Dmitry Antonov

Maxim Piskunov

Pavel Strizhak

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

Jérôme Bellettre

Dispersed phase structure and micro-explosion behavior under different

Keywords: emulsion drop, alternative fuels, two-component droplets, water, micro-explosion

come

Ts -surface temperature of the droplet, °C;

Tsub -copper substrate surface temperature, °C; Ua -air flow velocity, m/s; Vdinitial drop volume, μl.

Greek

α -heat transfer coefficient, W/(m 2 •°C); ɛd -emissivity factor of water droplet; ɛa -emissivity factor of air; λ -thermal conductivity, W/(m•°C); γ -volume concentration of water in the fuel drop, %; ν -kinematic viscosity, m 2 /s; ρ -density, kg/m 3 ; σ -Stefan-Boltzmann constant, W/(m 2 •°C 4 ).

Introduction

The main problems of utilization of a liquid fuel in such industries as transport, heat power engineering, chemical and petrochemical industries and others are stable flaming and ecologically efficient burning [START_REF] Lior | Energy resources and use: The present situation and possible paths to the future[END_REF]. Solving these problems, it is possible to attain more rational use of energy and to decrease the negative effect on the environment significantly. These environmental issues have drawn attention to the combustion of emulsified fuels as an efficient way to improve the combustion process [START_REF] Ismael | Investigation of Puffing and Micro-Explosion of Water-in-Diesel Emulsion Spray Using Shadow Imaging[END_REF], and to reduce pollutant emissions as well [START_REF] Kumar | Ethanol animal fat emulsions as a diesel engine fuel -Part 2: Engine test analysis[END_REF]. There is a group of studies about igniting and burning of hydrocarbon [START_REF] Syrodoy | The influence of the structure heterogeneity on the characteristics and conditions of the coal-water fuel particles ignition in high temperature environment[END_REF], organic coal-water [START_REF] Dmitrienko | Coal-water slurries containing petrochemicals to solve problems of air pollution by coal thermal power stations and boiler plants: An introductory review[END_REF], and oil-water [START_REF] Kichatov | Combustion of emulsion-based foam[END_REF] fuels. A decrease in the concentration of the sulfur and nitrogen oxides can be reached due to their interaction with the water vapor. Coal or fuel oil have surely a higher combustion heat as compared to the mentioned alternative fuels. Nevertheless, if we need to decrease anthropogenic emissions considerably, then one of the most efficient ways is to add water to the fuel. The phenomenon of micro-explosion [START_REF] Kadota | Recent advances in the combustion of water fuel emulsion[END_REF] that happens in a drop of emulsified fuel is related to the secondary atomization [START_REF] Ballester | Large-scale laboratory experiments on pollutant emissions in heavy oil combustion 2[END_REF] noticed in a spray of such emulsion drops, significantly improving its combustion characteristics [START_REF] Watanabe | Observation of droplet behavior of emulsified fuel in secondary atomization in flame[END_REF]. The controlled breakup of fuel droplets containing water will promote to enhance spraying in combustion chambers. Thus, the igniting and burning of fuel emulsions and suspensions will occur more efficiently, with less risk of incomplete burning of fuel and at lower atmospheric emissions of pollutants.

To study micro-explosion at the scale of a unique fuel drop, efforts have been made [START_REF] Moussa | Parametric study of the micro-explosion occurrence of W/O emulsions[END_REF] to identify both the external and internal parameters, i.e. water phase structure, heating temperature etc. that guarantee an optimal disintegration [START_REF] Watanabe | The characteristics of puffing of the carbonated emulsified fuel[END_REF]. Such an optimal disintegration is illustrated in Fig. 1. It is first defined by its short duration (less than 1 ms. Mura et al. [START_REF] Mura | Effect of dispersed water droplet size in microexplosion phenomenon forwater in oil emulsion[END_REF]) and by a maximum number of produced secondary droplets. Watanabe et al. [START_REF] Watanabe | The characteristics of puffing of the carbonated emulsified fuel[END_REF] distinguish between micro-explosion that fragments the whole emulsion drop, and puffing that is only a partial disintegration. The characteristics of an optimal microexplosion have been further explored in [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].

Experimental campaigns focusing on the behavior of a heated water-fuel emulsion drop [START_REF] Watanabe | The characteristics of puffing of the carbonated emulsified fuel[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] 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] together with in-depth numerical investigations [START_REF] Shinjo | Physics of puffing and microexplosion of emulsion fuel droplets[END_REF] are exploring small scales of space and time to identify and explain the phenomena resulting in a reproducible, optimal micro-explosion. Studies [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] 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][START_REF] Shinjo | Physics of puffing and microexplosion of emulsion fuel droplets[END_REF] discuss that aggregation and coalescence of dispersed water droplets considerably influence heating, evaporation, and explosive disintegration of the emulsion droplets. Thus, it allows a significant change of the limit heating temperature and the threshold oil concentration in the emulsion to attain the required breakup mode. We can conclude that an experimental database on the conditions of the explosive breakup, its quantitative and temporal characteristics is needed to develop physical and mathematical models to apply in designing and adjusting the heat and mass transfer equipment. Research [START_REF] Sazhin | Modelling of fuel droplet heating and evaporation: Recent results and unsolved problems[END_REF] explains the reasons for the creation of such models.

The present study gathers a large amount of experimental data concerning heated individual water-fuel emulsion drops. Their lifetime is recorded by a camera, enabling to distinguish successful micro-explosion -or not. The drops undergo one scheme of heating (conductive, convective and radiative) provided at the same temperature range. It is easy to set up an experimental test bench using conductive heating, whereas convective and radiative heating are dominant in industrial-scale spray combustion. These emulsion drops have different structures of their internal phase: a fine emulsion that is already known to prevent coalescence [START_REF] Mura | Effect of dispersed water droplet size in microexplosion phenomenon forwater in oil emulsion[END_REF][START_REF] Tarlet | Distribution of thermal energy of child-droplets issued from an optimal micro-explosion[END_REF], a larger emulsion that is known as promoting an inside coalescence [START_REF] Mura | Effect of dispersed water droplet size in microexplosion phenomenon forwater in oil emulsion[END_REF][START_REF] Tarlet | Distribution of thermal energy of child-droplets issued from an optimal micro-explosion[END_REF], and two-component emulsion drop where coalescence is already achieved.

To sum up, the purpose of this work is to experimentally determine the occurrence and efficiency of explosive disintegration of the heated water-fuel droplets when adding water, as a result of its internal parameters and heat transfer conditions.

Experimental setup and procedure

The present experimental study aims at testing separately different water-fuel droplets that are more or less favorable to coalescence of inside water under each of the three heating schemes. This is important since water coalescence is regarded as essential among the physical processes resulting in an optimal micro-explosion [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] Tarlet | Comparison between unique and coalesced water drops in microexplosions scanned by differential calorimetry[END_REF][START_REF] Shinjo | Physics of puffing and microexplosion of emulsion fuel droplets[END_REF]. Since many thermal and physical processes are interacting together in the heated water-fuel drop, reproducibility of experiments is also taken into account. Thus, each configuration is tested 10 times minimum on the experimental bench.

These emulsion drops have different structures of their internal phase. First, Fig. 2 depicts a fine and rather homogeneous emulsion (mean diameter of 1.2 µm) that is already known to prevent coalescence [START_REF] Mura | Effect of dispersed water droplet size in microexplosion phenomenon forwater in oil emulsion[END_REF][START_REF] Tarlet | Distribution of thermal energy of child-droplets issued from an optimal micro-explosion[END_REF]. This is due to the difficult aggregation of small (~1 µm) water droplets with a high Laplace pressure, into another one being the same diameter. Second, a larger and more heterogeneous emulsion (4 to 8 µm, mean diameter 6 µm) is tested under conductive heating. This emulsion is more likely to promote water coalescence, since a difference in diameter generates a difference in Laplace pressure, pushing the high-pressure small droplet into the bigger one. For this reason, this range of mean diameter of water inclusions has been tested a large number of times, and called the optimal emulsion for micro-explosion [START_REF] Mura | Effect of dispersed water droplet size in microexplosion phenomenon forwater in oil emulsion[END_REF][START_REF] Tarlet | Distribution of thermal energy of child-droplets issued from an optimal micro-explosion[END_REF]. Third, two-component water-fuel drops are also tested, where the water inclusion is a unique droplet generated by a pipette. In this third kind of water-fuel drop, inside water coalescence is already achieved from the beginning. This two-component configuration with a big, unique inside water droplet has been tested before in another experimental facility [START_REF] Tarlet | Comparison between unique and coalesced water drops in microexplosions scanned by differential calorimetry[END_REF] to investigate water coalescence. Fig. 2. Sub-droplets diameter distribution within the fine emulsion based on three repeated measurements.

Producing the tested emulsion droplets

Distilled water (density ρ≈997 kg/m 3 and viscosity ν≈0.96•10 -6 m 2 /s) was used in the experiments.

The main studied substance was fuels and flammable liquids (Table 1): tetradecane; rapeseed oil; diesel.

