 5). This illustrates the existence of asymptotic relation between inertia, viscosity (internal friction), and surface tension forces for the impact schemes of secondary atomization. There was an indication of such an asymptote in microexplosive droplet breakup experiments, though not in every experiment and not for every component composition. Most likely, the concentration of low-boiling component and droplet heating method have a crucial role here, being the defining factors of S1/S0 [START_REF] Stefanitsis | Numerical investigation of the aerodynamic breakup of Diesel and heavy fuel oil droplets[END_REF].

Comparing the necessary and sufficient conditions

It is of special interest to determine the necessary and sufficient conditions (Figs. 5 and6) of droplet disruption for different schemes of secondary atomization. The corresponding conditions for different liquid compositions are determined in studies [START_REF] Vysokomornaya | Breakup of heterogeneous water drop immersed in high-temperature air[END_REF][START_REF] Negeed | Experimental study on the effect of surface conditions on evaporation of sprayed liquid droplet[END_REF][START_REF] Zen | Ethanol drop impact on an inclined moving surface[END_REF][START_REF] Liang | Liquid sheet behaviors during a drop impact on wetted cylindrical surfaces[END_REF][START_REF] Liang | Review of mass and momentum interactions during drop impact on a liquid film[END_REF][START_REF] Josserand | Drop Impact on a Solid Surface[END_REF][START_REF] Liang | Review of drop impact on heated walls[END_REF][START_REF] Szakáll | Wind tunnel study on the size distribution of droplets after collision induced breakup of levitating water drops[END_REF][START_REF] Kuan | Study on high-Weber-number droplet collision by a parallel, adaptive interface-tracking method[END_REF][START_REF] Ithnin | An overview of utilizing water-in-diesel emulsion fuel in diesel engine and its potential research study[END_REF][START_REF] Stefanitsis | Numerical investigation of the aerodynamic breakup of Diesel and heavy fuel oil droplets[END_REF][START_REF] Sazhin | A simple model for puffing/micro-explosions in water-fuel emulsion droplets[END_REF]. Antonov et al. [START_REF] Antonov | Impact of holder materials on the heating and explosive breakup of two-component droplets[END_REF] summarized the boundary conditions of inhomogeneous droplet atomization through micro-explosive breakup as a result of conductive, convective, and radiative heating. A high-potential task is to evaluate the amount of energy necessary and sufficient to obtain the identical number of smaller liquid fragments. The number and size of fragments can be evaluated using the distributions and curves in Figs. 4 and5. Different ways of energy supply can be implemented in each of the secondary atomization schemes. First, we need to calculate the amount of electrical energy required for liquid flow and air flow generation, as well as for droplet heating. Fig. 6 shows the calculated amount of energy necessary and sufficient to obtain the rd/Rd and S1/S0 shown in Figs. 4 and5.

From Fig. 6a it is clear that the micro-explosive breakup scheme provides maximum S1/S0 and requires maximum electric energy for muffle heating. Considering the ratios of breakup parameters (for instance, S1/S0) to the required energy amount (i.e., to obtain specific characteristics of the secondary atomization), the advantages of micro-explosive scheme are not that substantial comparing to the others. In terms of specific characteristics, the difference will comprise 20 to 60%. Given that micro-explosive breakup provides maximum S1/S0 in the case of considerable droplet composition inhomogeneity [START_REF] Stefanitsis | Numerical investigation of the aerodynamic breakup of Diesel and heavy fuel oil droplets[END_REF], it will not demonstrate any significant increase in S1/S0 and corresponding decrease in rd/Rd when atomizing homogeneous droplets (water in particular).

Using the technique from study [START_REF] Zhao | Interaction of two drops in the bag breakup regime by a continuous air jet[END_REF], we have calculated the dimensionless time (duration) of breakup (secondary atomization) for all the four interaction schemes of liquid droplets (τ=t•Ud•(ρg/ρd) 0.5 /2Rd). Fig. 6b shows that the secondary atomization time can be varied in a wide range by changing the droplet interaction scheme. Efficient ratios between S1/S0 and τ can be chosen as well, considering Fig. 6.

