Heating, evaporation, fragmentation, and breakup of multi-component liquid droplets when heated in air flow

Chemical Engineering Research and Design 1 4 6 ( 2 0 1 9 ) 22–35

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Heating, evaporation, fragmentation, and breakup of multi-component liquid droplets when heated in air flow Dmitry V. Antonov ∗ , Pavel A. Strizhak National Research Tomsk Polytechnic University, Heat Mass Transfer Simulation Laboratory, 30, Lenin Avenue, 634050 Tomsk, Russia

a r t i c l e

i n f o

a b s t r a c t

Article history:

Current technologies of thermal and flame liquid treatment involve high energy con-

Received 14 January 2019

sumption, repeated supply of untreated liquid to the chamber, long-term heating and

Received in revised form 6 March

additive evaporation, hence quite low efficiency. These aspects are the main reason why

2019

high-temperature evaporation and burnout of impurities has limited technological imple-

Accepted 26 March 2019

mentation. The efficiency of such technologies may be improved by means of explosive

Available online 3 April 2019

breakup of untreated droplets in heating chambers. As a result, one parent droplet breaks up to form several dozens to several hundreds of the so-called child-droplets. The development

Keywords:

of such technologies requires fundamental understanding of heating, evaporation, boiling,

Two-liquid droplets

and explosive breakup of one-, two-, and multi-component droplets. The same processes

Multicomponent droplets

can be used to improve the environmental and energy performance indicators of burning

Evaporation

liquid, emulsion, and slurry fuels in combustion chambers of power plants and internal com-

Puffing

bustion engines. In this paper, we present the experimental research into the main heat and

Micro-explosion

mass transfer processes occurring during the heating, evaporation, boiling, and explosive breakup of two- and multi-component droplets in a heated air flow. We identify the princi-

Breakup

pal differences of two dispersion behaviors – puffing and micro-explosion – and indicate the conditions, in which this or that behavior dominates. There is also a transient parameter domain, in which both behaviors can occur. The curves are plotted showing droplet heating times until explosive breakup versus temperature, component concentration, and droplet radii. Finally, we single out the conditions for fragmentation and atomization of two-, three-, and multi-component droplets. © 2019 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

1.

Introduction

based on high-temperature (usually up to 1000 ◦ C) evaporation of a wide range of multi-component liquid droplets. However, droplet heating

The demand for drinking and disinfected water from both the popu-

and evaporation behaviors may differ considerably, depending on con-

lation and industry has been on the rise over the recent years. With this in mind, researchers all over the world are trying to make water

centrations and properties of additives (Vysokomornaya et al., 2017a,b; Vysokomornaya et al., 2016). Therefore, current models of heat and mass transfer and phase transformations in a liquid droplet – gas medium or liquid droplet – heated wall system (Chiu, 2000; Sazhin, 2006; Sazhin

treatment technologies more effective (Kalogirou, 2005; Global Issues Overview; World Water Day, 2017: Why waste water? UN Water, 2017; Shannon et al., 2008; Romero and Rodríguez-Martínez, 2008; Parham et al., 2016) by improving the current direct-contact heat exchangers or customizing them for droplet aerosol injection. These technologies are

∗

et al., 2004; Sazhin, 2017; Sazhin et al., 2005; Sawant et al., 2009; Brin et al., 2011; Harstad et al., 2003; Snegirev, 2013; Zeng and Lee, 2002; Terekhov and Shishkin, 2010) do not make it possible to forecast the cor-

Corresponding author. E-mail addresses: [email protected] (D.V. Antonov), [email protected] (P.A. Strizhak). URL: http://hmtslab.tpu.ru (D.V. Antonov). https://doi.org/10.1016/j.cherd.2019.03.037 0263-8762/© 2019 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

Chemical Engineering Research and Design 1 4 6 ( 2 0 1 9 ) 22–35

Nomenclature Ndroplet Rd Rd0 Rd1 Rdn S S0 S1 Sm T Ta t Ua Vd Vd0 We Greek   h

Number of small drops produced at a break-up of the initial drop Droplet radius, mm Initial two-component droplet radius, mm Droplet radius before breakup, mm Mean radius of droplets in a group, mm Total area of the droplet evaporation surface after breakup, mm2 Initial droplet surface area, mm2 Droplet surface area before breakup, mm2 Frontal cross-sectional area of a, mm2 Temperature, ◦ C Gas flow temperature, ◦ C Time, s High-temperature gas flow velocity, m/s Droplet volume, ␮l Initial droplet volume, ␮l Weber number

Flammable liquid (oil) concentration, vol% Two-component droplet breakup times, s Two-component droplet lifetimes, s

responding processes fully, especially considering the impact of solid and liquid additives. The more components heterogeneous droplets contain, the more processes of heat and mass transfer and chemical reactions are intensified (Yue et al., 2013; Mohammadi et al., 2014; Aliff

23

and Strizhak, 2018; Strizhak et al., 2017a,b). This is especially noticeable when using a two-liquid system featuring water – kerosene, water – diesel, water – petroleum or water – turbine oil (Strizhak et al., 2017a,b; Melo-Espinosa et al., 2018; Belkadi et al., 2018; Marchitto et al., 2018). The experiments in (Piskunov and Strizhak, 2018; Volkov and Strizhak, 2018) using two-component droplets and the optical technique of Planar Laser Induced Fluorescence (PLIF) established that a two-liquid droplet breaks up because a thin water layer near the inter-component interface exceeds the boiling temperature of water (100–120 ◦ C). Here, the main impact comes from the surface tension pressure of the main liquid in a droplet, which prevents the free release of water vapor bubbles at the inter-component interface. With the vapor pressure in a droplet exceeding the threshold value, the droplet breaks up to form an aerosol, mist, or fine droplets (Piskunov and Strizhak, 2018; Volkov and Strizhak, 2018). The patterns of heated two-liquid droplets (with liquid and solid inclusions) were studied theoretically and experimentally in (Vysokomornaya et al., 2017a,b; Piskunov and Strizhak, 2018; Volkov and Strizhak, 2018). The studies did not only involve contaminated water but also high-potential emulsion and slurry fuels. In practice, however, the water to be treated often contains dozens of components (Kalogirou, 2005; Global Issues Overview; World Water Day, 2017: Why waste water? UN Water, 2017; Shannon et al., 2008; Romero and Rodríguez-Martínez, 2008; Parham et al., 2016), and water-containing fuels are also traditionally based on more than one component (Vysokomornaya et al., 2017a,b; Piskunov and Strizhak, 2018; Volkov and Strizhak, 2018; Watanabe et al., 2009; Suzuki et al., 2011; Warncke et al., 2017; Tarlet et al., 2014, 2016a,b; Strizhak et al., 2017a,b; Melo-Espinosa et al., 2018; Belkadi et al., 2018; Marchitto et al., 2018). Therefore, the study of multi-component droplets is very promising in terms of feasibility. Heterogeneous liquids with several flammable components deserve special attention (Mitre et al., 2014; Vysokomornaya et al., 2017a,b; Antonov et al., 2018). These components have different thermophysical, rheological, optical, and thermokinetic