The 6 µm-emulsion with 5% wt. of water was produced as documented in [START_REF] Mura | Effect of dispersed water droplet size in microexplosion phenomenon forwater in oil emulsion[END_REF][START_REF] Tarlet | Distribution of thermal energy of child-droplets issued from an optimal micro-explosion[END_REF]. The volume concentration of water (γ) in the investigated inhomogeneous (two-liquid) drops is 10% in accordance with three main applications [START_REF] Sazhin | Modelling of fuel droplet heating and evaporation: Recent results and unsolved problems[END_REF][START_REF] Volkov | Using Planar Laser Induced Fluorescence to explore the mechanism of the explosive disintegration of water emulsion droplets exposed to intense heating[END_REF][START_REF] Strizhak | Evaporation, boiling and explosive breakup of oil-water emulsion drops under intense radiant heating[END_REF][START_REF] Volkov | Planar laser-induced fluorescence diagnostics of water droplets heating and evaporation at high-temperature[END_REF]: gasification of water fuel emulsions; thermal purification of liquids from unspecified impurities; creation of fuel emulsions with the use of waste oils, oil sludge, industrial effluents, etc.

The two-component drop was placed in the quartz cylinder using a motorized linear actuator.

Three holes with a diameter of 10 mm were made in the measuring area for introducing the drop into the quartz hollow cylinder, illuminating and video recording its heating and evaporation processes. Video recording of the inhomogeneous droplet heating began at reaching the last axis of symmetry of cylindrical quartz channel 10. The process of the droplet movement from the moment of entering in channel 10 (the wall of the quartz cylinder) to its symmetry axis was about 1 s. The initial time (t=0 s) is understood as a moment when the drop has reached the centre (the symmetry axis) of the quartz channel.

To generate droplets of the desired diameters, two dispensers, Finnpipette Novus Pipettes, were used (variation step of the generated volume of 0.1 µl). The initial volume of the two-component drop in the experiments varied within Vd=10-25 µl. This corresponded to the variation range of the radius Rd=1.3-1.8 mm. A drop of liquid fuel component was suspended on the holder. Further, a drop of water was placed on this drop by means of the second dispenser.

Test benches for the three heating schemes

Two experimental facilities are used in this study (Fig. 3). The emulsion drop is maintained on a heated plate using the Leidenfrost effect [START_REF] Tarlet | Distribution of thermal energy of child-droplets issued from an optimal micro-explosion[END_REF]. This phenomenon results on the rapid vaporization of the bottom layer of a droplet, creating a thin vapor film, thermally insulating the droplet. The hot plate illustrated in the Fig. 3b can achieve a temperature between 450 °C and 500 °C, which is higher than the Leidenfrost temperature [START_REF] Mura | Effect of dispersed water droplet size in microexplosion phenomenon forwater in oil emulsion[END_REF]. It is made of aluminum, and its diameter is 0.6 cm. Temperature is measured by an 80 µm K-type thermocouple with a measurement error of +/-1.5°C. The 6 µm-emulsion with 5% wt. water in tetradecane is tested on this Leidenfrost test bench shown on Fig. 3b. Whereas twocomponent and 1.2 µm-emulsions are tested on the conductive heated substrate fully documented in [START_REF] Volkov | Using Planar Laser Induced Fluorescence to explore the mechanism of the explosive disintegration of water emulsion droplets exposed to intense heating[END_REF][START_REF] Strizhak | Evaporation, boiling and explosive breakup of oil-water emulsion drops under intense radiant heating[END_REF][START_REF] Volkov | Planar laser-induced fluorescence diagnostics of water droplets heating and evaporation at high-temperature[END_REF] that is also maintained at 450°C. The experimental stand with convective or radiative heating schemes shown on Fig. 3a. A hollow metal rod with an inner and outer diameter of 0.5 mm and 0.8 mm, respectively, was used as a drop holder in the experiments. In [START_REF] Volkov | Using Planar Laser Induced Fluorescence to explore the mechanism of the explosive disintegration of water emulsion droplets exposed to intense heating[END_REF], the feasibility of such holder application in comparison with wires and other rods was substantiated (the latter had a significant effect on the rate of heating and evaporation of droplets of homogeneous and multicomponent fluids).

The heat fluxes have been calculated as follows: convectiveconv a s ( ) q T T α = ⋅ -, conductive heat flux in the case of the droplet being heated on a substrate -

sub s cond d ( ) T T q R λ - = , radiative - 4 4 4 rad d a s a a ( ( ) ) q T T T ε σ ε σ = ⋅ ⋅ -+ ⋅ ⋅ .
The quantitative values of heat fluxes might vary within the corresponding limits at T=450-500 °C: qconv=60-70 kW/m 2 ; qcond=70-200 kW/m 2 ; qrad=15-20 kW/m 2 . In each heating scheme, three heat fluxes existed but only one dominated. During computation, the assumptions concerning the optical properties of the drops and the gaseous environment were admitted according to [START_REF] Strizhak | Evaporation, boiling and explosive breakup of oil-water emulsion drops under intense radiant heating[END_REF]. The heat fluxes values can change following to the findings discussed in [START_REF] Sazhin | Droplets and sprays[END_REF] but their trends will remain unchanged. At the wavelengths for temperatures of the micro-explosion phenomenon, an index of absorption corresponds to the values of the order of 10 4 m -1 . The index of absorption was calculated by using a dimensionless absorption coefficient provided in [START_REF] Hale | Optical constants of water in the 200-nm to 200-μm wavelength region[END_REF]. Water absorbs the external radiation partially and, consequently, the transmitted part accumulates at the interfaces inside the tested droplets [START_REF] Kuznetsov | Experimental research of radiative heat transfer in a water film[END_REF].

The research methods are similar to those used in studies [START_REF] Volkov | Using Planar Laser Induced Fluorescence to explore the mechanism of the explosive disintegration of water emulsion droplets exposed to intense heating[END_REF][START_REF] Strizhak | Evaporation, boiling and explosive breakup of oil-water emulsion drops under intense radiant heating[END_REF][START_REF] Volkov | Planar laser-induced fluorescence diagnostics of water droplets heating and evaporation at high-temperature[END_REF]. The main difference of this work from experiments [START_REF] Volkov | Using Planar Laser Induced Fluorescence to explore the mechanism of the explosive disintegration of water emulsion droplets exposed to intense heating[END_REF][START_REF] Strizhak | Evaporation, boiling and explosive breakup of oil-water emulsion drops under intense radiant heating[END_REF][START_REF] Volkov | Planar laser-induced fluorescence diagnostics of water droplets heating and evaporation at high-temperature[END_REF] is the focus on the effect of adding water to fuel on the conditions and characteristics of heating and evaporation of two-component (two-liquid) drops. It is important to establish the necessary water concentration, as well as the temperature at which the explosive disintegration of a two-component drop can be stable. A system consisting of a blower, a heater, and a hollow transparent cylinder (inner diameter of 0.1 m) of heat-resistant quartz glass was used to generate a flow of heated air with controlled parameters (temperature Ta and velocity Ua). Temperature Ta was registered by a measuring complex consisting of a high-speed analog input board and a chromel-aluminum fast-response thermocouple. The latter was placed in the air flow before the drop injection. The motorized linear actuator was used. The velocity of its moving part was 0.5 m/s. The velocity of the air flow Ua in the quartz cylinder was controlled using the optical PIV method [START_REF] Volkov | Using Planar Laser Induced Fluorescence to explore the mechanism of the explosive disintegration of water emulsion droplets exposed to intense heating[END_REF]. Additional experiments were carried out to blow the tracing particles of titanium dioxide (average size of 5 µm) into the heated air flow and to register the flow velocity fields of the latter based on the velocities of the dispersed phase elements. The processes of disintegration of twocomponent drops were studied when they were heated in the air flow with a temperature of 20-1000 °C and a velocity of 0.1-5 m/s.

Results and discussion

The images recorded by the camera during heating of the emulsion drops enable to discriminate between a successful micro-explosion [START_REF] Moussa | Parametric study of the micro-explosion occurrence of W/O emulsions[END_REF] defined as a sudden and total atomization, and a series of partial puffing phenomena.

Influence of the emulsion structure

Table 2 shows the obtained results that are very clear under the different heating modes. Twocomponent water-fuel drops surely undergo a real micro-explosion, whereas the fine and rather homogeneous emulsion, known to prevent water coalescence [START_REF] Mura | Effect of dispersed water droplet size in microexplosion phenomenon forwater in oil emulsion[END_REF][START_REF] Tarlet | Distribution of thermal energy of child-droplets issued from an optimal micro-explosion[END_REF] goes into puffing events. However, the 10% vol. water-in-diesel fine emulsion exhibits 40% of micro-explosion. This result shows that the ~80% lower viscosity of diesel fuel compared with rapeseed oil (see Table 1) can enhance microexplosion in some cases. More generally, the presence of water as a dispersed phase always enables the possibility of a micro-explosion, with a 40% recorded probability in the present case.

