Measuring the temperature of a rapidly evaporating water droplet by Planar Laser Induced Fluorescence

Accepted Manuscript Measuring the temperature of a rapidly evaporating water droplet by Planar Laser Induced Fluorescence R.S. Volkov, P.A. Strizhak PII: DOI: Reference:

S0263-2241(18)31101-1 https://doi.org/10.1016/j.measurement.2018.11.047 MEASUR 6090

To appear in:

Measurement

Received Date: Revised Date: Accepted Date:

30 November 2017 29 October 2018 18 November 2018

Please cite this article as: R.S. Volkov, P.A. Strizhak, Measuring the temperature of a rapidly evaporating water droplet by Planar Laser Induced Fluorescence, Measurement (2018), doi: https://doi.org/10.1016/j.measurement. 2018.11.047

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An abbreviated title: Measuring the temperature of droplet Measuring the temperature of a rapidly evaporating water droplet by Planar Laser Induced Fluorescence Volkov R.S., Strizhak P.A.* National Research Tomsk Polytechnic University 30, Lenin Avenue, Tomsk, 634050, Russia *Corresponding author. Tel.: +7 (3822) 701-777, ex. 1910. E-mail: [email protected]. Website: http://hmtslab.tpu.ru. Abstract In this paper, we present the experimental research into the unsteady temperature fields of an evaporating water droplet with a 1–2 mm initial radius attached to a holder in a flow of air heated up to 1,000 °C. The limitations of Planar Laser Induced Fluorescence are established. We identify four distinct stages of droplet evaporation, in which the use and calibration of Planar Laser Induced Fluorescence differ significantly. Changes in the dye concentration in the droplet are found to result from the dye evaporation from the free surface of the droplet and its sedimentation onto the holder. A correction factor is introduced, based on the experimental results and dependent on a number of effects discussed. The factor is used to adjust the experimental measurements made via Planar Laser Induced Fluorescence and to obtain the reliable temperature fields of a rapidly evaporating water droplet. Keywords: Planar Laser Induced Fluorescence; Rhodamine B fluorophore; calibration; evaporating water droplet; temperature field; temperature profile. 1. Introduction Experimental and theoretical research of liquid droplet evaporation in the case of high temperatures (500 °C to 1,000 °C) and considerable thermal flux (e.g., [1–12]) is important for the development and improvement of several applications, including firefighting, thermal water treatment, thermally loaded surface treatment and cleaning, fuel spraying (droplet pulverization) in combustion chambers, etc. Overviews [11, 12] show that the evaluation of the integral characteristics of droplet evaporation (heating and evaporation rates in particular) remains the most pressing task. When conducting such experiments (including the integral characteristics evaluation of droplet evaporation), the most common techniques used are non-contact panoramic optical methods, such as Particle Image Velocimetry (PIV) [13, 14], Particle Tracking Velocimetry (PTV) [15], Stereo PIV [16], Interferometric Particle Imaging (IPI) [17], Planar Laser Induced Fluorescence (PLIF) [18–22]. The PLIF technique [18– 22] deserves special attention, since it provides for capturing instant temperature distribution in the

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droplet, leading to a more detailed analysis of the droplet heating and evaporation, as well as to the evaluation of the liquid temperature effect on its evaporation rate [23]. However, just as any other panoramic technique, Planar Laser Induced Fluorescence has its own limitations. Thus, to increase the reliability of measurement results, it is advisable to improve the calibration process (e.g., [19]) or to adjust the obtained measurement results (e.g., [20]) in each individual case. The need for adjustment is caused by the variation in the dimensions (volume) of the droplet under test. For example, in [22], the authors adjust the fluorescent dye concentration, which changes due to the thermal expansion of ethanol droplet. In high-temperature droplet evaporation analysis [23], the dimensions of the droplet decrease nonlinearly, leading to possibly unreliable temperature distribution data. For now, there is no experimental information about the effect of droplet evaporation on PLIF measurement reliability. It means that the experimental evaluation of the validity range for the traditional PLIF measurement [23], as well as the technique calibration and measurement result adjustment in the case of a rapidly evaporating droplet are of high interest. The purpose of this work is to experimentally determine the aspects of PLIF application and calibration to evaluate the temperature field of a rapidly evaporating water droplet. 2. Traditional PLIF calibration and application Planar Laser Induced Fluorescence is based on the natural fluorescence of fluorophore molecules (in this work, it is Rhodamine B, similar to [23]), stimulated by 532 nm wavelength laser light. The intensity of the dye-emitted light per volume depends on the stimulating light energy, dye quantum yield, dye light absorption factor, and dye concentration [24]. There are several modifications of the technique, e.g., 2Color PLIF [20–22], which uses two laser beams for point measurement, or Planar LIF [23], which registers temperature distribution in the plane section. The main distinction of these modifications is in measurement accuracy: a typical error is 0.17–0.4 °С for 2Color PLIF [24, 25] and 1.7–2 °С for Planar LIF [26]. In this research, we used the Planar LIF technique. In theory, Rhodamine B luminosity decreases by 2% for every 1°С of a rise in the liquid temperature [27]. Traditional consideration is that for every discrete value of brightness (dye luminosity) there is a certain corresponding temperature of liquid. Fig. 1 shows a calibration curve for PLIF obtained via thermocouple measurements [23]. We used the calibration curve, similar to the one in Fig. 1, to plot the temperature field. The most common way to process the instant PLIF images consists of two stages. The first is to adjust the image lightness by multiplying the brightness of the point by the corresponding calibrating factor. Then, according to the calibration curve (Fig. 1), a temperature field is plotted, based on the resulting image. There are also several methods to lower the measurement error, accounting for the non-uniform distribution of laser light energy [28], local variation of refraction coefficient due to temperature gradients in the way of the emitted light [29], etc. All these aspects are thoroughly studied [27–29]. As a result, we did not address these problems in this work. The main limitation of the described traditional PLIF -2-