Radzuan et al., 2016). Moreover, each of the components is often used

properties and significantly aggravate the environmental situation. It is sensible to study the heating and breakup of two-, three-, and

to improve one of the parameters of the mixture but has a negative effect on other parameters. For instance, adding one of the components increases heat release but also intensifies gas or ash emissions.

four-component droplets under the conditions that would allow us to detect the effect of each liquid individually (Volkov and Strizhak, 2018). The corresponding schemes and methods for the experiments

Alternatively, a specialized additive may improve the environmental characteristics of the combustion but reduce the time it remains stable (i.e. accelerate lamination). These are the main reasons behind dosing each component or even using more additives to reduce the

are described in (Volkov and Strizhak, 2018; Strizhak et al., 2017a,b). Simultaneous experimental research into the effect of five or more components on the heating, evaporation, and fragmentation of the

adverse effects of earlier ones. Among the simplest examples are the cases when homogeneous droplets are changed into highly heteroge-

parent droplet is complicated and impractical. After all, experimental results with 1–4 components are enough to reliably forecast changes in heat and mass transfer for 5 and more components in a mixture. Currently, there is a wide range of experimental setups with various

neous ones, which leads to their lamination. Lamination is most often observed in slurry and emulsion droplets under various storage, trans-

types of energy supply to a droplet (see (Vysokomornaya et al., 2017a,b;

portation, and heating conditions (Vysokomornaya et al., 2017a,b; Shao

Piskunov and Strizhak, 2018; Volkov and Strizhak, 2018; Watanabe et al.,

et al., 2017; Carpintero-Tepole et al., 2017). Therefore, the role of com-

2009; Suzuki et al., 2011; Warncke et al., 2017; Tarlet et al., 2014, 2016a,b;

ponent composition is of paramount importance. However, the more

Strizhak et al., 2017a,b; Melo-Espinosa et al., 2018; Belkadi et al., 2018;

components a droplet contains, the more difficult it is to reliably predict

Marchitto et al., 2018) for schemes and appearances of the most popular ones). The most frequently used setups are based on conductive,

the heating and phase transformation rates, especially at high heating temperatures. One of the promising ways to improve the evaporation performance is by increasing the vaporization surface area through the explosive breakup of droplets in the partial or full fragmentation regime (Vysokomornaya et al., 2017a,b; Piskunov and Strizhak, 2018; Volkov and Strizhak, 2018; Watanabe et al., 2009; Suzuki et al., 2011; Warncke et al., 2017; Tarlet et al., 2014, 2016a,b; Strizhak et al., 2017a,b; Antonov et al., 2018; Melo-Espinosa et al., 2018; Belkadi et al., 2018; Marchitto et al., 2018). This effect is often represented as repeated spraying of droplets in an aerosol cloud (the first spraying occurs at the inlet of the chamber and the second one inside it). Explosive breakup is provided by flammable liquids (oil, petroleum, kerosene, gasoline, acetone, alcohol, etc.) in water-containing droplets or, vice versa, when even a small fraction of water is added to a droplet of fuel or combustible liquid. The greater the difference between the boiling temperatures of liquid components, their thermal diffusivity, transmittance, and the thermal effects of their vaporization, the more massive the effects triggered by the explosive breakup of a two-component droplet (Volkov

convective, and radiative heat transfer or mixed heat exchange at the droplet surface. The real-life droplet heating conditions of thermal and flame water treatment or combustion chamber processes are best reproduced by placing a droplet, fixed on a specialized holder (thermocouple junction, wire, rod, thread, etc., see Vysokomornaya et al., 2017a,b; Piskunov and Strizhak, 2018; Volkov and Strizhak, 2018), into a heated gas flow (Terekhov and Shishkin, 2010; Vysokomornaya et al., 2017a,b; Vysokomornaya et al., 2016). This makes it possible to record the main heat and mass transfer processes by optical methods (e.g., Particle Image Velocimetry (PIV) (Yan and Rinoshika, 2013), Particle Tracking Velocimetry (PTV) (Damiani et al., 2014), Stereo Particle Image Velocimetry (Stereo PIV) (Stepanov et al., 2009), Interferometric Particle Imagine (IPI) (Bilsky et al., 2011), Shadow Photography (SP) (Akhmetbekov et al., 2010), Planar Laser Induced Fluorescence (PLIF) (Kravtsov et al., 2016), and Laser Induced Phosphorescence (LIP) (Lemoine and Castanet, 2013) and high-speed video recording (Strizhak et al., 2017a,b). For some examples of using cross-correlation software and hardware systems and high-speed video recording to study the heating and breakup of two-

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Chemical Engineering Research and Design 1 4 6 ( 2 0 1 9 ) 22–35

component droplets, see (Vysokomornaya et al., 2017a,b; Piskunov and Strizhak, 2018; Volkov and Strizhak, 2018). The purpose of this work is to study experimentally the patterns in heating, surface transformation, fragmentation, and breakup of twoand multi-component droplets heated on a holder in a hot air flow. The scientific novelty and practical value of this research come from the differences established in the heating times of heterogeneous droplets with various component compositions until micro-explosion as well as the number and size of the resulting child-droplets. Such features are extremely challenging to establish using the present-day droplet micro-explosion models (Sazhin et al., 2019). The more components a droplet contains, the more inter-component interfaces it has. The overheating of these interfaces triggers bubble nucleation and determines the dynamics of their growth and further breakup. The development of such models requires reliable data, which is what our experiments were aimed at. Secondary atomization of droplets to form an aerosol is possible not only through micro-explosive breakup of heated droplets. Collisions of droplets with each other can be regarded as the least expensive way to achieve that. It seems relevant to compare the size and number of child-droplets resulting from droplet micro-explosions and collisions.

2.

Experimental setup and procedure Fig. 1 – Experimental setup (Volkov and Strizhak, 2018).