The results from Table 2 are shown in Fig. 4, in the form of a graph describing the influence of the initial structure of the emulsion (Din/Dd) onto the micro-explosion success rate. A large number of repeated experiments (160 experiments) results in a clearly increasing tendency. The fine emulsion is limited to puffing phenomena, whereas the two-component drops always undergo a successful microexplosion. The optimal emulsion [START_REF] Mura | Effect of dispersed water droplet size in microexplosion phenomenon forwater in oil emulsion[END_REF][START_REF] Tarlet | Distribution of thermal energy of child-droplets issued from an optimal micro-explosion[END_REF], with nearly 80% of micro-explosion over the 50 experiments,

shows that the ability to coalescence of the dispersed phase is an essential parameter in the emulsified fuel process, even with different thermo-physical properties of the oil shell (Diesel, Rapeseed oil, Tetradecane). This global tendency is observed under each of the three heating schemes at the present temperature range, between 450 and 470°C. It should be noted that (Din/Dd) is in a logarithmic scale. The present results (Fig. 4) show that the microexplosion success rate (M.E.) is actually not a linear function of the initial ratio (Din/Dd), but rather a linear function of its logarithm: ln (Din/Dd). Too small water droplets (Din/Dd → 0) cannot undergo all these successive events in the heating duration, leading to a drastically decreasing value of the success rate (M.E). In this case, the emulsion is too stable to activate coalescence. Two-component drops have already achieved their coalescence events, which results in the maximum value of the success rate (M.E).

At this point, it should be noted that logarithmic behavior was also observed in a previous work [START_REF] Tarlet | Distribution of thermal energy of child-droplets issued from an optimal micro-explosion[END_REF] concerning the fragmentation of parent emulsion into secondary droplets, leading to a log-normal distribution of their thermal energy. The mathematical meaning of logarithmic behavior is the power applied to a number, in other words successive multiplications of a number. Here, the behavior as a function of ln(Din / Dd) suggests that successive multiplications of the diameters of inside water droplets, for example through a series of successive events of coalescence, plays a key role for the successful micro-explosion.

Comparison of the lifetimes during heating

Table 3 shows the lifetimes of the heated water-fuel drops until their complete evaporation.

Concerning convective or radiative heating schemes, micro-explosion delays are in the same order of magnitude whether micro-explosion is successful (two-component drop) or not (fine emulsion). In these cases with more distant heating modes less powerful than the conductive surface, drops last for some seconds until complete evaporation. Whereas conductive, fast heating enables us to observe a real difference between a succeeded micro-explosion that happens quickly, in less than a second concerning the optimal 6 µm-emulsion and the Two-component. Under conductive heating, the non-optimal puffing sequence reaches an order of magnitude longer, since it lasts for some seconds.

Efficiency of the obtained atomization

At the atomization, a sample of child-droplets is visualized using the optical camera (see Section 2.2). The number of child-droplets in the sample is between 9 and 19. Their diameter distribution is taken into account to calculate the sum of the surfaces and the volumes of the child-droplets in the sample (typical frames have been presented in Fig. 5). Then, the increase in the interfacial area (S/S0) is calculated, supposing that this recorded distribution of diameters is the same among all the child-droplets.

Table 4 shows the obtained increase in interfacial area (S/S0) in the present cases. It is nearly one order of magnitude higher in all cases, even when puffing is observed. These results illustrate the significant improvement of water-fuel spray combustion, based on 120 repeated experiments under the different heating modes.

Conclusions

The present experimental campaign was conducted using chosen alternative fuels and range of temperature under the different modes of heating. These experiments were successfully reproducible in the present range of heating parameters and intrinsic properties.

(i) The conducted experiments allowed us to establish the influence of ln (Din/Dd) upon the occurrence of micro-explosion under all heating modes. It confirms the principle of successive events of coalescence [START_REF] Moussa | Parametric study of the micro-explosion occurrence of W/O emulsions[END_REF][START_REF] Watanabe | The characteristics of puffing of the carbonated emulsified fuel[END_REF][START_REF] Mura | Effect of dispersed water droplet size in microexplosion phenomenon forwater in oil emulsion[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] Tarlet | Distribution of thermal energy of child-droplets issued from an optimal micro-explosion[END_REF] leading to a successful micro-explosion.

(ii) The increase in interfacial area (S/S0) is nearly one order of magnitude, even when a sequence of puffing is observed. A remarkable fact is that it does not depend on the heating scheme. This is important for spray combustion, since convective and radiative heat transfers are dominant in this situation.

(iii) The lifetime of the heated water-fuel drop differs between successful micro-explosion and puffing only on the conductive heat bench. At the present temperature range, convective and radiative heat transfers are promoting a more distant, slower heating that does not cause a significant difference between the lifetimes when micro-explosion or puffing are observed.

Fig. 1 .

 1 Fig. 1. Micro-explosion of an water-in-oil emulsion drop [12] -A : Optimal micro-explosion, B: Nonoptimal disintegration.

Fig. 3 .

 3 Fig. 3. (a) The scheme of the facility with convective or radiative heating schemes [20]: 1 -pulse laser; 2 -a lens for forming a laser sheet; 3 -laser sheet; 4 -cross-correlation video camera; 5 -macro-lens; 6light filter; 7 -high-speed video camera; 8 -motorized linear actuator; 9 -drop; 10 -transparent quartz cylinder; 11 -blower; 12 -heater. (b) The scheme of the Leidenfrost facility [10]: A: Threaded support for the hot wire; B: Droplet holder; C: Position of the 80-µm type-K thermocouple

Fig. 4 .

 4 Fig. 4. Micro-explosion success rate, as a function of the initial structure of the emulsion. The number of reproduced experiments [nb] is indicated.

Fig. 5 .

 5 Fig. 5. Typical frames with child-droplets.

Table 1 .

 1 Typical properties of the considered fuels and flammable liquids.

	Liquid	Density at 20°C, kg/m 3	Kinematic viscosity at 25°C, Cst	Flash point, °C	Ignition temperature, °C	Heat of combustion, MJ/kg	Boiling temperature, °C	Heat of evaporation, MJ/kg
	tetradecane	762	2.8	100	202	47.5	254	0.36
	rapeseed oil	920	75	107	260	42.1	204	0.209
	diesel	820	15	57-67	300	42.4	240-347	0.210

Table 2 .

 2 Experimental results. All the configurations were tested 10 times. The 6 µm-emulsion was tested 50 times. Percentages are in volume, unless otherwise indicated.

	Heating scheme	Conductive	Convective Radiative
		Micro-explosion success rate

Table 3 .

 3 Lifetimes during heating of water-fuel drops until complete evaporation. All the configurations were tested 10 times. The 6 µm-emulsion was tested 50 times.These recorded lifetimes indicate that a conductive test bench for micro-explosion enables to quickly trigger and observe a successful micro-explosion. Although its powerful and fast heating significantly differs from the distant convective and radiative heating that are dominant within industrial spray combustion where temperatures are as high as 2000 K.

	Heating scheme	Conductive	Convective Radiative
		Average lifetime [s]
	6 µm-emulsion	5% wt. water-Tetradecane	0.53
	Two-component	10% water in Diesel 10% water in Rapeseed	0.5466 0.2333	5.8704 6.4977	7.0914 6.8252

Table 4 .

 4 The increase in interfacial area (S/S0). All the configurations were tested 10 times.

	Heating scheme	Conductive	Convective Radiative
		(S/S0)
	Two-component	10% water in Diesel 10% water in Rapeseed	10.72 11.90	8.40 11.43	15.49 6.86
	1.2 µm-	10% water in Diesel	9.66	20.44	11.38
	emulsion	10% water in Rapeseed	12.51	9.60	7.03

Acknowledgments

Work on this paper was supported by National Research Tomsk Polytechnic University (project VIU-ISHFVP-60/2019) (contributions by Pavel Strizhak, Maxim Piskunov, Dmitry Antonov). It was also supported by the Région Pays de la Loire (Chaire Connect Talent ODE) concerning contributions by Dominique Tarlet and Jérôme Bellettre.


Moussa Omar

Tarlet Dominique

Massoli Patrizio

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

Investigation on the conditions leading to the micro-explosion of emulsified fuel droplet using two colors LIF method

Keywords: Fluorescence, biofuels, atomization, emulsions Highlights:

Biofuels in the form of water-in-oil (W/O) emulsions are a promising substitution for hydrocarbon fuels, mainly thanks to the micro-explosion phenomenon that occurs under strong heating. Micro-explosion is the atomization of a W/O emulsion drop into daughter droplets because of the water embedded droplets phase change. This atomization leads to the reduction of pollutants and unburnt hydrocarbons emissions. However, micro-explosion is not a systematic phenomenon: indeed, for some cases the water phase change is weak and leads to a partial atomization, called "Puffing". This paper relates a novel approach to better understand the occurrence of micro-explosion. It consists on the identification of the drop triggering the atomization, called the trigger drop, and measure its properties (temperature, size and position within the emulsion drop) thanks to non-intrusive optical diagnostics. Two colors laser induced fluorescence (LIF2C) is the main method used in this work for temperatures. These temperature measurements showed promising results of both quantitative and qualitative aspects. After the calibration steps and the method validation, it is applied for the temperature measurements of water droplets embedded in oil with the maximum temperature recorded around 130°C. Using these measurements methods, a correlation is found between quality of atomization (either micro-explosion or puffing) and the properties of the trigger drop (temperature, size and position). When one of these parameters is not optimal, it can indeed be compensated by the others.