measurements is the assumption that the concentration of fluorescent dye is constant in the volume under test. This, in turn, limits the PLIF applicability for analyzing the temperature fields of rapidly evaporating droplets. Fig. 1. Calibration curve [23] (for γin≈1,000 μg/l). 3. Research procedure In our experiments, we used a setup schematically shown in Fig. 2. In terms of its main elements, the setup is similar to the one described in [23]. In our experiments we used twin solid-state Nd:YAG laser Quantel EverGreen 70 (wavelength 532 nm, pulse frequency 20 Hz, maximum pulse energy 74 mJ) to illuminate the water droplet. To generate the light sheet we used cylindrical lenses with an opening angle of 8°. The light sheet width and thickness in the measuring area are 60 mm and 0.3 mm correspondingly. An optical mirror was used for light sheet positioning. We used a motorized manipulator (positioning accuracy 0.05 mm, positioning speed 0.15 m/s) to introduce the droplet into the cylinder channel with the air flow. The manipulator was controlled via the Motomaster software. Water droplet images were captured with a CCD camera ImperX IGV-B2020M (frame resolution 20482048 pix, maximum frame rate 20 fps, digit capacity 16 bit). The camera was supplied with the Nikon 200mm f/4 AF-D Macro lens. We also used an interference filter of 600–10 nm. Image capturing dimensions were 2525 mm in all the experiments. Alternatively to [23], in the current work we focused on PLIF technique limitations in the case of rapid evaporation of a water droplet, with the necessary adaptation of the software-hardware system to obtain the reliable measurement results. Fig. 2. Scheme of the experimental setup (top view). 3.1. Heated air flow A system featuring a Leister CH 6060 hot-air blower (air velocity 0.5–5 m/s) and a Leister LE 5000 HT air heater (temperature range 20–1,000 °С) was used to generate a hot airflow, similar to [23]. The system delivered hot air to the hollow transparent cylinder (outer diameter 0.1 m, wall thickness 2.5 mm) made of heat-resistant silica glass (maximum allowable temperature 1,800 °С). Four round openings 10 mm in diameter each were made in the cylinder to position the droplet holder and thermocouple, as well as to provide illumination and video capturing (Fig. 2). To control the air flow velocity, we used the PIV technique, similar to [23]. For air temperature measurement inside the channel, we used a platinum/platinum-rhodium thermocouple (S type, 0.05 mm junction diameter, 0.1 s response delay, accuracy ± 1 °C) connected to the National Instruments 9213 analog input card. The thermocouple used in the experiments is 1.5–2.5 more accurate than the PLIF technique used in the experiments, which makes the thermocouple the tool of choice. Air velocity Ua inside the cylinder ranged from 3 to 5 m/s. Air -3-