2.1. Components of liquid compositions under study and main procedures for multi-component droplet production The substances used in the experiments are typical of thermal and flame water treatment as well as fuel technologies (Table 1): kerosene, transformer oil, petroleum, and tap water. According to earlier experiments (Strizhak et al., 2017a,b), explosive breakup at relatively low temperatures (250–450 ◦ C) was steadily reproduced when using two-component droplets based on water and transformer oil. A two-component kerosene – water droplet only broke up at 500 ◦ C and above. Experiments with a water – petroleum composition featured the most massive droplet breakup with fine aerosol formed as a result (dozens or even hundreds of child-droplets). Here we intend to focus on how a third component – transformer oil – added to a two-component droplet (e.g., kerosene – water) will affect the breakup times and outcomes. It is sensible to study combinations of components with significantly different thermophysical, rheological, and thermodynamic characteristics (Table 1).

2.2.

High-temperature gas flow

To generate a hot air flow with controlled parameters (temperature Ta , air velocity Ua ), we used a system featuring a hot-air blower, air heater, and hollow transparent cylinder (0.1 m in inner diameter) made of heat-resistant quartz glass. The temperature Ta was recorded by a measurement system consisting of a high-speed analog input card and fast chromel-alumel thermocouple. The errors of the Ta definition did not exceed 2–3 ◦ C. The thermocouple was introduced into the air flow by a motorized manipulator at a speed of 0.5 m/s. The PIV technique (Vysokomornaya et al., 2017a,b; Piskunov and Strizhak, 2018; Volkov and Strizhak, 2018) was used to control the air velocity Ua in the quartz-glass cylinder. The errors of the Ua definition did not exceed 2%. In additional experiments, we used titanium dioxide tracer particles with an average size of 5 ␮m to determine the air flow velocity fields. We studied the breakup of two-component droplets heated in an air flow at a temperature of 20–1000 ◦ C and velocity of 0.1–5 m/s (Fig. 1).

2.3.

Methods of studying the boiling droplet breakup

The heating, evaporation and breakup of two- and multicomponent droplets were recorded using a high-speed video camera. The resulting video frames were processed using the Tema Automotive (Strizhak et al., 2017a,b) and ActualFlow (Volkov and Strizhak, 2018; Strizhak et al., 2017a,b) software packages to determine the initial droplet radius Rd and the aggregate liquid evaporation surface area S before and after the breakup (Fig. 2). In Volkov and Strizhak (2018) and Strizhak et al. (2017a,b)), the experimental data processing stages are presented in detail. The droplet was assumed spherical and its frontal cross-sectional area, a circle. The mean radius of the initial droplet Rd before the breakup and the radii of droplets Rdn after the breakup (i.e., in an aerosol cloud) were calculated using the formula Rd = (Sm /)0.5 . Fragments formed in the breakup of a parent droplet are referred to as child-droplets (Melo-Espinosa et al., 2018; Belkadi et al., 2018; Marchitto et al., 2018). The errors of the Rd calculation did not exceed 2.5%. After that, we calculated the total area of the droplet evaporation surface using the formula S = 4Rd 2 . By analyzing these parameters we could evaluate the role of the so-called repeated spraying of multi-component droplets due to explosive breakup.

3.

Results and discussion

3.1.

Droplet disintegration regimes

In Fig. 3, you can see snapshots showing the heating and breakup of two- and multi-component droplets. Typical video frames are given in Supplementary materials A, B. The component composition of a droplet significantly affects the threshold temperatures of its surface transformation and breakup, evaporation surface area, and breakup times. The shortest breakup times were recorded in the experiments with three-component droplets, whereas four-component droplets provided the largest number of child-droplets and their total surface area. Based on many experiments with various quantitative component compositions of droplets under study, we have

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Chemical Engineering Research and Design 1 4 6 ( 2 0 1 9 ) 22–35

Table 1 – Main specifications of tap water and liquid flammable components (based on data from Vysokomornaya et al., 2017a,b; Piskunov and Strizhak, 2018; Volkov and Strizhak, 2018) similar to those used in the experiments in this study. Component

Density, kg/m3

Heat diffusivity, m2 /s

Surface tension, N/m

Dynamic viscosity, mPa s

Flash point Ignition Calorific temperature, temperature, value, MJ/kg ◦ ◦ C C

Boiling Vaporization temperature, heat, MJ/kg ◦ C

Transformer oil Kerosene Petroleum Water

877 885 885 1000

8.19 × 10-8 6.11 × 10-8 9.02 × 10-8 1.43 × 10-7

0.029 0.024 0.026 0.073

6.5 3.9 2.022 1.4

148 30–60 55–120 –

320–330 180 105–160 100

169 140 300 –

44.98 43.8 44.31 –

0.167–0.209 0.261 0.210 2.26

Fig. 2 – Recording heated droplet breakup and aerosol generation.

Fig. 3 – Breakup or fragmentation for various compositions: a — two-component droplets (water–oil); b — three-component droplets (water–oil–kerosene); c — four-component droplets (water–oil–kerosene–petroleum). established that the droplet breakup outcomes can be controlled by adding certain components depending on their behavior in a two-liquid droplet. For instance, adding a small mass fraction of petroleum increases the number of childdroplets (fragments) formed. According to the experiments (Strizhak et al., 2017a,b), the evaporation surface area of a two-component water – petroleum droplet increases almost ten-fold after breakup. The breakup times, however, were long. By combining various component compositions, we can provide shorter breakup times and the greatest possible increase in the evaporation surface area of a droplet after its breakup. For example, adding a third component

– kerosene – to a water – petroleum system will reduce the droplet heating times by 15–18% due to higher evaporation rates of kerosene. At the same time, the evaporation surface area after the breakup of a three-component droplet did not differ by more than 7–9% from that of a water – petroleum system. The comparison of all the experimental video frames shows that the heating, fragmentation, and explosive breakup of two- and multi-component droplets had the same patterns in line with earlier ideas (Volkov and Strizhak, 2018; Strizhak et al., 2017a,b). High-speed video recording made it possible to reliably register different evaporation rates of