Introduction

Most pollutants and harmful particles produced by humankind (NOx, PM, CO, soot…) are generated by fuels combustion, in the area of transportation, heating systems, energy production…. Knowing the effects induced by these emissions on the atmosphere composition, the energy overconsumption led to tremendous damages to our health and planet [START_REF] Barker | Summary for policymakers[END_REF][START_REF] Solomon | Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change[END_REF].

Liquid fuels (either fossil or biofuels) are injected into the combustion chamber in the form of a spray of droplets. This is called the primary atomization. Previous works showed that smaller are the droplets the more complete is the combustion reaction and this is mainly due to a better air/fuel ratio [START_REF] Vellaiyan | The role of water-in-diesel emulsion and its additives on diesel engine performance and emission levels: A retrospective review[END_REF]. However, by changing the physicochemical properties of the fuels, a secondary atomization can occur, generating even smaller fuel drops. This phenomenon is called micro-explosion and is specific to emulsified fuels, like water-in-oil emulsions [START_REF] Marchitto | Optical investigations in a CI engine fueled with water in diesel emulsion produced through microchannels[END_REF][START_REF] Ithnin | An overview of utilizing water-indiesel emulsion fuel in diesel engine and its potential research study[END_REF][START_REF] Khan | Current trends in waterin-diesel emulsion as a fuel[END_REF][START_REF] Geng | Effects of alternative fuels on the combustion characteristics and emission products from diesel engines: A review[END_REF]. Micro-explosion strongly relies on the difference in the boiling points of oil ([200-300] °C) and water (100°C). Under a strong heating, the water dispersed droplets undergo a phase change that breaks up the emulsion drop into child droplets (Fig. 1). The emulsion drop atomization permits a cleaner and complete combustion thanks to the emulsion drop break up [START_REF] Marchitto | Optical investigations in a CI engine fueled with water in diesel emulsion produced through microchannels[END_REF][START_REF] Ithnin | An overview of utilizing water-indiesel emulsion fuel in diesel engine and its potential research study[END_REF][START_REF] Khan | Current trends in waterin-diesel emulsion as a fuel[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].

One may observe that micro-explosion is characterized by its apparent random aspect. Sometimes the water embedded droplets phase change is not powerful enough to break the oil layer, leading to a partial break up called "puffing" [START_REF] Shinjo | Physics of puffing and micro-explosion of emulsion fuel droplets[END_REF][START_REF] Watanabe | The characteristics of puffing of the carbonated emulsified fuels[END_REF]. Thus, the atomization can be defined by a statistical parameter called "occurrence of micro-explosion", 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].

The present paper relates the experimental analysis of the micro-explosion on-set of water/ntetradecane emulsion drops in Leidenfrost regime. The aim of this work is the identification of the physical conditions leading to a successful micro-explosion. Thus, the drop whose phase change generates the atomization (trigger drop) is sought and the study of the influence of its main parameters (size, temperature and position within the emulsion drop) on the occurrence of micro-explosion is performed. The measurements were conducted using non-intrusive Laser Induced Fluorescence (LIF) for size and position measurements and 2-Colors LIF for the temperature measurements.

Micro-explosion occurrence

Micro-explosion is defined as the fragmentation, in a very short amount of time [START_REF] Mura | Effect of dispersed water droplet size in micro-explosion phenomenon for water in oil emulsion[END_REF] of an emulsified fuel drop into child droplets which provide ideal conditions for a complete combustion. Several authors have investigated the influence of several parameters on the microexplosion phenomena as heating temperature [START_REF] Moussa | Parametric study of the micro-explosion occurrence of W/O emulsions[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], quantity of surfactant or emulsifier [START_REF] Moussa | Parametric study of the micro-explosion occurrence of W/O emulsions[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] 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] 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] 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][START_REF] Nam | An experimental investigation of micro-explosion in emulsified vegetablemethanol blend[END_REF][START_REF] Khan | Experimental investigation of micro-explosion occurrence in water in diesel emulsion droplets during the Leidenfrost effect[END_REF][START_REF] Mura | Emulsion droplet microexplosion: Analysis of two experimental approaches[END_REF][START_REF] Calabria | Combustion fundamentals of pyrolysis oil based fuels[END_REF]. These papers outlined the major role played by the coalescence of dispersed droplets on micro-explosion occurrence, however, without providing quantitative correlation. In a previous work [START_REF] Moussa | Parametric study of the micro-explosion occurrence of W/O emulsions[END_REF], Moussa et al. carried out a parametrical study where micro-explosion occurrence was investigated for different conditions, as a function of the Ohnesorge number (Oh). A particular attention is paid to ensure the same initial parameters for all the drops tested (same size, composition…). Indeed, the emulsion elaboration lasts long enough (15 to 20 minutes) to ensure a steady and homogenous mixture. Micro-explosion occurrence is defined as the ratio between the number of micro-explosion and the number of drops tested while Oh relates the viscous forces to inertial and surface tension forces and its expression is:

𝑂𝑂ℎ = (µ 𝑐𝑐 ) � 𝛾𝛾 𝑊𝑊/𝑂𝑂 ×𝜌𝜌 𝑤𝑤 × 𝐷𝐷 ( 1
)
Where µc is the continuous phase viscosity, γ 𝑊𝑊/𝑂𝑂 is the interface tension between water and oil, 𝜌𝜌 𝑤𝑤 the water density and D the water droplet average size. From the Fig. 2, we can see that micro-explosion is favored for low Oh emulsions (low viscosity, high interface tension and size). This can be explained by an enhancement of the water dispersed droplets motion through the oil phase, which leads to their coalescence. However, High Oh emulsions prevent the water droplets motion and cause a decrease of the micro-explosion rate.

More recently, Moussa et al. [START_REF] Moussa | Insight of a W/O emulsion drop under Leidenfrost heating using LIF optical diagnostics[END_REF] conducted an experimental campaign, aiming to identify the drop whose phase change triggers the atomization (called trigger drop), and try to correlate its [START_REF] Moussa | Parametric study of the micro-explosion occurrence of W/O emulsions[END_REF] properties (size and position) to the occurrence of micro-explosion. Size measurements were performed using Laser Induced Fluorescence (LIF) based techniques with a tracer soluble only in water. This configuration creates the visual contrast needed to identify water droplets from oil phase. Results showed that micro-explosion does not rely on the size and position of the trigger droplets, since it can happen when the trigger droplet is in the center of the emulsion drop or near the interface air/emulsion and is not dependent on its size.

LIF technique for temperature measurements

Laser Induced Fluorescence is an optical, non-intrusive technique allowing the measurements of different properties like concentration of species, temperature and size distributions. It involves the dissolution of a chosen tracer in the gas or liquid to be studied. Each tracer is characterized by its absorption and emission spectrum [START_REF] Chaze | The saturation of the fluorescence and its consequences for laser-induced fluorescence thermometry in liquid flows[END_REF].

The intensity of the emission light 𝐼𝐼 𝑓𝑓 depends on several parameters [START_REF] Delconte | Fluorescence induite par laser multibande appliquée à la mesure de température dans les milieux complexes[END_REF]:

𝐼𝐼 𝑓𝑓 = ∫ 𝐾𝐾 𝑜𝑜𝑜𝑜𝑜𝑜 𝐾𝐾 𝑠𝑠𝑜𝑜𝑠𝑠𝑠𝑠 𝐶𝐶 𝑜𝑜 𝐼𝐼 0 𝜆𝜆+∆𝜆𝜆 𝜆𝜆-∆𝜆𝜆 𝑣𝑣𝑒𝑒 𝑠𝑠 𝑇𝑇 � 𝑑𝑑𝜆𝜆 = 𝐾𝐾 𝑜𝑜𝑜𝑜𝑜𝑜 𝐾𝐾 𝑠𝑠𝑜𝑜𝑠𝑠𝑠𝑠 𝐶𝐶 𝑜𝑜 𝐼𝐼 0 𝑣𝑣𝑒𝑒 𝐴𝐴 𝑇𝑇² � + 𝐵𝐵 𝑇𝑇 � (2)
Where 𝐾𝐾 𝑜𝑜𝑜𝑜𝑜𝑜 and 𝐾𝐾 𝑠𝑠𝑜𝑜𝑠𝑠𝑠𝑠 are optical constants, 𝐶𝐶 𝑜𝑜 the tracer concentration, 𝐼𝐼 0 the intensity of excitation light, T the temperature of the medium and 𝑣𝑣 the collection volume. A and B are constants related to the temperature.

For the configurations where only one detection wavelength is used, temperature can be measured thanks to Eq.3, where A and B are previously computed thanks to a calibration process:

𝑙𝑙𝑙𝑙 � 𝐼𝐼 𝑓𝑓 𝐼𝐼 𝑓𝑓0 � = 𝐵𝐵 � 1 𝑇𝑇 - 1 𝑇𝑇 0 � + 𝐴𝐴 � 1 𝑇𝑇² - 1 𝑇𝑇 0 ² � (3)
Where 𝑇𝑇 0 is the reference temperature, generally room temperature.