temperature Ta inside the glass cylinder was varied up to 1,000 °С. Just like in [23], our experiments showed that at Ta>500 °С the droplet surface deformed extensively, and the droplet temperature field generation only took 1–3 s. These conditions make a reliable PLIF measurement very difficult due to abruptly changing droplet luminosity, caused by the nature of laser light transmission rather than by droplet heating. 3.2. Water droplet To create a droplet for our experiments, we used a solution of Rhodamine B and distilled water (national standard GOST 6709–72). We chose the Rhodamine B fluorophore for our study, similar to [23], since this dye shows decent stability when exposed to laser light. The intensity of fluorescent emission from this dye has a distinct dependence on temperature [23]. Rhodamine B has also performed well in experiments with significant droplet overheating [23]. Alternatively to experiments in [23], in this study we varied the initial volume concentration of fluorophore γin in a wide range from 500 to 10,000 μg/l. Hereafter the Rhodamine B water solution is referred to as water. To generate a droplet we used a Finnpipette Novus dispenser with a pitch variation of 0.1 µl. The initial droplet volume Vd varied from 10 μl to 20 μl. This corresponded to the variation of droplet initial radius Rd from 1.3 to 1.7 mm. In some experiments, we managed to widen this range to Rd=1–2 mm. A droplet generated by a dispenser was placed onto a holder further positioned by a manipulator (Fig. 2). To evaluate the effect of a holder on the PLIF measurement error, we used three different holders in our experiments (Fig. 3): a hollow metal tube with a 0.5 mm inner and 0.8 mm outer diameter; a hollow metal tube with a 0.3 mm inner and 0.6 mm outer diameter; a nichrome wire 0.2 mm in diameter. In other aspects, the generation, placement and insertion of the droplet into a glass channel is identical to [23]. Table 1 shows thermal and physical properties of the holders. The use of different holder materials (N80CR20 and steel X6CrNiMoTi 17-12-2) stems from the need to determine the influence of thermal conductivity, heat capacity, and thermal diffusivity of metal on the concentration of Rhodamine B in a heating and evaporating droplet. Using steel holders of two different sizes is necessary to estimate how the droplet-holder contact area affects the heating and evaporation of a droplet as well as changes in the fluorophore concentration in the process. Table 1. Thermal and physical properties of the holders. We have discovered that the metal tube with a 0.3 mm inner and 0.6 mm outer diameter as a holder has the least impact on the PLIF measurement accuracy. Therefore, we used this configuration for all the further analysis.

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Fig. 3. Holders used in experiments (also given are the formulas for droplet surface area – Se and dropletto-holder contact area – Sh). 3.3. PLIF measurements The experiments included two stages. The first one was the temperature calibration of the measurement system described in detail in [23], giving us the curve of water temperature versus the luminous intensity of fluorophore. The second one involved capturing the temperature field in a certain section of the droplet. For the second stage, the droplet was vertically cut by a light sheet, and the droplet image was captured and saved to a PC. The configuration of the optical system is identical to [23]. Droplet images were captured at a 4 fps framerate by a 16-bit CCD camera. Image capturing continued until the complete evaporation of the droplet. The images acquired were processed and analyzed with the help of the Actual Flow software. The result of the analysis was the luminous intensity of Rhodamine B () as well as droplet temperature fields plotted with the PLIF Reconstruction algorithm. A series of at least five experiments was performed for each initial value of γin, Rd, and Ta. The experimental results were averaged for each series, with the resulting dependences plotted afterwards. The results were averaged within one series with identical initial conditions. In every other regard, this stage is identical to [23]. 4. Results and discussion 4.1. Special aspects and limitations of PLIF technique used for analyzing the temperature fields of evaporating droplets Fig. 4 shows image sequences of evaporating water droplets attached to a metal holder tube (0.3 mm inner and 0.6 mm outer diameter) in a flow of heated air. Fig. 4. Frames of the evaporating water droplet at different moments of time for Vd≈15 μl, Rd≈1.53 mm, Ta≈300 °C, Ua≈3 m/s, γin≈3,000 μg/l (additionally shown is the average droplet brightness, i.e. ). It is clearly seen from Fig. 4 that Rhodamine B luminosity in the water droplet during its evaporation changes constantly. At first, there is a decrease in luminous intensity () illustrating the droplet heating and its temperature rising. Then there is a short period when  is stable. However, already 10 seconds from the droplet introduction into the air flow, we may observe a nonlinear growth of fluorescence indicating the Rhodamine B concentration surge due to the rapid evaporation of a droplet. This feature occurs consistently for a wide range of the initial Rhodamine B concentrations γin=500– 10,000 μg/l (see Fig. 5). Variations of  relative to its initial value (for any given γin) reaches up to 25% at the end of heating and 16% at the peak of fluorescence, when  reaches its maximum. Thus, the resulting -5-