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Chemical Engineering Research and Design 1 4 6 ( 2 0 1 9 ) 22–35

flammable and non-flammable components, and PLIF was used to continuously measure the temperature of water and inter-component interfaces in a droplet. Just as in (Volkov and Strizhak, 2018; Strizhak et al., 2017a,b), we have established that flammable components heat up and evaporate faster because the heat of their phase transition is 7–11 times lower than that of water (despite much higher thermal diffusivity of water). This caused liquid flammable components to quickly exceed the boiling temperature of water. The droplet breakup lag largely depended on the time of water reaching its boiling temperature. The smaller the water fraction in a multi-component droplet, the faster these processes came to an end. However, for the most massive effects of the multicomponent droplet breakup, the inter-component interface must have a large area. Therefore, the volume of water in two- and multi-component droplets should not be reduced dramatically relative to flammable components. The number and concentrations of components should be varied in line with the highest-potential applications of the research findings. For instance, in thermal and flame water treatment, the relative mass fractions and volume concentrations of liquid flammable components cannot exceed 3–5 vol%. In fuel technologies, however, water concentration may reach 30–40 vol% for slurry and emulsion fuels. In some cases, for the best possible environmental performance of slurry fuel combustion, the proportion of water is increased up to 50–60 vol%. Sazhin et al. formulate the main criteria for the microexplosive breakup of heterogeneous droplets (Sazhin et al., 2019). One of these is water overheating up to boiling temperature (373 K) at the interface with the combustible components. The other is the droplet reaching the critical ratio of the new size after bubble nucleation to its initial size. The critical values of this ratio normally range from 2 to 4. The video frames of our experiments show that both of these criteria held for all the droplet compositions under study. But the higher the volume concentration of the liquid combustible component was in a droplet, the more difficult it was to reliably determine the droplet temperature by PLIF, as the latter is meant for temperature measurement of water in a droplet. Like in the experiments by Volkov and Strizhak (2018), we used Rhodamine B as a fluorophore. It does not dissolve in combustible liquids and, thus, cannot be used to record their temperature. We compared the data obtained from high-speed video recording and the temperature fields obtained by PLIF. The former involved tracking the droplet dimensions and the latter, tracking the temperature near the inter-component interface. As a result, we formulated a hypothesis that the criterion of the interface (or its portion) approaching water boiling temperatures is the primary one, whereas the critical droplet size ratio remains the secondary one. High-speed video recording shows that the difference between the heating times, at which the first and second criteria hold, does not exceed 1.5–2% from the established times of micro-explosive breakup. The higher the heating temperature, the smaller this difference, which may be as small as 1%. Therefore, mathematical modeling can apparently use any of the two criteria to reliably predict the threshold thermal conditions of micro-explosive breakup: necessary and sufficient values of heat fluxes and heating times. Both of these criteria can be applied for conductive, convective, radiative, or combined heat exchange, since none of the heat supply mechanisms heats up a heterogeneous droplet throughout all of its layers. For micro-explosive breakup, it is enough to provide the local overheating of

Fig. 4 – Droplet heating times until micro-explosive breakup vs. heating temperature (Vd ≈ 15 ␮l, Ua ≈2 m/s): 1 — two components (97 vol% water – 3 vol% oil); 2 — two components (97 vol% water – 3 vol% kerosene); 3 — two components (97 vol% water — 3 vol% petroleum); 4 — three components (94 vol% water — 3 vol% oil – 3 vol% kerosene); 5 — three components (94 vol% water – 3 vol% oil – 3 vol% petroleum); 6 — four components (91 vol% water – 3 vol% oil– 3 vol% kerosene – 3 vol% petroleum). a liquid–liquid interface. The more thermal diffusivity, boiling temperature, and vaporization heat differ between the combustible and non-combustible liquid in a heterogeneous droplet, the greater the temperature gradients near the intercomponent interface (Volkov and Strizhak, 2018; Sazhin et al., 2019) and the sooner the droplets break up to form a fine aerosol.

3.2.

Impact of key factors

Fig. 4 shows the breakup times of two- and multi-component droplets vs. gas medium temperature. The resulting curves for all the component compositions under study have a similar nature. When the gas medium temperature rises, the droplet lifetimes decrease nonlinearly (the curves are described by approximations with exponential functions). Total droplet breakup times can be varied by adding a third and fourth component to them, especially if these components are flammable. The shortest droplet heating times until breakup were observed in the experiments with threecomponent droplets (water–oil–kerosene) almost throughout the whole range of heating temperatures. The reason for that was the content of kerosene with its high evaporation rate in this temperature range. This accelerated bubble nucleation and droplet breakup. Almost all the curves in Fig. 4 intersect in the 250–350 ◦ C range. The maximum differences in the breakup times of all the multi-component droplets under study reach 50–60% in this range. The surface transformations of multi-component droplets in the threshold temperature range during the heating and breakup are difficult to forecast. Droplets with high thermal diffusivity, low surface tension and viscosity, low boiling temperature and vaporization heat were filled with water vapors quite quickly to form an irregularly shaped vapor bubble. Its growth and breakup characteristics largely depended on the heating and evaporation rates of droplet components at the inner interface. Since the components (Table 1) differed

Chemical Engineering Research and Design 1 4 6 ( 2 0 1 9 ) 22–35

significantly in terms of these characteristics, the heating and evaporation rates varied, too. The main heat and mass transfer processes in the system under study made a noticeable contribution. At high temperatures, the dominating process was the heating of the inter-component interface in the droplet to the boiling temperature of water. Therefore, the heating and breakup times became comparable with a growing temperature, irrespective of the number of components in a heterogeneous droplet (Fig. 4). At 400–550 ◦ C, water and flammable components are heated due to thermal conductivity, convection, and radiative heat transfer, with the latter two being the most influential. As a result, the differences in the thermophysical characteristics or vaporization heat of liquid flammable components become less prominent. The higher the heating temperature, the more significant the role of radiant heat absorption and accumulation near inter-component interfaces (Strizhak et al., 2017a,b). This increases their temperature and intensifies thermogravitational convection. Kim et al. (2014) and Voloshin et al. (2014) attribute these effects at the molecular level to the cloudiness of water droplets with variable concentration of additives. The droplet holder impact on the heating and breakup of one-, two-, and multi-component droplets is important, too. The experiments in this study as well as the data from (Volkov and Strizhak, 2018; Strizhak et al., 2017a,b) suggest that the heating of single-component droplets (water, oil, kerosene, and petroleum) within the temperature range in Fig. 4 provided steady evaporation. The times of complete evaporation of liquid flammable components differed from those of water by a factor of 8–35 (the higher the heating temperature, the greater the difference). However, even at high heating temperatures, the explosive breakup of homogeneous liquid droplets was not observed. Droplets evaporated steadily and boiled locally at the holder surface, usually after heating for several dozens of seconds. The final stage frames were similar to the starting ones with partial fragmentation of multi-component droplets. In the case of homogeneous droplet heating, the impact of the holder on the droplet temperature field may be considered significant. The energy transferred to the liquid from the rod becomes comparable to that from the incoming air flow. In the case of two- and multicomponent droplets, however, the explosive breakup times usually did not exceed the metal holder heating times. With an increase in the heat flux supplied to the droplet surface, the role of thermogravitational convection increases as well (hence the higher the heating temperature, the more noticeable the effect). Moreover, at heating temperatures under 300 ◦ C, the extra heating due to the holder contact sometimes intensifies the explosive breakup of droplets (Volkov and Strizhak, 2018; Strizhak et al., 2017a,b). The direct contact of a non-flammable component (water) with the heated surface of the holder plays a major part. Earlier experiments (Volkov and Strizhak, 2018; Strizhak et al., 2017a,b) established that the heating of twocomponent droplets becomes more rapid when the core of the droplet is water and the cover is oil. This happens because oil has high absorption coefficients and less energy is spent on its evaporation. Therefore, oil is heated faster than water, although it has lower thermal conductivity and diffusivity than water. When the heating temperature reaches the values typical of fuel technologies (over 800 ◦ C) or thermal and flame water treatment (over 500 ◦ C), the holder impact on droplet heating and breakup will be minimal, since the times of these processes will be less than 1 s.