To calculate the amount of energy spent for droplet atomization in different schemes, we considered the energy required for an hour-worth hardware operation (heating chamber, air compressor, etc.). For the micro-explosive breakup scenario, we considered the second hour of the setup operation, since it takes about 40 to 60 minutes to heat up the muffle furnace. The calculated surface area ratio is a mean average from the whole operation of the setup. Size and velocity are similar for all the four schemes, meaning that we can compare the experimental results for similar We numbers. Hardware technical documentation for the air compressor and water pump mentions 7.5 kW/h consumed power at 10 bar pressure and 1.1 kW/h at 1 bar pressure. The power was chosen based on the required pressure. To heat the muffle furnace up to 1100 °С, about 2000 kW of power is needed. This data was used to calculate the required power and to plot the curves in Fig. 6. Fig. 6 demonstrates that the secondary atomization scheme with significant droplet overheating requires the highest energy consumption, as expected. The comparative analysis provides us with several important findings. First, calculation results in Fig. 6 are shown disregarding the amount of simultaneously atomized droplets. It is clear that in the case of impact schemes, i.e., droplet collision, wall or air jet impact, the droplet concentration in aerosol will play an important role. In the case of high-temperature droplet heating, the dispersion and breakup occur with no significant interference from adjacent droplets [START_REF] Antonov | Impact of holder materials on the heating and explosive breakup of two-component droplets[END_REF]. Thus, considering the number of simultaneously atomized droplets, the micro-explosive scheme will be far less expensive than in the case of a single isolated droplet. Second, when comparing the impact atomization schemes, we can see a close amount of required energy. In terms of engineering aspects, the droplet collision scheme as well as droplet and wall (including a heated one) interaction scheme can be considered the simplest ones. The implementation of these two schemes looks more efficient comparing to the air jet impact scheme. Third, the S1/S0 differences do not change much with an increase in the Weber number and thermal flux density. This means that Fig. 6 can be used to predict S1/S0 when droplet velocity and size, as well as heating temperature are varied in a wide range for the four secondary atomization schemes under study.

The result of the comparative analysis predicts considerable energy savings if several secondary atomization schemes are combined. For example, injecting several liquid jets at an impact angle of 60 to 90° to each other can decrease the size of droplets by 5-7 times due to their collisions. Then the falling fragments can be dispersed even more by placing walls, meshes, edges, and other types of obstacles to implement the wall impact scheme of atomization. A heater can be placed in the lower portion of the atomization chamber, overheating the falling fragments to their boiling temperatures and causing further breakup. Such a combination provides substantial thermal and electric energy savings. The initial droplet size prior to the micro-dispersion will be 10-30 times smaller than the ones used in the described experiments with fragmentation through droplet collisions, wall impact or air jet impact. The resulting curves and diagrams form the original experimental database for efficiency evaluation and further development of physical and mathematical predictive models (in particular, [START_REF] Watanabe | Numerical simulation of emulsified fuel spray combustion with puffing and micro-explosion[END_REF][START_REF] Sazhin | Multi-component droplet heating and evaporation: Numerical simulation versus experimental data[END_REF][START_REF] Strotos | Numerical investigation of aerodynamic droplet breakup in a high temperature gas environment[END_REF][START_REF] Warncke | Experimental and numerical investigation of the primary breakup of an airblasted liquid sheet[END_REF][START_REF] Liu | Numerical simulation of liquid droplet breakup in supersonic flows[END_REF][START_REF] Shao | Direct numerical simulation of droplet breakup in homogeneous isotropic turbulence: The effect of the Weber number[END_REF]).

The analysis of the research presented in this paper and the data from studies [START_REF] Vysokomornaya | Breakup of heterogeneous water drop immersed in high-temperature air[END_REF][START_REF] Negeed | Experimental study on the effect of surface conditions on evaporation of sprayed liquid droplet[END_REF][START_REF] Zen | Ethanol drop impact on an inclined moving surface[END_REF][START_REF] Liang | Liquid sheet behaviors during a drop impact on wetted cylindrical surfaces[END_REF][START_REF] Liang | Review of mass and momentum interactions during drop impact on a liquid film[END_REF][START_REF] Josserand | Drop Impact on a Solid Surface[END_REF][START_REF] Liang | Review of drop impact on heated walls[END_REF][START_REF] Szakáll | Wind tunnel study on the size distribution of droplets after collision induced breakup of levitating water drops[END_REF][START_REF] Kuan | Study on high-Weber-number droplet collision by a parallel, adaptive interface-tracking method[END_REF][START_REF] Ithnin | An overview of utilizing water-in-diesel emulsion fuel in diesel engine and its potential research study[END_REF][START_REF] Stefanitsis | Numerical investigation of the aerodynamic breakup of Diesel and heavy fuel oil droplets[END_REF][START_REF] Sazhin | A simple model for puffing/micro-explosions in water-fuel emulsion droplets[END_REF] brings us to a conclusion that the synergistic effects provided by a combination of any of the four schemes under study can be studied reliably through experimental research only. There are several reasons for it. First, in the case of high-temperature heating of the gas environment and droplets, we should consider the vapor buffer layer formed around the latter. It constrains the surface transformation and lowers the heat flux, changing the heat exchange conditions. No reliable models have yet been developed to describe these conditions, especially if the heating temperature exceeds 500 °С. Second, liquid fragments generated by droplet collisions or impact with a wall usually form a cloud that is polydisperse in terms of size. Further disruption of this cloud is difficult to describe in detail. Third, the incoming gas jet deforms the droplet into a shape that is difficult to describe mathematically without significant computational resources. All the three above mentioned problems mean that there is no sufficient base yet for rigorous mathematical modeling.