variation of Rhodamine B fluorescence from its real value in the case of rapid droplet evaporation can exceed 40% (Fig. 5). Fig. 5. Rhodamine B fluorescence variations in the water droplet (Vd≈15 μl, Rd≈1.53 mm) during its evaporation for various initial dye concentrations at Ta≈300 °C, Ua≈3 m/s. To evaluate the effect of the droplet size on Rhodamine B luminous intensity, we have conducted additional experiments with droplets of three different initial radii (Fig. 6a). We have established that at the stage of droplet heating and temperature stabilization, variations of  do not exceed 5–6%, which relates to a temperature variation of 1–3 °C for droplets of different size. Apart from that, it is evident (Fig. 6) that the previous trend (Fig. 5) remains the same. The difference in  maximums for droplets of different size is only due to different initial mass of Rhodamine B in the droplet. For example, droplets of Rd≈1.33 mm and Rd≈1.69 mm differ in volume twofold, just as the respective initial fluorophore mass. That said, in the case of Rhodamine B constant evaporation rate (including the sedimentation onto the holder), a droplet of a larger radius is characterized by a higher peak of . Fig. 6. Rhodamine B fluorescence variation in the evaporating water droplet: a – for different initial droplet size (at Ta≈300 °C, Ua≈3 m/s, γin≈3,000 μg/l); b – for different air flow temperature (at Vd≈15 μl, Rd≈1.53 mm, Ua≈3 m/s, γin≈3,000 μg/l); c – for different air flow velocity (at Vd≈15 μl, Rd≈1.53 mm, Ta≈300 °C, γin≈3,000 μg/l). Additionally, we studied the effect of temperature (Ta) and velocity (Ua) of the air flow on the variation of Rhodamine B luminous intensity (see Fig. 6b,c). Since the droplet evaporation rate and time vary significantly with the temperature change from 100 °C to 500 °C [23], we used the relative linear size of the droplet (Rd*/Rd) instead of time (t) as a generalizing parameter. Fig. 6b shows that after the droplet heating is complete, Rhodamine B fluorescence becomes stationary (stat*) for a short period (1 to 3 s). Minimums of  deviate up to 37% for the studied temperatures Ta, since the droplet temperature – and, consequently, dye fluorescence – is directly proportional to Ta (it varies from 36 °C to 67 °C with a Ta increase from 100 to 500 °C). We have established (Fig. 6b) that for the same initial concentration of Rhodamine B, the increase in the fluorescence intensity caused by rapid evaporation gets lower with a rise in Ta. This fact leads us to a conclusion that Rhodamine B evaporation rate is directly proportional to the evaporation rate of the droplet itself: the higher the droplet evaporation rate, the more dye molecules are carried away from its free surface by the flow and the lower the droplet fluorescence. A thorough analysis of this aspect is given in Section 4.3. Experiments show that the air flow velocity (Ua) does not have any substantial influence on Rhodamine B fluorescence characteristics (Fig. 6c). Thus, increasing Ua from 3 up to 5 m/s leads to a 5–7 -6-

s decrease in the droplet evaporation time. However, a deviation in the fluorophore luminosity at the stage of heating and temperature stabilization did not exceed 2.5–4% for different Ua values. That is because water mass evaporation rate grows only slightly when Ua increases from 3 m/s to 5 m/s [23], and, therefore, this parameter does not have much influence on the droplet fluorescence. We have also evaluated the effect of γin on PLIF measurement accuracy. Usually, it is recommended to use the lowest possible concentration of dye in the liquid [30, 31], since fluorophore (Rhodamine B in particular) emission spectrum and absorption spectrum do overlap. Therefore, the reabsorption of the light emitted by the dye can affect the measurement result in the case of higher concentrations [26]. Our experiments show (Fig. 5) that at the stage of droplet heating, the initial concentration of Rhodamine B does not affect the measurement result. On the contrary, for higher γin (over 1,000 μg/l), the dynamic range χ (brightness units per 1 °C) is 2–8 times higher than for γin≤500 μg/l (Fig. 7a). We used the following equation for χ calculation: χ=(0-stat*)/(T0- Tstat*) (count/°C). To measure the water temperature (T0, Tstat*), just like in [23], a fast-response miniature thermocouple was introduced into the droplet prior to the experiment (S-type, junction diameter 0.05 mm, delay 0.1 s, accuracy ± 1 °C). Fig. 7. PLIF measurement dynamic range (a) and error (b) versus initial Rhodamine B concentration (data from Fig. 5 was used for calculations). At this level of refinement (Fig. 7a), the uncertainty of PLIF temperature measurement decreases significantly with higher γin (Fig. 7b). To calculate the measurement error ΔT, we used the following equation: ΔT=(ǀ stat(1)*- aver ǀ/χ + ǀ stat(2)*- aver ǀ/χ +…+ ǀ stat(n)*- aver ǀ/χ)/n (°C). For studying the temperature fields of an evaporating droplet via PLIF at the stage of droplet heating and temperature stabilization, we may now recommend using higher (over 1,000 μg/l) Rhodamine B concentration in the initial solution. Here are the conclusions we can make for Section 4.1:  After the droplet is heated, its fluorescence starts to grow nonlinearly, with deviations reaching 40%. This is caused by an increase in the concentration of Rhodamine B in the droplet as a result of its rapid evaporation.  The removal (evaporation) rate of Rhodamine B molecules from the droplet surface is directly proportional to the liquid evaporation rate.  At the stage of droplet heating and temperature stabilization, such parameters as initial droplet size as well as air flow temperature and velocity do not affect PLIF measurement results. -7-