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According to the experimental results, the dimensions of component droplets (water, oil, petroleum, and kerosene) generated by a dispenser have practically no effect on the heating times of a multi-component droplet. For instance, the breakup times of droplets with equal concentrations of water and petroleum, water and kerosene, water and oil, but different initial volumes of these liquids (the radii of the parent droplets ranged from 0.3 mm to 1.5 mm) did not differ by more than 11%. Moreover, the differences reached 11% only if the heating temperature was lowered down to 250–350 ◦ C. At higher temperatures, the impact of the initial droplet size under 1.5 mm was negligible as compared to the component concentration and heating temperature. In present-day fuel injection systems as well as thermal and flame water treatment, the radii of droplets in an aerosol do not usually exceed 0.5 mm and heating temperatures are above 500 ◦ C (Kalogirou, 2005; Global Issues Overview; World Water Day, 2017: Why waste water? UN Water, 2017; Shannon et al., 2008; Romero and RodríguezMartínez, 2008; Parham et al., 2016; Chiu, 2000; Sazhin, 2006; Sazhin et al., 2004; Sazhin, 2017). Therefore, the primary spraying parameters are unlikely to play a major role in the heating and breakup of relatively small multi-component droplets (under 1–1.5 mm). We compared our experimental results with the data obtained from droplet heating by conductive, convective, radiative, and combined heat exchange mechanisms (Tarlet et al., 2014, 2016a,b; Volkov and Strizhak, 2018; Antonov et al., 2018). The result shows that the shape of curves in Fig. 4 can be considered typical of different schemes of heat supply to a droplet. However, two typical regions can be singled out for all the curves obtained: a highly nonlinear reduction in the heating time until breakup down to 350–400 ◦ C; and rather a slight change in the micro-explosion times at temperatures above 350–400 ◦ C. Thus, for two-, three- and multi-component droplets of the liquids under study, there is a certain minimal amount of heat to be supplied to a droplet for its massive fragmentation. According to our hypothesis, most of the energy supplied goes to the water core of the droplet. For all the compositions in Fig. 4, the volume concentration of the non-combustible component was the same (50 vol%). The greater the proportion of the non-combustible component, the more noticeably the heating temperature threshold will shift towards increase. When all the compositions under study reach this threshold, the micro-explosion times will be similar. If we analyze various mechanisms of energy supply to a droplet with due consideration of data from (Tarlet et al., 2014, 2016a,b; Volkov and Strizhak, 2018; Antonov et al., 2018), we can make the following conclusion. In the conductive heating schemes, the heating times and minimum sufficient temperatures may be lower than those given in Fig. 4 but convective schemes will provide more child-droplets at the same temperatures. The maximum number of fine child-droplets can be obtained using radiative heating (without vapor drifting from the droplet surface). In this case, the energy is supplied evenly throughout the free surface of a droplet, but it will take much longer time than shown in Fig. 4 to heat the droplet until micro-explosion. Therefore, the values given in Fig. 4 can be considered average as compared to the schemes with the prevailing conductive and radiative heat exchange at the droplet surface. In Fig. 4, the curves obtained for the compositions with highly different concentrations and properties of the components intersected several times with varying heating temperature. On the one hand, this result reflects the relatively

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Fig. 5 – Times of droplet heating until micro-explosive breakup vs. concentration of flammable liquid or a mixture of flammable liquids in equal amounts (Vd ≈ 15 ␮l, Ua ≈ 2 m/s, Ta ≈ 350 ◦ C): 1 — two components (water–oil); 2 — three components (water–oil–kerosene); 3 — four components (water–oil–kerosene–petroleum). low scattering of the experimental micro-explosion times for the droplets under study, which becomes lower with an increase in the heat flux supplied. On the other hand, the microexplosion times clearly changed at different rates in various regions of the heating temperature variation range for the compositions under study. This stems from differences in the scale and dynamics of the curves of thermal and physical component characteristics versus temperature. The thermal diffusivity and heat capacity of the droplet played a major role here. The more significantly they differed from those of water, the faster the droplet micro-explosion times decreased with an increase in the heating temperature in Fig. 4. Fig. 5 shows the breakup times of two- and multicomponent droplets vs. flammable liquid (oil) concentration. By varying the concentration of liquid flammable and non-flammable components in two- and multi-component droplets, we can vary the breakup time (heating until breakup) by a factor of 2–3 (Fig. 5). Four-component droplets of different concentrations show the greatest difference in breakup times. This result can be considered quite logical and even predictable, since the more components a droplet contains, the more interfaces it has with significantly different heating and evaporation conditions. However, when the main properties of the flammable additives were similar, multi-component and two-component droplets had almost identical breakup characteristics provided their initial concentrations of the flammable and non-flammable component were comparable. There is a common pattern for two- and four-component droplets: the breakup times are at their highest when relative concentrations of the flammable and non-flammable component are almost equal. For three-component droplets, this pattern was not observed, since the properties of two flammable additives were significantly different. The breakup times changed unstably, depending on the concentration of the flammable liquid (oil), which means that the experimental values of the parameters scattered significantly.