However, this method presents few drawbacks when applied to the temperature measurements of emulsion drops. All the parameters presented (except temperature) in the Eq.2 must remain constant in order to measure the intensity evolution generated only by temperature changes. This is hardly the case when it comes to the heating of emulsified fuel droplets. Indeed, for high temperature environments, it is highly probable that the tracer concentration 𝐶𝐶 𝑜𝑜 increases because of droplets evaporation. Moreover it is difficult to quantify the collection volume when coalescence, evaporation and fragmentation of droplets may occur.

In 2001, Lavieille et al. [START_REF] Lavieille | Mesure de la température de gouttelettes en combustion par fluorescence induite par laser à deux couleurs: résultats préliminaires et perspectives[END_REF] improved the temperature measurement using LIF by introducing the two colors LIF (2CLIF). This method relies on the measurement of fluorescence emission intensity on two different wavelengths 𝜆𝜆 1 and 𝜆𝜆 2 and was used for the temperature measurements of mono-disperse ethanol drops jet and evaporating ethanol drops. Considering two different wavelengths we obtain two different fluorescence intensities 𝐼𝐼 𝑓𝑓1 and 𝐼𝐼 𝑓𝑓2 :

𝐼𝐼 𝑓𝑓1 = 𝐾𝐾 𝑜𝑜𝑜𝑜𝑜𝑜,1 𝐾𝐾 𝑠𝑠𝑜𝑜𝑠𝑠𝑠𝑠,1 𝐶𝐶 𝑜𝑜 𝐼𝐼 0 𝑣𝑣𝑒𝑒 𝐴𝐴 1 𝑇𝑇² � + 𝐵𝐵 1 𝑇𝑇 � (4)
𝐼𝐼 𝑓𝑓2 = 𝐾𝐾 𝑜𝑜𝑜𝑜𝑜𝑜,2 𝐾𝐾 𝑠𝑠𝑜𝑜𝑠𝑠𝑠𝑠,2 𝐶𝐶 𝑜𝑜 𝐼𝐼 0 𝑣𝑣𝑒𝑒 𝐴𝐴 2 𝑇𝑇² � + 𝐵𝐵 2 𝑇𝑇 � (5)
The fluorescence ratio 𝑅𝑅 𝑓𝑓 , defined as the intensity ratio of 𝐼𝐼 𝑓𝑓1 and 𝐼𝐼 𝑓𝑓2 can be expressed as:

𝑅𝑅 𝑓𝑓 = 𝐾𝐾 𝑜𝑜𝑜𝑜𝑜𝑜,1 𝐾𝐾 𝑜𝑜𝑜𝑜𝑜𝑜,2 𝑒𝑒 (𝐴𝐴 1 -𝐴𝐴 2 ) 𝑇𝑇² � + (𝐵𝐵 1 -𝐵𝐵 2 ) 𝑇𝑇 � = 𝐾𝐾𝑒𝑒 𝛼𝛼 𝑇𝑇² � + 𝛽𝛽 𝑇𝑇 � (6) 𝛼𝛼 = 𝐴𝐴 1 -𝐴𝐴 2 (7) 𝛽𝛽 = 𝐵𝐵 1 -𝐵𝐵 2 (8)
Considering the fluorescence ratio 𝑅𝑅 𝑓𝑓 instead of the fluorescence intensity 𝐼𝐼 𝑓𝑓 solves the issue of the concentration dependence. Besides, the influence of the collection volume, incident light intensity are also eliminated by computing the fluorescence ratio on two different wavelengths.

Calibration of the 2CLIF method

The calibration of the 2CLIF technique is a critical step in measuring temperature of water dispersed droplets in oil. To this aim, it was studied a single demineralized water drop, previously mixed with Rhodamine B, and embedded in a silicone oil bath. This setting is close enough to the emulsion configuration and enables us to fix the water drop's position in a nonintrusive way.

Experimental set up and procedure

The Figure 3 and 4 represents the experimental setup used for the study of the fluorescence ratio 𝑅𝑅 𝑓𝑓 as a function of temperature. The aim of the study is to measure the influence of the temperature on the evolution of the fluorescence ratio 𝑅𝑅 𝑓𝑓 . The heating device is a VMS-C4 (VWR) heat plate on which the cuvette relies. The temperature is measured thanks to a PT100 sensor which is connected to a proportional-integral-derivative (PID) controller, allowing the temperature to be measured and regulated.

The cuvette containing the different fluids is made of quartz with a square section of 10x10 mm² and a 45 mm height. Quartz is chosen for two main reasons. First, it offers an optimal transmittance for visible light (>95%), and moreover it is also known for its thermal resistance.

The quartz cuvette contains an aluminum support, selected for the high thermal conductivity, on which the water drop is placed. Both the support and the drop are embedded in a silicone oil bath. Silicone oil was chosen as the continuous phase because of its high viscosity that inhibits the water drop displacement. Besides, silicone oil absorption (and excitation) is not concerned by the wavelength range we're interested in, and thus it will not affect the measurements. Thus, we should assume that changing tetradecane into silicone oil doesn't induce any bias.

The measurements are conducted when a stationary state is achieved. When the fixed temperature is achieved, we wait a few minutes for the temperature homogenization and then, we illuminate the water drop with a λ=532nm laser beam (Nd-YAG 2 nd harmonic, Spectra Physics). The 5.5 Watts laser beam is transformed to a planar sheet, whose thickness is around 150 µm, by means of a pair of concave lenses. The fluorescence emitted light is then acquired and visualized thanks to the setup described in the next section.

Acquisition and optical systems

The light emitted by the fluorescent tracer inside the water drop is recorded by a Photron V4 Fastcam high speed camera mounted perpendicularly to the incident beam. It allows the capture of pictures up to 12000 fps with a maximum resolution of 1080x1024 pixels. However, in this paper, the frequency acquisition is fixed to 5000 fps with an exposure time of 0.125 ms. The high speed camera is equipped with a "Gemini" optical splitter device (Hamamatsu) (Fig. 5). The Figure 5 illustrates the optical path of the incident light to the camera sensor. It's a three steps process. First the incident light is splitted into two beams by the means of a dichroic mirror with a defined separation wavelength. The beams go through two band pass filters, defined by the two detection wavelengths λ1 and λ2 (550 and 600 nm for Fluorescein, 600 and 650 nm for Rhodamine B) and are focused on the camera sensor thanks an optical lens. Using this device enables the visualization of the same event at two different wavelengths, as we can see in the Figure 6.

Image treatment process

The raw images recorded by the acquisition system are treated with the Image Processing Toolbox of Matlab. The Fig. 7 highlights the different steps of the process. First, the two similar size images (𝑚𝑚 × 𝑙𝑙) are extracted. They undergo some translation/rotation operations in order to accurately overlay one picture on the other. Each pixel of the resulting image corresponds to the intensity ratio of the two initial pictures (Eq.9): The key point that should be controlled is the amplitude of the fluorescent light signal. Indeed, it should be high enough to be detectable by the sensor, but always below the saturation threshold. Several parameters govern the emitted light intensity, as described in the Eq. 2. Thus, a dedicated study was carried out to define the most appropriate configuration of the experimental system.

𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟(𝑟𝑟, 𝑗𝑗) = 𝑖𝑖𝑖𝑖𝑜𝑜𝑠𝑠𝑖𝑖𝑠𝑠𝑖𝑖𝑜𝑜𝑠𝑠 𝜆𝜆 1 (𝑖𝑖,𝑗𝑗) 𝑖𝑖𝑖𝑖𝑜𝑜𝑠𝑠𝑖𝑖𝑠𝑠𝑖𝑖𝑜𝑜𝑠𝑠 𝜆𝜆 2 (𝑖𝑖,𝑗𝑗) (9)
The first critical aspect we are called upon to take is the choice of the tracer because of some constraints.

-The tracer needs to be soluble in water but not in oil. This a necessary condition to create the contrast needed for the visualization of the water embedded droplet.

-The tracer has to be excitable by a 532 nm laser sheet.

-The fluorescent light emitted by the tracer needs to be temperature-sensitive, between 20 and 150°C and its amplitude suitable with the actual acquisition system.

The two tracers selected are Fluorescein and Rhodamine B. The fluorescence was detected at 550 and 600 nm for Fluorescein, and 600 and 650 nm for Rhodamine B. In the Table 1, are presented the experimental conditions studied. As it was stated, different configurations are tested (Tab.1). As it is highlighted, 𝑅𝑅 𝑓𝑓 decreases with temperature for Rhodamine B with a ratio range between 1 and 3. The trend is different for Fluorescein. Indeed the ratio is increasing between 2 and 3.

Fluorescein

The increasing of the ratio means that the intensity itself is increasing with temperature, which may represent an advantage because of the quality enhancement of the images.

However, in the fluorescein case, the trend does not seem to be monotonous as two local maxima can be observed. This implies that the relation between 𝑅𝑅 𝑓𝑓 and temperature is non bijective and therefore the fluorescein cannot be selected. All of the following experiments and results are conducted using Rhodamine B.