 If the initial Rhodamine B concentration in the water droplet increases in the range of 500–10,000 μg/l, the PLIF temperature measurement error decreases 1.5–2 times. 4.2. Typical stages of droplet heating and evaporation. Effects on PLIF measurement Fig. 8 shows a set of curves with distinct stages of water droplet heating and evaporation, as well as temperature fields for each stage. The stages in Fig. 8 are numbered I, II, III, IV. Let us take the evaporation of droplet with the initial size Rd≈1.53 mm in the air flow with Ta≈300 °C and Ua≈3 m/s as an example. The PLIF measurement deviation from the thermocouple measurement was calculated as a modulus of the difference between the temperature readings from two measurement tools: ΔTPLIF=│TPLIFTTherm│. From Fig. 8 you can see that the PLIF results for temperature field plotting in the droplet section differ significantly. Regarding these results, we can describe the stages as follows: (I)

Droplet heating stage (0–7 s). Steady temperature growth (from 24 °C to 55 °C) in the droplet and the corresponding decrease of Rhodamine B luminous intensity (be 20–22%). The droplet size decreases by less than 5% comparing to the initial one. The PLIF measurement deviation from the thermocouple measurement (ΔTPLIF) does not exceed 1.5 °C. At this stage, the traditional PLIF technique is applicable for reliable plotting of temperature fields.

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Droplet temperature stabilization stage (7–12 s). Almost constant droplet temperature level (55–56 °C). Rhodamine B fluorescence at this stage varies by less than 5–6%. The droplet size decreases by less than 11% comparing to the initial one. The PLIF measurement deviation from the thermocouple measurement (ΔTPLIF) does not exceed 2.5 °C. At this stage, the traditional PLIF technique is applicable for reliable temperature field plotting.

(III) Rapid droplet evaporation stage (12–28 s). Droplet temperature remains stationary at 55–56 °C. Rhodamine B fluorescence increases nonlinearly due to its concentration change, exceeding the initial value by 5–10% at the end of the stage. Droplet size decreases by 45– 50% comparing to the initial one. The PLIF measurement deviations from the thermocouple measurement (ΔTPLIF) are substantial, increasing nonlinearly up to 39–40 °C. At this stage, the traditional PLIF technique is not feasible for reliable temperature field plotting. An adjusting factor is needed for the PLIF technique to regain its applicability. (IV) Droplet evaporation completion (28–45 s). Droplet temperature rises steadily up to 57–58 °C. Rhodamine B fluorescence decreases nonlinearly. This result is most likely caused by the shadow from the holder obscuring the droplet, since the size of the droplet at this stage is comparable to the size of the metal tube holder. Besides, there are frequent flares appearing on the image caused by the light sheet re-reflection from the holder. At this stage, the droplet evaporates completely and the PLIF technique is not applicable for temperature field plotting. -8-

Fig. 8. Typical stages of water droplet heating/evaporation (a) and corresponding temperature fields obtained by the traditional PLIF measurement technique (b) (for Vd≈15 μl, Rd≈1.53 mm, Ta≈300 °C, Ua≈3 m/s, γin≈3,000 μg/l). Here are the conclusions we can make for Section 4.2:  Four distinct stages are defined for droplet heating/evaporation: I – heating; II – temperature stabilization; III – rapid evaporation; IV – evaporation completion.  Traditional PLIF measurement is applicable for temperature field plotting at stages I and II: PLIF measurement error here does not exceed 1.5–2.5 °C. To make the PLIF technique applicable at stage III. an adjustment factor is required. PLIF measurement is not feasible at stage IV, since the measurement error may increase substantially. 4.3. Assessment of changes in Rhodamine B concentration in the evaporating water droplet As we mentioned before, the evaluation of Rhodamine B fluorophore concentration at the stage of rapid droplet evaporation (stage III) (Section 4.2) was of high interest to us. For this we assumed that the Rhodamine B concentration does not change (γ*=γin) during droplet heating and temperature stabilization (stages I and II). To illustrate the change of Rhodamine B concentration in the water droplet during its rapid evaporation, we examined three cases (Fig. 9a). The first case (ideal): there is no Rhodamine B concentration decrease (i.e., it does not evaporate). It means that the current fluorophore concentration (γ*) is inversely proportional to the overall droplet volume and increases over time. The second case (ideal): Rhodamine B evaporates along with the water (i.e., dye evaporation rate is similar to water evaporation rate). This means the constant value of its concentration (γ*=γin). The third case (realistic): Rhodamine B concentration change is calculated using the experimental results of this work. Fig. 9. a – Rhodamine B concentration variation (γ*) during droplet heating and evaporation for the three described cases (for Vd≈15 μl, Rd≈1.53 mm, Ta≈300 °C, Ua≈3 m/s, γin≈3,000 μg/l); b – Rhodamine B concentration (γin) versus luminous intensity (stat*) (for Vd≈15 μl, Rd≈1.53 mm, Ta≈300 °C). To calculate the concentration change for the third case, we used the following algorithm (assuming the evaporating droplet size Rd≈1.53 mm). For each initial Rhodamine B concentration (γin), we determined the luminous intensity after the stationary temperature mode is reached (Fig. 5), i.e., the stat*. Then we plotted the curve for Rhodamine B concentration (γin) versus luminous intensity (stat*) shown in Fig. 9b. Then, considering the droplet temperature is constant for the whole evaporation period (Fig. 8a), we assumed that Rhodamine B fluorescence only changes because of its concentration -9-