According to the experimental results, any composition under study has an optimal relative volume concentration of components that provides the shortest heating times until micro-explosion. The main pattern is that these times are the shortest for almost any composition, when it has the lowest possible concentration of the non-combustible component – water (Fig. 5). In our experiments, it was 3 vol% due to the limitations of the dispenser. In actual practice, even less than 3 vol% of water would most likely be enough for microexplosive breakup. The heat capacity and vaporization heat of water are several times higher than for any of the liquid combustible components under study. Hence, when increasing the proportion of water in a droplet, the effective (total) heat capacity and heat spent on evaporation increase as well. This prolongs the heating times until breakup. The lower the proportion of water, the faster its local overheating is achieved, sufficient for breakup. The surface tension of the liquid combustible component is much lower than that of water. Thus, even when water was overheated locally, the parent-droplet rapidly broke up. When heated, the surface tension, viscosity, and density of the combustible and non-combustible components went down. Therefore, a fine aerosol formed due to micro-explosion does not seem surprising. However, our experiments show that 97 vol% of water in heterogeneous droplets also provides a micro-explosive breakup (Fig. 5). Most likely, this happens because the liquid combustible component heats up fast when it is this small in volume. This leads to the overheating of the inter-component interface above the water boiling temperature. Therefore, bubbles do emerge at this interface but they do not grow as rapidly as in the experiments with 97 vol% of the combustible component. Therefore, with high water concentrations in droplets, micro-explosions occurred after a longer heating time and produced fewer child-droplets. When the concentrations of the combustible and non-combustible components were equal in a droplet, both mechanisms affected the overheating of the interface

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up to the water boiling temperature. In this case, the heating times were longer than in the experiments with 97 vol% of the combustible component or 97 vol% of water (Fig. 5). However, if droplets contained several combustible components, the micro-explosion was affected not only by the thermophysical properties and vaporization heat but also by differences in the surface tension and viscosity. The lower these parameters, the faster the parent-droplets broke up and the more childdroplets were produced. The more combustible components in a heterogeneous droplet, the more complex the functions of heating times to micro-explosion versus volume concentration of the combustible or non-combustible component. For droplets with several combustible components, the shortest heating times to micro-explosion may be provided by several combinations of relative volume concentrations. For instance, several extrema are shown in Fig. 5 for curve 2. Thus, the results obtained once again substantiate the main hypothesis: it is enough to heat a small volume of liquid up to the water boiling temperature to provide an extensive micro-explosive breakup. The experiments from (Volkov and Strizhak, 2018; Strizhak et al., 2017a,b) used PLIF and two-component droplets with water concentrations varying within the range shown in Fig. 5. These established that the breakup of a two-component droplet could not be caused by a significant overheating and boiling of the liquid flammable component alone. It is rather difficult to heat the whole volume of the added water up to its boiling temperature due to its high heat capacity. Therefore, the breakup (atomization) of a droplet is based on the nucleation of bubbles at the inter-component interface. The bubbles are filled with vapors of a more heated liquid (in our case, it is a liquid flammable component). Due to their growing in size, merging and moving, bubbles with increased pressure are formed in a two-liquid droplet. As soon as the pressure in these bubbles exceeds the pressure caused by the surface tension forces acting on the droplet, it breaks up. If the growth of bubble pressure in a droplet is significant, it breaks up to form child-droplets. If the pressure increases slowly, the droplet fragmentation of different scales is observed. The more components a droplet contains, the more intense its partial fragmentation is, which reduces the vapor pressure in a droplet and prolongs the breakup time. Therefore, to intensify the explosive breakup of multi-component droplets, it is sensible to increase the heating temperature up to 400–600 ◦ C, at which the breakup times of two-, three- and multi-component droplets become comparable (Fig. 4). Another way is to add a component with high thermal diffusivity and low vaporization heat (hence high vaporization rate and low surface tension) in high concentration. These findings are important for reducing the time and energy consumption while intensifying the corresponding heat and mass transfer processes in high-potential practical applications. Fig. 6 shows typical curves of the breakup time of twocomponent droplets versus their size. The visual differences in these curves come not only from the influence of the gas flow and the possibility to fix a droplet of a certain size on a holder but also from its component composition. Minimum breakup times with various dimensions of two-component droplets are provided by droplets containing 50 vol% of oil and 50 vol% of water. This function is practically linear (breakup times increase with the growing droplet size), because at 350 ◦ C the explosive breakup of such a droplet is stable. As a result, the heating and breakup times are mostly affected by the droplet size, all other controllable parameters being

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Fig. 6 – Breakup times vs. dimensions of two-component droplets (Ta ≈ 350 ◦ C, Ua ≈ 2 m/s, composition: 50 vol% flammable liquid and 50 vol% water): 1 — water – oil; 2 — water–kerosene; 3 — water–petroleum. equal (breakup behavior does not change). The curve of breakup times versus dimensions of a two-component droplet (50 vol% kerosene and 50 vol% water) is similar. However, the breakup times throughout the size range are longer, because a kerosene-based two-component droplet breaks up at higher temperatures (at 350 ◦ C, its breakup is less intense than that of two-component droplets based on oil). The breakup times of two-component droplets (50 vol% oil and 50 vol% water) decrease as their size grows, most likely because the explosive breakup of such a droplet always yields fine aerosol. The smaller the parent droplet, the larger the scale of breakup consequences: small droplets are formed in the aerosol. The breakup becomes more massive depending on how much thermal stress a droplet has accumulated. Fig. 6 shows that the times of micro-explosive breakup depend heavily on the initial size of the droplets and thermophysical properties of the liquid. Curves 1 and 2 can be considered typical and their shape not unexpected. The smaller the droplet, the faster it is heated up to the conditions that are necessary and sufficient for a micro-explosive dispersion. Curve 3 shows that the reverse trend is possible as well: the larger the droplet, the faster it overheats until breakup due to water boiling. Such conditions are only possible if the combustible component has high thermal diffusivity, density, and viscosity. Petroleum fits perfectly well. The larger the parentdroplet, the thicker the liquid combustible component around the water core. The liquid combustible component with high thermal diffusivity may heat up faster, and the temperatures at the inter-component interface reach water boiling temperatures. Using the video frames of our experiments, we recorded the conditions of faster local overheating of the intercomponent interface in the experiments with the growing size of a two-component water–oil droplet. These results show that a fine aerosol can be obtained using heterogeneous droplets with various initial dimensions, so they do not necessarily have to be smaller than 1 mm.

3.3.