Validation of the initial assumptions

As previously stated, different configurations are tested for the study of the influence of parameters like the tracer concentration (Fig. 9 a) or the incident light power (Fig. 9 b). The most remarkable result emerging from the data in the Fig. 9 is the non-dependency of 𝑅𝑅 𝑓𝑓 on both the concentration ratio and the incident light power, despite some variation caused by experimental errors. These findings confirm and validate the assumptions made in the section 1.2.

Estimation of the coefficient

The fluorescence ratio 𝑅𝑅 𝑓𝑓 can be expressed as a function of the medium temperature (Eq.6). If we consider a reference ratio 𝑅𝑅 𝑓𝑓0 computed at 𝑇𝑇 = 𝑇𝑇 0 (the room temperature is around 20°C), we obtain:

ln � 𝑅𝑅 𝑓𝑓 𝑅𝑅 𝑓𝑓0 � = 𝛼𝛼 � 1 𝑇𝑇 2 - 1 𝑇𝑇 0 2 � + 𝛽𝛽 � 1 𝑇𝑇 - 1 𝑇𝑇 0 � (10)
A variable substitution can be operated, thus obtaining a second order polynomial. This procedure is then applied to several droplets in identical experimental conditions. Six cases were selected because of their high determination coefficient (R²>0.97). The Table 2 lists the values of the coefficient α, β and K computed for each case. The average values of these parameters were integrated into a "model correlation" that will be used for the temperature measurements. The Figure 11 shows the 𝑅𝑅 𝑓𝑓 evolution with temperature for all the cases selected and the model correlation.

Y = ln � 𝑅𝑅 𝑓𝑓 𝑅𝑅 𝑓𝑓0 � (11)
𝑋𝑋 = � 1 𝑇𝑇 - 1 𝑇𝑇 0 � ( 12
)
𝑌𝑌 = 𝛼𝛼𝑋𝑋 2 + �𝛽𝛽 - 2𝛼𝛼 𝑇𝑇 0 � 𝑋𝑋 (13)
The next step consists of expressing temperature as a function of the ratio (Eq.14), by computing the inverse function of the Eq.6. ) should be positive. Thus, there is a critical value of 𝑅𝑅 𝑓𝑓,𝑠𝑠𝑐𝑐𝑖𝑖𝑜𝑜 above which the result (temperature) be will complex.

𝑇𝑇 = 2𝛼𝛼 -𝛽𝛽∓�𝛽𝛽 2 +4𝛼𝛼ln ( 𝑅𝑅 𝑓𝑓 𝐾𝐾 𝑜𝑜𝑜𝑜𝑜𝑜 ) ( 14
)
𝑅𝑅 𝑓𝑓,𝑠𝑠𝑐𝑐𝑖𝑖𝑜𝑜 = 𝐾𝐾 𝑜𝑜𝑜𝑜𝑜𝑜 𝑒𝑒 -𝛽𝛽² 4𝛼𝛼 � (15)
All the results presented are deduced from experiments conducted at atmospheric pressure. For this reason, the temperature could not exceed the boiling point of water, which is 100°C. The range studied is [20-100°C]. However, during the heating of water-in-oil emulsion droplet, temperature of the water dispersed droplet may achieve metastable levels. This means that the water temperature is higher than 100°C, which is hardly reproducible for calibration experiments. For these specific cases (temperature >100°C), the temperature is computed by extrapolation of the theoretical model.

Validation of the measurement method

The aim of this section is to validate the 2CLIF method for temperature measurements. The 2CLIF results will be compared to thermocouple measurements during the heating of a W/O emulsion drop under Leidenfrost effect.

Experimental method

The experimental setup bears a close resemblance to the one used in a previous paper [START_REF] Moussa | Insight of a W/O emulsion drop under Leidenfrost heating using LIF optical diagnostics[END_REF].

However, we adapted it for the temperature measurement which requires two detection wavelengths by using an optical splitter device.

The acquisition and visualization material is the same as the setup described in the Fig. 5 and6.

Concerning the heating device, it consists of a customized heat plate and is composed on several elements (Fig. 12). A 6 mm diameter aluminum drop holder is designed with a circular convex geometry in order to trap the emulsion drop, avoiding its lateral displacement and eventually its fall. A resistive wire is mounted around the drop holder and is connected to a power supply.

Temperature of the plate is measured by means of a 80 µm K-type thermocouple placed at the bottom of the drop holder, with an accuracy of ±1.50°C. The thermocouple is coupled with a proportional integral derivative controller for the temperature regulation.

In the present study, the emulsion studied is a demineralized water/n-tetradecane emulsion, with 5% vol of water. Demineralized water is favored because of its relative purity that enhances the recording quality. n-tetradecane, like silicone oil that can only be excited in the UV band. It will not affect the 2CLIF measurements based on visible light excitation and detection. SPAN 83 is added (0.1%vol) to the emulsion in order to lower the interface tension between the two phases and improve the system stability. Rhodamine B is the fluorescent tracer, with a concentration of 2.2 g/L. This concentration may seem high and different from the concentration used for the calibration process, but it is needed for the visualization. Indeed, in the case of Rhodamine B, the fluorescent light intensity decreases with the temperature. Therefore, a high concentration of tracer is needed in order to ensure the visualization at the final stages of the fuel drop lifetime. The emulsification is performed using a mechanical stirrer at 1500 rpm during 10 minutes at room temperature. The recorded images undergo the treatment described in 2.1.3. As it is mentioned, each pixel of the resulting image corresponds to the fluorescence ratio computed. This ratio used for the temperature computation thanks to the Eq.14 (Fig. 13).

Emulsion drop

Time (ms) Processed image Description 0

The emulsion drop is about to be put on the 500°C heat plate. We can see the thermocouple located few millimeters above the heat plate so that it can be embedded in the drop.

Dispersed droplet temperature is still close to room temperature. Their size is also too small for identification 69 Partial coalescence of the water droplets, increasing their size. Temperature seems also to be slightly increasing. 197 Significant increase of the water droplet temperature. We can observe few colder droplets on the close to the heat plate. This can be due to convection motions 326

Intermediate puffing leading to the ejection of a small part of the emulsion drop. In this specific droplet, one can observe that its temperature is decreasing, since it's not in contact with the heat plate. On the same time, the water temperature inside the remaining emulsion drop keeps increasing and is getting homogenous.

Table 3 : Qualitative analysis of the temperature evolution of water dispersed droplets

Quantitative validation

In this section, the 2CLIF results will be compared to the temperature measured by a 80 µm Ktype thermocouple located inside the emulsion drop. As we can see from the Fig. 14, this process is applied to 4 different cases with identical initial conditions. The emulsion contains 5%vol of demineralized water, 0.1%vol of surfactant (Span83) and n-teradecane and the heat plate temperature is fixed at 500°C. For the 2CLIF method, the temperature is computed in a small area (10x10 µm²) located close to the thermocouple. This configuration enables to compare both temperatures at nearly the same location, which is an important issue considering the temperature gradient within the emulsion drop. The marked observations to emerge from the data comparison illustrated in the Fig. 14 are: -The maximum temperature achieved in the studied cases is around 100°C, which represents the boiling point of water at atmospheric pressure. The metastable state is inhibited by the presence of the thermocouple inside the emulsion drop.

-The 2CLIF results are not smoothed because we couldn't differentiate between noise oscillation and oscillations caused by physical phenomena that may happen inside the emulsion drop like phase change, puffing and mainly internal convection [START_REF] Antonov | Temperature and convection velocities in two-component liquid droplet until micro-explosion[END_REF].

-Both methods seem to be in agreement whit each other as the trend is nearly the same.

The average error ΔT is lower than 5°C after 100 ms for all the studied cases.

Investigation of the micro-explosion onset

After the calibration and the validation of the 2CLIF method, the interest was laid on the temperature distribution of water dispersed droplets as well as its evolution during the lifetime of the emulsion drop. The emulsion contains 5%vol of water, 0.1%vol of surfactant and ntetradecane. This composition is chosen because it offers a high rate of micro-explosion [START_REF] Moussa | Insight of a W/O emulsion drop under Leidenfrost heating using LIF optical diagnostics[END_REF], and therefore, it's optimal for studying the atomization trigger. Regarding the random aspect of the atomization process, 58 drops were studied, resulting in 38 micro-explosions (65.5%) and 20 puffings (34.5%). As previously stated, a special effort is made in order to ensure that the 58 drops tested contains the same amount of water and that the size distribution is unchanged.

In this section, three aspects are considered. First, the temperature evolution of a single water dispersed droplet, then the temperature spatial distribution. Finally, we investigated the influence of the trigger drop properties (size, temperature and position) on the quality of atomization.

Temperature evolution

The temperature evolution measurements rely on the processing of "n" successive images where the concerned water droplet is visible and identifiable. Internal convective motions within the emulsion drop can elicit the water droplet to move from the laser sheet and therefore to disappear. For this reason, the temperature evolution is computed for only few ms while the emulsion drop lifetime lies between 300 and 900 ms.