variation. Thus, knowing that each fluorophore concentration at 56-57 °C temperature has its own corresponding fluorescence value (Fig. 9b), we used the obtained approximation to convert fluorescence (*) into concentration (γ*). As a result, we can see from Fig. 9a that Rhodamine B concentration in the droplet increases during the rapid evaporation stage. The curve obtained from the experimental results is close to that of the second ideal case, when it was assumed that the fluorophore is evaporating from the droplet surface along with the water. To confirm the discovered effect, we plotted the curve for the maximum deviation of Rhodamine B luminous intensity (Δ) versus the mass evaporation rate of water (We) shown in Fig. 10. For this we used the evaporation rate values from [23] for the air temperature range of 100–500 °C. Fluorescence deviation (Δ) was calculated using the data from Fig. 6b for the five given temperature points by this equation: Δ=(max-stat)/max100%. Fig. 10. Maximum deviation of Rhodamine B luminous intensity (Δ) versus mass evaporation rate of water (We) (for Vd≈15 μl, Rd≈1.53 mm, Ta=100-500 °C, Ua≈3 m/s, γin≈3,000 μg/l). Fig. 10 shows that Δ decreases nonlinearly with the increase in We (growth of Ta). The parameter Δ indirectly indicates the amount of Rhodamine B fluorophore left in the droplet after the rapid evaporation stage. The lower the Δ, the less fluorophore is left in the droplet. This way, the amount of Rhodamine B that evaporated from the droplet surface grows with the increase of water evaporation rate. Fig. 11 contains the curve for the experimental Rhodamine B fluorophore concentration variation (γ*) during droplet heating and evaporation for the three holder types described in Section 3.2. And since the complete evaporation time of a droplet is different for each holder, a relative linear size of the droplet was used – Rd*/Rd. The algorithm described earlier in this section was used to calculate the concentration change. Fig. 11. Rhodamine B fluorophore concentration variation (γ*) during droplet heating and evaporation for three different holder types (for Vd≈15 μl, Rd≈1.53 mm, Ta≈300 °C, Ua≈3 m/s, γin≈3,000 μg/l). We can see from Fig. 11 that γ* differs more than 2 times between the three holder types during droplet evaporation. By preliminary evaluations, we have established that the droplet-holder contact area (Sh) at the initial moment of a droplet introduction into the quartz cylinder was Sh=3.88 mm2 for a 0.8 mm diameter metal tube, Sh=2.95 mm2 for a 0.6 mm diameter metal tube, and Sh=1.48 mm2 for a 0.2 mm diameter nichrome wire holder.

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The results obtained prove the Rhodamine B sedimentation onto the holder. The sedimented amount of fluorophore during the rapid droplet evaporation is directly proportional to contact area Sh. We can also say that Rhodamine B sedimentation onto the holder is somewhat affected by the initial concentration of fluorophore (γin). For instance, we can see from Fig. 5 that Δ for different concentrations will be 500 μg/l – 23.8%; 1,000 μg/l – 26.5%; 2,000 μg/l – 27.1%; 3,000 μg/l – 31.3%; 10,000 μg/l – 38.1%. I.e., there is a finite amount of Rhodamine B that can be sedimented onto the holder. Fig. 11 shows that with Rd*/Rd≈0.4 the difference of γ* for the metal tube (0.6 mm) and Nichrome Wire exceeds 70%. Sh for metal tube (0.6 mm) and nichrome wire (calculated using the formulas from Fig. 3) amounted to 1.15 mm2 and 1.48 mm2, respectively. That is, the difference between Sh for the two holder types under study did not exceed 30%. Different Sh values cannot be the only explanation for such a difference between concentrations γ*. Thermal and physical properties of the holder material interfere as well. Due to high values of thermal conductivity λ and heat capacity Cp (Table 1), the metal holder (steel X6CrNiMoTi 17-12-2) shows greater metal tube surface heating as compared to the holder made of the N80CR20 alloy. Therefore, Rhodamine B settles on the metal tube surface more rapidly as compared to the nichrome wire, which leads to different values of γ* (Fig. 11). Here are the conclusions we can make for Section 4.3:  Rhodamine B concentration increases nonlinearly at the stage of rapid droplet evaporation.  The experimental results show two independent events taking place during the rapid droplet evaporation. The first one is Rhodamine B evaporation from the free droplet surface; the amount of dye evaporating depends on the mass evaporation rate of water. The second one is Rhodamine B sedimentation onto the holder; the amount of dye sedimenting is directly proportional to the droplet-holder contact area.  The intensity of Rhodamine B sedimentation onto the holder is significantly affected by its thermal and physical characteristics: the higher the heat capacity and thermal conductivity of the material, the more rapid the process. 4.4. Evaluating the rate of Rhodamine B evaporation from the droplet surface and the rate of its sedimentation onto the holder In this section, using the results from Sections 4.1 and 4.3, we will calculate the rate of Rhodamine B evaporation from the free surface of the droplet (WRe) as well as the rate of this fluorophore sedimentation onto the metal holder (WRh). As an example we took the evaporation of the droplet with the initial dye concentration γin≈3,000 μg/l for Ta≈300 °C, Ua≈3 m/s. When calculating the rates, we made an assumption based on the results from Sections 4.1 and 4.3 that both of these events occur simultaneously, i.e.: WR=WReSe+WRhSh. - 11 -