Droplet breakup outcomes

By analyzing the outcomes of the explosive breakup (Fig. 7) of two-, three- and multi-component droplets, we have established that four-component droplets

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Fig. 7 – Ratios of droplet evaporation areas vs. concentration of flammable liquid or a mixture of flammable liquids in equal amounts (Vd ≈ 15 ␮l, Ta ≈ 350 ◦ C, Ua ≈ 2 m/s): a — two components (water–oil); b — three components (water–oil–kerosene); c — four components (water–oil–kerosene–petroleum). (water–oil–kerosene–petroleum) yield the droplet aerosol with the maximum quantity of small fragments. The liquid evaporation surface area increased more than 30-fold under such conditions. This result shows a consistent pattern for all the component compositions and concentrations under study. We can hypothesize on the mechanism of the multi-component droplet breakup. In particular, the more components a droplet contains, the more interfaces there

are between components with significantly different thermophysical, rheological, and thermodynamic characteristics. This makes the system unstable (ill-balanced) during the droplet heating, evaporation, and surface transformation. However, the maximum increment of the liquid surface area when the parent droplet broke up was in good agreement with the experiments with comparable concentrations of the combustible and non-combustible component (Fig. 7).

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This most likely results from higher temperatures of all the deep droplet layers because of the long droplet lifetime. Fig. 5 shows the maximum droplet heating times until breakup with  ≈ 50 vol%. Figs. 5 and 7 are in good agreement. Therefore, the micro-explosive dispersion of heterogeneous droplets may be triggered not only by fast and local overheating of the intercomponent interface. On the contrary, the longer the droplet heating time, the deeper into the droplet the heated layers of liquids penetrate due to thermogravitational convection and thermal conductivity. This promotes bubble growth near intercomponent interfaces, increases the number of bubbles, and intensifies the motion within droplets. Under such conditions, the number of vaporization centers increases significantly. This accelerates droplet size growth and helps its breakup producing a large number of fine child-droplets. This hypothesis is confirmed by the S/S0 ratios given in Fig. 7 for various component concentrations, considering the corresponding curves of micro-explosion times versus component concentrations (Fig. 5). Thus, in actual technologies, rather high S/S0 can be ensured for component compositions with various concentrations of combustible and non-combustible liquids, provided that the heating times are long, for instance through longer soaring in heating chambers. Such conditions will be more effective in terms of maximum S/S0 values than, for example, droplet dispersion through contact with heated walls. Based on the above hypothesis, we can assume that for emulsion or slurry fuels, which have been actively studied over the recent years (see, for example, Vysokomornaya et al., 2017a,b; Piskunov and Strizhak, 2018; Volkov and Strizhak, 2018; Watanabe et al., 2009; Suzuki et al., 2011; Warncke et al., 2017; Tarlet et al., 2014, 2016a,b; Strizhak et al., 2017a,b; MeloEspinosa et al., 2018; Belkadi et al., 2018; Marchitto et al., 2018), the liquid surface area may grow more rapidly during the droplet breakup. A promising course of development for multi-component water-containing fuels would be a shift towards micro-emulsions or micro-slurries, i.e., producing liquid mixtures containing micro-volumes of water throughout the system (the most popular mixture is diesel–water (MeloEspinosa et al., 2018; Belkadi et al., 2018; Marchitto et al., 2018)). The hypothesis of the authors (Melo-Espinosa et al., 2018; Belkadi et al., 2018; Marchitto et al., 2018) received extra confirmation in our experiments (Fig. 5). With 2–3 vol% water concentrations in two-component droplets, it takes about two seconds for them to reach the breakup conditions. Even small water fractions in combination with flammable liquids encourage breakup after short-term heating. With this pattern, it is possible to improve the performance of sprayed liquid fuel combustion. Adding small fractions of water (up to 3 vol%) to kerosene, fuel oil, or diesel provides a basis for the secondary atomization of liquid fuel, this time in the combustion chamber, without any significant expenses on the development of polydisperse spraying systems of the initial fuel. The explosive breakup of liquid fuel droplets with very small fractions of water can very likely be used for changing the fraction composition of droplets in quite a wide range after the primary spraying by injectors. Moreover, it prevents a significant temperature reduction in the combustion chamber due to small fractions of water (MeloEspinosa et al., 2018; Belkadi et al., 2018; Marchitto et al., 2018). At high water vaporization rates, the most hazardous oxides from the combustion of diesel vapors are captured by water vapors. In our case, we can forecast that droplets of multicomponent micro-emulsions or micro-slurries will break up

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with a much greater area ratio than that shown in Fig. 7. Therefore, this can be regarded as the most promising avenue for future research.

3.4. Comparison of child-droplets produced by micro-explosion with those produced by droplet collisions Child-droplet size and number distributions in Fig. 7 show that micro-explosion has significant advantages over many other well-known and least expensive approaches based on various secondary droplet atomization schemes. In particular, Fig. 8 gives the results of additional experiments recording the characteristics of child-droplets produced by droplet collisions. The experimental parameters were as follows: initial droplet size 0.1–5 mm, velocities 0.1–10 m/s, and impact angles 0–90◦ . The interaction was recorded by two high-speed video cameras (resolution 1152 × 864, frame rate 1000–5000 fps). Two cameras focused on the recording area to obtain the spatial pattern of the interaction between droplets. The video fragments were processed using Tema Automotive, Photron Fastcam Viewer. The systematic measurement error did not exceed 3.4% for droplet velocities, 2.1% for their dimensions, and 1.8% for impact angles. Typical video frames are given in Supplementary materials C. Fig. 8 shows typical initial volumes of colliding droplets, velocities, and the corresponding Weber numbers. The experimental methods were in line with those used in (Antonov et al., 2016). In this research, however, the colliding droplets were of two-component mixed liquids (emulsions) and immiscible fluids, as well as droplets of combustible and noncombustible components separately. We used this approach to show the differences in child-droplet size and number distributions, since their surface tension, density, and viscosity differed several-fold. According to the general pattern, these three liquid parameters have a significant effect on the number and size of child-droplets. In particular, to obtain a fine aerosol, it is necessary to use liquids with lower surface tension and viscosity in droplet collision schemes. Low surface tension weakens the bonds in the droplet contact zone. A large number of liquid chains are produced, which then break up. The higher the liquid viscosity, the faster the small fragments took the shape of individual droplets without further disruption. The lower the viscosity, the more stages of consecutive droplet atomization we observed. The droplets broke up for a long time to produce smaller droplets, which further broke up into even finer fragments. We observed an important pattern in the changing fragmentation regime of emulsion droplets and two-component immiscible fluid droplets as compared to oil and water droplets. The surface tension, density, and viscosity of emulsions were average relative to the similar parameters for the combustible and non-combustible components separately. In the video frames showing the experiments with twocomponent immiscible droplets, the number and size of the post-collision child-droplets scattered quite noticeably in some cases. This happened because water broke up slower due to high surface tension but the breaking droplets of the combustible component entrained water fragments, thus intensifying their atomization. This promoted the growth in the number of child-droplets as compared to the experiments with a water droplet without combustible liquid. The higher the viscosity of the latter, the faster the resulting fragments became spherical and stopped breaking up. Due to high viscosity and density, they generated additional energy promoting