Two water drops (D1) and (D2) are studied. The first one has an ascending motion (Fig. 15) and the second one a downward motion (Fig. 16). Initially, the drop (D1) is located in the bottom part of the emulsion drop. It is important to remind that the heat source is located underneath the emulsion drop. The temperature gradient generates an ascending motion of the water droplet that affects its temperature evolution. As depicted by the Fig. 16, the water droplet temperature decreases from 63 to around 45°C in 6 ms. For similar reasons, the temperature of droplet (D2) increases with time, gaining around 20°C in 5 ms (Fig. 16). The presented evidences (Fig. 15 and16) suggest the existence of a "temperature cycle" that concerns the majority of the water droplets (when convective motion effects are higher than gravity's). The first phase is its temperature increasing resulting into the emergence of a density gradient (Boussinesq effect) as well as an interface tension gradient (Marangoni effect). As a result, it triggers the water drop ascending motion towards the top part of the emulsion drop, naturally cooler than the rest of the drop. Moreover, this water drop motion is also driven by the natural convection of the oil phase. From this moment the second phase is triggered: the temperature decreases noticeably, inducing the rise of its density. Thanks to gravity effects, the water droplet goes back near the heat source and another cycle is about to begin. It is hard to quantify the frequency of these "temperature cycles" due to the tridimensional aspect of the convective motions, but the order of magnitude ranges between 10-20 ms for smaller droplets up to 70-90 ms for bigger ones. It must be emphasized that our experimental set up allows us to visualize only the water droplets located in the laser sheet. Moreover, these convection motions could also be induced by mechanical means. Indeed, when the drop falls on the heat plate, it swells and gets deformed (this happens also after an intermediate puffing), which may induce a flow within the emulsion drop.

Convective motions are not the only phenomenon that influences the temperature evolutions. Indeed, between each cycle, the temperature of a given water droplet can vary because of coalescence events. The temperature of a water droplet created by the coalescence of two water droplets is the weighted average of these two droplets temperature (Fig. 17). Coalescence permits the generation of bigger droplets, which reinforce the impact of gravity, inertia and drag force and reduces the internal convective motions. One coalesced water drop tends to stay next to the heat source, which may lead to faster temperature rise. After each temperature cycle, the temperature level increases. When it's getting close to the saturation temperature (100°C for the water), two scenarios are possible: The droplet can undergo additional cycles, its temperature can achieve metastable levels and its phase change may induce a micro-explosion. The other option consists in a phase change at low temperature (100°C) which may generate a puffing. This point will be discussed further.

Temperature distribution within the emulsion drop

The heating method (Leidenfrost effect in this case) implies the existence of a spatial temperature gradient within the emulsion drop. In this section, the evolution of the temperature gradient is investigated through the temperature measurements of different water drops at the same moment (Tab.4).

Time (ms) Images Comments

43.2

This image is taken a short time (2 ms) before touching the heat plate.

The water droplets temperature is homogenous around 45°C with a deviation of 3°C (less than the accuracy of the method) 97.2

A small spatial temperature gradient appears within the emulsion drop. The average temperature of the water droplets located in the top part is 35°C in average while it increases to 50°C for the droplets located next to the heat source 184

The first effects of convection motion are noticeable since the temperature distribution tends to get more homogenous.

264.8

Same observations can be made. One may notice that the temperature undergoes a significant rise (+11°C in average)

366.4

This image represents the last moments preceding the puffing. The temperatures are getting close to saturation point except for the large water drop in the right part. This specific drop underwent a double coalescence, which can explain its surprisingly low temperature

Table 4: Evolution of the temperature distribution

The emulsion drop studied in the Tab.4 underwent a puffing generated by the phase change of the water droplets whose temperature is 92.4°C (Fig. 18) It is interesting to notice that the temperature of the other water droplets is consistently lower than the trigger drop's. The atomization occurs before the temperature homogenization within the emulsion drop. If the temperature of the surrounding droplets is higher, the first phase change can lead to the phase change of these droplets leading to a more powerful break up. This point is discussed in the next section.

Occurrence of micro-explosion

This section is dedicated to the study of the atomization of emulsion drops, containing 5%vol of water, 0.1% of surfactant (SPAN 83) and n-tetradecane. As mentioned earlier, 58 drops are considered, resulting in 38 micro-explosions (65.5%) and 20 puffings (34.5%).

The average lifetime of the emulsion drop is 482.7 ms. From the Fig. 19 it appears that the lifetime of the emulsion drop is influenced by the number of intermediate puffing that occurred. Intermediate puffing can be defined as a water droplet phase change without causing the atomization (even partial) of the emulsion drop. For lifetimes higher than 550 ms, microexplosion is dominant over puffing.

Figure 19: Emulsion drops lifetime as a function of number of puffings occured

For each drop investigated, our intention is to identify the trigger drop and measure its properties at the moment of atomization (temperature, size and relative position). The identification of the trigger drop is the key point of this study, and three different configurations are possible: -The trigger drop is not identifiable due to a low image quality at the moment of phase change or because it is not crossing the laser sheet. This concerns 29 drops among the 58 studied (50%).

-The trigger drop is identifiable but disappears from the vision field few ms before the phase change. Its properties are then measured at 𝑟𝑟 = 𝑟𝑟 𝑎𝑎𝑜𝑜𝑜𝑜 -∆𝑟𝑟, where ∆𝑟𝑟 is the time delay between the atomization and the last moment where the trigger drop is visible and lies between 0.2 et 12.4 ms. This configuration concerns 13 among the 29 cases where the trigger drop is identifiable (44.8%).

-The trigger drop is identifiable and visible at the moment of the phase change. In this case ∆𝑟𝑟 = 0. (55.2%).

Two aspects need some clarification before the results presentation:

-The temperatures measured are average temperatures within the water droplet. For larger drops, it seems highly probable that temperature gradients exist within the water droplet. Unfortunately, the resolution of the acquisition system is not suitable for measuring such spatial gradient with accuracy, since each pixel of the acquisition system computes an average value of ratio Rf that is converted to temperature. However, the temperature gradient ranges between 5°C/mm for smaller water drops up to 20°C/mm for larger drops.

-The size and position of the trigger drops are "normalized". At the moment of the atomization, the emulsion drop size is not always the same, from one case to another. This is a consequence of the evaporation rate and the intermediate puffing occurring during the emulsion drop lifetime. For this reason, size is considered as non-dimensional parameter𝑅𝑅 𝑜𝑜 , defined by the Eq.16:

𝑅𝑅 𝑜𝑜 = 𝐷𝐷 𝑜𝑜𝑡𝑡𝑡𝑡𝑡𝑡 𝐷𝐷 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 (16)

Micro-explosion

As outlined earlier, 29 trigger drops were identifiable and among them 22 leaded to a microexplosion (76%). The position, size, temperature of these trigger drops are illustrated in the Fig. 20.

As displayed in the Fig. 20, most of the trigger drops are located in the bottom part of the emulsion (17 out of 22 or 77%). This can be explained by the density difference between dispersed and continuous phase (water and oil). However, smaller trigger drops can be located in the top part of the emulsion drop, mainly because of ascendant convective motions, that are dominant for smaller drops. The non-dimensional size 𝑅𝑅 𝑜𝑜 range lies between 7.8 and 33%, with an average value of 18%. Temperature of phase change varies between 93 and 129°C. One may observe that smaller trigger drops are the warmer. This could be attributed to a faster temperature homogenization within the smaller drops and a wider temperature distribution within the larger ones (Fig. 21).

Two cases can be examined in greater details (a) and (b), representing the respectively the trigger drop with a phase change temperature of 129°C and 93°C. -The accuracy of this temperature measurement methods needs to be taken into account -The trigger drop temperature is not measured at the exact moment of atomization. The measure is made 5.8 ms before the atomization. It's highly that temperature of the trigger drop increased, since it is located in the bottom part of the emulsion drop.

-As stated below, the temperature measured is an average temperature. And since we stated that there may be a temperature gradient within the trigger drop, the measured temperature may not be representative of the phase change temperature.

-In this case, the micro-explosion is triggered by the phase change of two different droplets (Fig. 23). The first phase change occurs at T=93°C and triggers the phase change of a second droplet which temperature is 98.5°C. It appears the first phase change has created perturbations (with the swelling and deformation of the emulsion drop) that lead to the second phase change. Therefore, micro-explosion can occur even if the trigger droplet temperature has not reached metastable temperatures, provided a good temperature homogenization within the emulsion drop. This observation corroborates the findings obtained by Moussa et al. [START_REF] Moussa | Parametric study of the micro-explosion occurrence of W/O emulsions[END_REF] (Section 1.2). Indeed, it was concluded that micro-explosion is enhanced for low Ohnesorge emulsions, because of the ability of the dispersed droplets to move within the continuous phase. In other words, internal convection motions result in the temperature homogenization where the water droplets are acting as energy vectors, but enhance also the coalescence rate of the water droplets, leading to the increase of their average size and size distribution.

Puffing

Puffing occurred for 7 times over the 29 cases where the trigger drop is identifiable. The properties of the trigger drops are depicted in the Fig. 24. As illustrated in the Fig. 25 and 26, many water drops can be potential trigger droplets. For the case (c), the phase change temperature is very low (86°C) and the temperature of the surroundings droplets is not sufficient to trigger a second phase change. For the case (d), the phase change temperature is around 92°C. It could have triggered a micro-explosion but the position of the trigger droplet is not optimal, and the temperature of the surrounding droplet is not close enough to the saturation point in order to trigger a second atomization.