(1)

Still assuming that during the droplet heating and temperature stabilization γ*=γin, we calculate WR for the rapid droplet evaporation stage by the following algorithm. Using the experimentally obtained curves for γ* variation during droplet evaporation (similar to those in Fig. 9a and Fig. 11), for each point on the curve we determine the current mass mR of Rhodamine B in the droplet. Next, we calculate the instantaneous release rate WR of Rhodamine B for each point as a ratio of the calculated fluorophore mass variation ΔmR to the corresponding period Δt. We used the following equation: mR= γ*Vd*, μg. The instantaneous Rhodamine B release rate can be calculated as follows: WR=ΔmR/Δt =(mR(n)-mR(n-1))/(t(n)-t(n-1)), μg/s. Fig. 12 shows instantaneous Rhodamine B release rate (removal rate) WR, which corresponds to several initial droplet sizes Rd=1.33–1.68 mm and to 3 different holder types. And again, we use a relative linear droplet size Rd*/Rd for data generalization due to different evaporation times. Fig. 12. Instantaneous Rhodamine B release rate WR corresponding to several initial droplet sizes (a) (0.6 mm diameter metal tube holder, Ta≈300 °C, Ua≈3 m/s, γin≈3,000 μg/l) as well as three different holder types (b) (for Vd≈15 μl, Rd≈1.53 mm, Ta≈300 °C, Ua≈3 m/s, γin≈3,000 μg/l). To calculate WRe and WRh, we assume that these parameters are constant for the fixed Ua, Ta, γin and holder type. To verify our assumption, we have plotted curves for WR versus droplet surface area Se and droplet-holder contact area Sh (Fig. 13). Fig. 13. Instantaneous Rhodamine B release rate WR corresponding to several initial droplet sizes (a) versus Se (0.6 mm diameter metal tube holder, Ta≈300 °C, γin≈3,000 μg/l) as well as three different holder types (b) versus Sh (for Vd≈15 μl, Rd≈1.53 mm, Ta≈300 °C, Ua≈3 m/s, γin≈3,000 μg/l). It is evident from Fig. 3a that for the same holder type WRh=const (and, correspondingly, WRe=const), WR is only dependent on the evaporation surface area: WR=f(Se). As a result, using the obtained approximation (Fig. 13a) and equation (1), we have developed the following set of equations: 0.0012=WRe10+WRh1.8, 0.0025=WRe25+WRh2.6. As for the numerical estimation of the droplet-holder contact area, here we used the following expression: Sh=πdhRd*, where dh is the outer diameter of the metal tube, mm. Solving the above set of equations gives us the following: WRh≈2.6410-4, μg/(mm2s) for a metal tube holder 0.6 mm in the outer diameter, WRe≈0.7310-4, μg/(mm2s). - 12 -