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Fig. 8 – Droplet breakup and droplet collisions outcomes: a – child-droplet size distributions produced by collisions (1 — emulsion (70 vol% water – 30 vol% oil); 2 — two-component (70 vol% water — 30 vol% oil); 3 – oil; 4 – water); b — ratio of the evaporation surface areas before and after collisions (1 — emulsion (70 vol% water — 30 vol% oil); 2 — two-component (70 vol% water – 30 vol% oil); 3 — oil; 4 — water); c — ratio of the evaporation surface areas before and after micro-explosion (1 — two components (water–oil); 2 — three components (water–oil–kerosene); 3 — four components (water–oil–kerosene–petroleum)).

the atomization of water droplets colliding with them despite the large size of those droplets. Thus, if diesel or oil, with their low surface tension and high viscosity, are used as the combustible component, we can reliably predict that the S/S0 ratios will be greater than those shown for oil in Fig. 8. When We > 80, many homogeneous, two- and multicomponent droplets consistently break up to form an aerosol (Orme, 1997; Focke et al., 2013; Krishnan and Loth, 2015). Therefore, size distributions in Fig. 8 are given for We ≈ 100. Based on the experiments, even if the impact angle approaches 90◦ and droplet velocity and size increase so that the Weber numbers will reach 200–300, the S/S0 area ratio still cannot exceed 6–8. The micro-explosive breakup, however, can push this parameter up to 30–50. The characteristics of child-droplets change according to several patterns observed in the experiments with colliding parent-droplets. First, the component composition of parent-droplets significantly affects the size and number of child-droplets in a limited variation range of dimensions and velocities. In particular, at We < 50, typical child-droplet size distributions correlated well for oil, water, and emulsion droplets. Large child-droplets dominated due to low kinetic energy in the collision zone. At We > 200, child-droplet size distributions in the experiments with colliding oil, water, and emulsion droplets also became rather close. Under such conditions, there were over 80% of child-droplets 10 or more times as small as parent-droplets. Only in the range of 50 < We < 200, the liquid properties had a noticeable effect on the characteristics of child-droplets. Second, impact angles (between droplet trajectories) may affect the number and size of child-droplets at 50 < We < 200 as well. In particular, the maximum number of child-droplets was produced by parent-droplet collisions at an angle of 0 (head-on) or /2. The higher the relative velocities of droplets, the fewer child-droplets are produced by a head-on collision. Third, in the range of We < 50, depending on the droplet impact angle as well as liquid viscosity, density, and surface tension, four collision regimes may occur: bounce, separation, coalescence, and disruption. The first two regimes (bounce and separation) do not change the number of new droplets relative to the initial ones. Coalescence consistently occurred throughout the impact angle variation range only until We = 20–25. At 25 < We < 50, coalescence was only observed in the medium impact angle variation range (/4–/3). At other angles, disruption occurred but newly formed child-droplets were much larger than those shown in Fig. 8 for We ≈ 100. Fourth, the distributions of child-droplets produced by the collision of two droplets and by droplet collision with a wall are overall comparable. This remains true if we consider wall heating and inclination, different degree of its roughness, thermal and physical properties of the material, and other factors (Liang and Mudawar, 2017). The difference between the number of small fragments produced by parent-droplets colliding with a wall and with each other at comparable Weber numbers may not exceed 15–18%. Thus, S/S0 ratios will correspond to those given in Fig. 8 for the scheme of droplets colliding with each other. Five, at low droplet velocities during wall impact, a thin film of liquid is formed on the wall surface. The interaction with this film is similar to droplet collisions with each other in terms of conditions and physical processes involved. Thus, in many cases, the schemes with droplet collisions with each other and with a wall will provide almost identical S/S0 ratios at We < 50. Based our experimental results, we can hypothesize that the most promising for real application will be the systems

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of step-wise droplet atomization due to their collisions with each other and with chamber walls as well as overheating until micro-explosion. In this case, the S/S0 ratios may even exceed 50. Depending on the required size and number of child-droplets, atomization schemes may vary in terms of droplet collisions with each other and with a wall but the micro-explosive breakup should be used at the last step. To provide shorter heating times until breakup and small size of child-droplets, the parent-droplet has to be overheated up to water boiling temperature. The smaller the resulting childdroplets, the more massive the micro-explosion.

4.

Conclusions

The experiments helped us define the nature of the markedly different dispersion behaviors of two- and multi-component droplets. In particular, depending on the composition of a multi-component droplet, the threshold temperatures, times, and outcomes of droplet breakup vary in accordance with the properties of each component. The experimentally established patterns in the heating, boiling, and explosive breakup of two- and multi-component droplets with various concentrations show that atomization can be successfully implemented in a wide range of technologies. Moreover, using different combinations of temperatures and concentrations makes it possible to change the times  by a factor of 3–5. This result is especially valuable in this research, since it shows the allowable ranges of parameter variation and the preferred specifications of the corresponding combustion or thermal treatment chambers as well as their injection systems. It is important to provide a staged consecutive droplet atomization in the course of heating and evaporation. The patterns should be taken into account when designing thermal chambers and developing regulations for the corresponding technologies. According to the charts showing breakup outcomes of twoand multi-component droplets, the maximum increase in the evaporation surface areas (up to 30–40 times) can be provided using a combination of different types of flammable liquids. The more components with substantially different thermophysical characteristics a droplet contains, the more noticeable growth it provides. Combined secondary atomization schemes, for instance, parent-droplet collisions followed by micro-explosion, can provide more than a 50-fold increase in the area of the free liquid surface.

Acknowledgment The research was supported by the Russian Science Foundation (project 18-71-10002).

Appendix A. Supplementary data Supplementary material related to this article can be found, in the online version, at doi:https://doi.org/10.1016/ j.cherd.2019.03.037.

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