Criterion for optimal atomization

Temperatures and sizes of trigger droplets are presented in the Fig. 27 for both puffings and micro-explosion. According to the Fig. 27, the smaller is the trigger drop, the higher should be the phase change temperature.

One exception is observed (points circled in red) near the virtual line separating microexplosions from puffings. For these two cases, the size and phase change temperature are similar, but one drop leads to puffing when the other undergoes a micro-explosion. For this kind of configurations, there are two possible explanations:

-The trigger drop position can be an important parameter, since a trigger drop located near the interface emulsion/air is more likely to generate a puffing.

-Even if the phase change temperature of the trigger drop is not high enough, temperature homogenization within the drop can lead to a micro-explosion by triggering "chain" phase changes. As discussed earlier, the temperature homogenization is permitted by internal convection motions The enthalpy level of a given drop is proportional to both its radius 𝑅𝑅 and its phase change temperature 𝑇𝑇 𝑜𝑜𝑐𝑐𝑖𝑖𝑡𝑡 . As illustrated in the Fig. 28, the higher is the distance from the emulsion drop center, the higher should be the trigger enthalpy level in order to trigger an optimal atomization. The points ( 1) and ( 2) are characterized by a relatively high level of energy, however the phase change temperature is low (respectively 85 and 91°C). For the drop (3), a micro-explosion occurred with a phase change temperature of 112°C, which compensates the large distance to the emulsion drop center.

To sum up, temperature size and position of the trigger drop are the three parameters influencing the quality of an atomization (either puffing or micro-explosion). When one or two of these parameters is not optimal, they can be compensated by the influence of the third one. However, they can be ranked by order of importance. If the phase change temperature is high enough (115-130°C), micro-explosion occurs regardless of the size and position of the trigger drop. For lower temperatures (100-115°C), micro-explosion can happen if the trigger drop's size is high enough to provide a sufficient enthalpy level, or if the temperature is homogenized within the emulsion drop. For temperatures between 90-100°C, position of the trigger drop can enhance micro-explosion over puffing.

Conclusion

To investigate micro-explosion of emulsion drops, the study first presents the design and set up of a non-intrusive temperature measurement method of the inside water droplets, based on fluorescence and called LIF2C. This method is well suited for the visualization of processes like the atomization of an emulsified fuel droplet under Leidenfrost effect. Indeed, thanks to this method, the quantification of the tracer concentration, collection volume and incident light intensity is no longer needed.

The first calibration step is crucial. The tracer type and concentration is chosen, as well as the two detection wavelengths. In our case, Rhodamine B is selected over the other tracers: first, its high solubility in water and negligible in oil, the temperature dependence of the fluorescence light intensity emitted, and its compliance with the incident light wavelength. First measurements showed appreciable results both on the quantitative and qualitative aspects, even though they can be improved: The LIF2C calibration process is conducted for temperatures between 20 and 100°C, while some water drops can achieve metastable states.

Concerning micro-explosion occurrence, the influence of the temperature, size and position of the trigger drop were investigated. We also observed the importance of internal convective motions: Inside water droplet are frequently observed changing their temperature rapidly, while moving from the hotter bottom to the colder top of the emulsion drop undergoing Leidenfrost effect.

Successful micro-explosion is triggered in most cases by water droplets reaching the highest temperature, and the highest enthalpy depending on its distance to the center of the emulsion drop. To sum up, temperature size and position of the trigger drop are the three parameters influencing the quality of an atomization (either puffing or micro-explosion). When one or two of these parameters is not optimal, they can be compensated by the influence of the third one.

Future work should focus on the LIF 2C calibration at higher temperatures, in a high-pressure cavity. Increasing the pressure should increase the boiling point of water, and therefore, it should achieve temperatures higher than 100°C, while it is still liquid. Another focal point is the temperature evolution measurement of the oil phase that can be conducted using Laser Induced Phosphorescence methods. This information may enlighten us on the heating kinetics of the two phases as well as the temperature difference between them.

Nomenclature:

Figure 1 :

 1 Figure 1: Schematic representation of a micro-explosion

Figure 2 :

 2 Figure 2: Influence of Oh number on the micro-explosion occurrence[START_REF] Moussa | Parametric study of the micro-explosion occurrence of W/O emulsions[END_REF]

Figure 3 :Figure 4 :

 34 Figure 3: Experimental design for the calibration of the LIF2C method

Figure 5 :

 5 Figure 5: Scheme of the optical splitter device

Figure 7 :

 7 Figure 7: Image treatment process

2. 2

 2 Preliminary results2.2.1 Tracer selectionThe Figure8illustrates the evolution of the fluorescence ratio 𝑅𝑅 𝑓𝑓 as a function of temperature for both Rhodamine B (a) and Fluorescein (b).

Figure 9 :

 9 Figure 9: Influence of the Rhodamine B concentration (a) and the incident light power (b)

Figure 8 :

 8 Figure 8: Fluorescence ratio Rf vs temperature for Rhodamine B (a) and Fluorescein (b)

Figure 10

 10 Figure 10 (a) illustrates the evolution of 𝑅𝑅 𝑓𝑓 as a function of the temperature of a water droplet mixed with Rhodamine B. The tracer concentration is 100 mg/L and the incident light power is fixed at 5.5 Watts. After the application of the variable change (Eq.11-12), we can plot the evolution of Y as function of X.

Figure 10 :

 10 Figure 10: Evolution of Rf as a function of temperature and estimation of the coefficientsFigure 10 (b) indicates that the second order polynomial is suitable to fit the experimental data, with a good accuracy determination coefficient better than 0.99. From the coefficients of the fit, one can compute the values of α, β and K and thus, by using the Eq.(6), to correlate the fluorescence ratio to the medium temperature In this specific case, 𝛼𝛼 = -1.79 × 10 6 , 𝛽𝛽 = 1.21 × 10 4 and 𝐾𝐾 = 3.03 × 10 -9 .

Figure 11 :

 11 Figure 11: Evolution of Rf with temperature for all the cases selected

Figure 12 :

 12 Figure 12: Heat plate design. A: Aluminum support; B: Drop holder; C: Location of the thermocouple

Figure 13 :

 13 Figure 13: Steps of the image treatment process 3.3 Qualitative validation

Figure 14 :

 14 Figure 14: Temperature evolution measured by both LIF2C method and thermocouple

Figure 15 :Figure 16 :

 1516 Figure 15: Temperature evolution of a water droplet with a downward motion

Figure 17 :

 17 Figure 17: Temperature of water droplets before and after coalescence

Figure 18 :

 18 Figure 18: Puffing of the emulsion drop studied in the Tab.4

Figure 20 :

 20 Figure 20: Temperature, size and position of trigger drops that lead to micro-explosion

Figure 22 :

 22 Figure 22: Micro-explosion of the emulsion drop (a)The case (a) is depicted in the Fig.22, The trigger drop is circled in red. The temperature phase change is around 130°C, which create a brutal metastable phase change leading to break-up of the emulsion drop. As we can see in the Fig.22, the emulsion drop totally disappears from the view field within 0.2 ms.The case (b) is presented in the Fig.23. As it was mentioned earlier, the phase change temperature in this case is 93°C. It may seem illogical that the phase change temperature measured is 93°C, since the saturation point is 100°C.

Figure 21 :

 21 Figure 21: Temperature gradient within a water droplet

Figure 23 :

 23 Figure 23: Micro-explosion of the emulsion drop (b)

Figure 24 :

 24 Figure 24: Temperature, size and position of the trigger drops that lead to a puffingIn average, the phase change temperature is lower for puffings (92°C) than micro-explosion (106°C). The non-dimensional size is also lower (14% against 19% for micro-explosions). When it comes to the size and position of the trigger drops, the same observations than microexplosion can be made. Two cases (c) and (d) are considered, with a size of respectively 10 and 33% (Fig 25and 26).

Figure 25 :

 25 Figure 25: Puffing of the emulsion drop (c)

Figure 27 :

 27 Figure 27: Size vs temperature of all the trigger dropsConcerning the influence of the trigger drop position, we have computed the enthalpy level of each drop ∆𝐻𝐻 𝑑𝑑 (Eq.17) as a function of the distance between the center of the trigger drop and the center of the emulsion drop: ∆𝐻𝐻 𝑑𝑑 = 𝑚𝑚 𝑑𝑑 𝑐𝑐 𝑜𝑜 �𝑇𝑇 𝑜𝑜𝑐𝑐𝑖𝑖𝑡𝑡 -𝑇𝑇 𝑐𝑐𝑠𝑠𝑓𝑓 � ∝ 𝑇𝑇 𝑜𝑜𝑐𝑐𝑖𝑖𝑡𝑡 𝑅𝑅 3[START_REF] Khan | Experimental investigation of micro-explosion occurrence in water in diesel emulsion droplets during the Leidenfrost effect[END_REF]

Figure 28 :

 28 Figure 28: Energy level of the trigger drop as a function of the distance to the emulsion drop center

Table 1 :

 1 Experimental conditions

Table 2 :

 2 Calibration coefficient for all the cases selected

Acknowledgment:

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