We analyzed the experimental results in terms of the two traditional assessment criteria for newly designed system or technology: quality and efficiency. This brought us to a conclusion that the microexplosive atomization scheme, being mostly thermal, has the greatest potential in internal combustion engines and other advanced power machinery. The advantage of this scheme over the other three, which are mostly gas-dynamic, can be described as follows. Any gas-dynamic technology can only be implemented in a combustion chamber with additional hardware for air compressing, which is not readily available in contemporary engine designs. At the same time, the energy produced by the engine itself or by fuel combustion power facility cannot be spent for droplet vaporization or its breakup by a gas jet. So, it demands an additional power source and hardware for droplet and gas propelling. However, the thermal micro-explosive scheme can be implemented using the immediately available heat from fuel combustion that is removed for engine cooling. No additional power sources will be needed when utilizing the excess heat, just like in other heat and power industry technologies, and about 250-350 °С will be enough for the micro-explosive atomization. In this regard, the secondary micro-explosive atomization technology will have a clear advantage over any other droplet disruption scheme for traditional fuels, slurries or emulsions [START_REF] Morozumi | Effect of Physical Properties on Microexplosion Occurrence in Water-in-Oil Emulsion Droplets[END_REF][START_REF] Ithnin | An overview of utilizing water-in-diesel emulsion fuel in diesel engine and its potential research study[END_REF][START_REF] Tarlet | Distribution of thermal energy of child-droplets issued from an optimal micro-explosion[END_REF][START_REF] Tarlet | Comparison between unique and coalesced water drops in microexplosions scanned by differential calorimetry[END_REF].

Conclusions

(i) The experiments allowed us to determine the integral characteristics of droplet size and total surface area variation, as well as disruption time for the most commonly used secondary atomization schemes. We gathered enough experimental data to consider the three modes of heat transfer to the emulsion drop leading to its micro-explosion, and also its disruption under plasma jet impact in the "sheet stripping" disruption regime. The comparative analysis revealed a several-fold advantage of the heated droplet microexplosion scheme in terms of these parameters. Droplet size can be decreased 3-10 times depending on the density of the supplied heat flux. Minimum breakup duration can reach 10-20 ms. Total liquid surface area increases 60-100 times.

(ii) In terms of minimum required power for the secondary atomization, micro-dispersion requires the most. The amount of energy required is several or even more than 10 times higher than in the case of collisions, wall impact or air jet impact schemes. Overall, considering the surface area growth and the required amount of smaller liquid fragments, all the five schemes are practicable. However, the droplet micro-explosion and collision schemes have preference, since their efficiency has little dependence on the number and concentration of simultaneously injected droplets.

(iii) The most promising direction for the development of the results presented in this paper is the combined secondary atomization approach by consecutive application of two or three schemes based on different mechanical and physical ways of droplet disruption. For homogeneous droplets, the most practical

Fig. 1 .Fig. 2 .

 12 Fig. 1. Secondary droplet atomization schemes with key parameters: a -collisions; b -wall impact; c -air jet impact; d -micro-explosive breakup by overheating.

Fig. 3 .

 3 Fig. 3. Two video series of frames of the micro-explosion of a 2.5 mm water-in-oil emulsion drop,undergoing Leidenfrost effect onto a 363 °С heated plate (reproduced from Mura et al.[START_REF] Mura | Effect of dispersed water droplet size in microexplosion phenomenon for water in oil emulsion[END_REF]). Microexplosion is optimal in the upper sequence of frames.

3 bFig. 6 .

 36 Fig. 6. Variation of the newly formed fragments' surface area to the initial value ratio (a) with an increase in the consumed energy (for We≈50, 100, 150, and for scheme 4, the heat flux values were 240, 280, 320 kW/m 2 ), as well as parent-droplet disruption time (for rapeseed oil emulsion) (b): 1 -droplet collision; 2wall impact; 3 -air jet impact; 4 -micro-explosive breakup by overheating.

Acknowledgments

Research was supported by the Russian Science Foundation (project 18-71-10002).

combination is droplet collisions at the first stage followed by the impact of the generated fragments with the wall. This combination increases the S1/S0 ratio several-fold. For inhomogeneous droplets, the most promising combination is droplet collision or wall impact at the first stage. After that, the resulting liquid fragments are heated to the boiling temperature followed by micro-explosive breakup. This combination increases the S1/S0 ratio more than 100 times. The air jet impact scheme of droplet disruption can be recommended as an option if need be. This is because in this scenario the generated liquid fragments may stick to the chamber wall opposing the air jet direction, or coalesce with the incoming droplet flow. The parameters of secondary atomization will be heavily dependent on the droplet generation technique. In the case of large-scale aerosol flow, generated by the primary liquid atomization, it is difficult to vary the droplet parameters in a wide range in different sections of the aerosol cloud. experimental data from study [START_REF] Mura | Effect of dispersed water droplet size in microexplosion phenomenon for water in oil emulsion[END_REF] at 100 kW/m 2 and from study [START_REF] Watanabe | The characteristics of puffing of the carbonated emulsified fuel[END_REF] at 375 kW/m 2 ).