Next, knowing the WRe and using the data from Fig. 13b, we calculate WRh for a metal tube holder 0.8 mm in the outer diameter and a nichrome wire holder correspondingly: WRh≈2.6910-4, μg/(mm2s) for a metal tube holder 0.8 mm outer diameter, WRh≈1.5810-4, μg/(mm2s) for a 0.2 mm nichrome wire holder. Table 2 summarizes the rates of Rhodamine B evaporation and sedimentation. Table 2. Rhodamine B evaporation rate WRe and sedimentation rate WRh. From the results in Table 2, three interesting aspects can be distinguished. First, for holders made of the same material (steel X6CrNiMoTi 17-12-2) WRh is virtually identical, deviating by less than 2%, which points to the fact that holder dimensions do not affect the Rhodamine B sedimentation rate. Second, for holders made of different materials, WRh can deviate severalfold. This result stems from the different thermal and physical characteristics of various materials (Table 1). The higher the thermal conductivity and thermal diffusivity of the holder material, the more fluorophore settles on its surface (due to more significant heat transfer from the holder to the droplet). Third, it is the Rhodamine B sedimentation onto the holder that has a decisive influence on the fluorophore concentration variation during the rapid droplet evaporation stage. As a result, we can make the following conclusions for Section 4.4:  The rate of Rhodamine B sedimentation onto the holder is 2–4 times higher than the rate of its evaporation from the free droplet surface during the rapid droplet evaporation.  The rate of Rhodamine B sedimentation onto the holder is determined by the holder material only, and virtually non-dependent on its dimensions. The fluorophore sedimentation rate for different holder materials may differ by two or more. 4.5. Adjusting factor for PLIF measurement accounting for dye evaporation or its concentration growth in a droplet The traditional PLIF technique (see Section 2) for temperature field plotting implies converting the brightness of each pixel into the temperature value with the help of a calibration curve (Fig. 1). Therefore, one of the easiest and most reliable ways to adjust the water droplet temperature field at the rapid evaporation stage is to multiply the brightness of each pixel by a corresponding adjusting factor K immediately before field plotting. This approach makes it possible to use the same calibration curve (Fig. 1) for each stage of droplet heating and evaporation. The factor K is defined for droplet images of the third stage (rapid evaporation) as a ratio of Rhodamine B mean luminous intensity at the temperature stabilization stage to the current Rhodamine B luminous intensity: K=aver/*. - 13 -

Fig. 14 contains values of K for droplet evaporation. We considered the droplet evaporation for Vd≈15 μl, Rd≈1.53 mm, Ta≈300 °C. To calculate K, we used the experimental results from Fig. 5. For the stages of droplet heating and temperature stabilization we assumed the value of adjusting factor K=1. Fig. 14 Adjusting factor K during the droplet heating and evaporation (for Vd≈15 μl, Rd≈1.53 mm, Ta≈300 °C, Ua≈3 m/s): a – for various γin; b – resulting approximation curve. It is evident (Fig. 14a) that the initial concentration of Rhodamine B in the droplet has no influence on K. This fact allows us to summarize the calculation results and to plot the resulting approximation curve (Fig. 14b). Fig. 15 shows the adjusting factor K for various temperatures of the air flow. With an increase in the air temperature and mass water evaporation rate, K decreases almost linearly. This is another confirmation of hypothesis (Section 4.3) that water evaporation rate has a major influence on Rhodamine B particle entrainment from the free surface of the droplet during its rapid evaporation. Fig. 15 Adjusting factor K during droplet heating and evaporation (for Vd≈15 μl, Rd≈1.53 mm, Ua≈3 m/s, γin≈3,000 μg/l): a – for various Ta; b – comparison of K (25 s after the droplet introduction into the air flow) and the mass water evaporation rate We (using the data from [23]). To evaluate the reliability of the results obtained via this approach, we plotted the droplet temperature field during its rapid evaporation using the adjusting factor K (Fig. 16). Fig. 16. Water droplet temperature field during its rapid evaporation: a – without the adjusting factor; b – after the recalculation of Rhodamine B fluorescence using the adjusting factor K; c – combined temperature trends obtained with the thermocouple measurement and PLIF technique, with the adjusting factor applied (for Vd≈15 μl, Rd≈1.53 mm, Ta≈300 °C, Ua≈3 m/s, γin≈3,000 μg/l). It is clear (Fig. 16) that the suggested approach of brightness adjustment of the initial droplet image at the stage of the rapid evaporation makes it possible to apply the traditional PLIF technique for image processing (temperature field plotting). The error of PLIF measurement in this case does not exceed 3–4 °C (Fig. 16c). The initial concentration of Rhodamine B in the droplet has no effect on the adjusting factor. 5. Conclusion As a result of the experiments conducted, several distinct stages of water droplet heating and evaporation are defined and thoroughly described, with the PLIF technique applicability analysis for each - 14 -

of these stages. We have discovered that at the stage of rapid droplet evaporation, the luminous intensity of Rhodamine B changes nonlinearly. It is experimentally proven that this event is due to the changing fluorophore concentration in the droplet. Moreover, a change in the Rhodamine B concentration from 500 to 10,000 μg/l is a result of two simultaneous events: the evaporation of the fluorophore from the free surface of the droplet and its sedimentation onto the holder. We have, for the first time, evaluated the relative mass rate of Rhodamine B evaporation (0.7310-4 μg/(mm2s)) and its sedimentation onto the holder (1.5810-4 to 2.6910-4 μg/(mm2s)). We have proven that sedimentation has the definitive influence on the fluorophore concentration change, and that the rate of Rhodamine B sedimentation is dependent on the material of the holder and is not related to its dimensions. Finally, we have shown that the introduction of an adjusting factor makes it possible to apply the PLIF technique for plotting the temperature field of a rapidly evaporating droplet. This is especially helpful for the cases when smallsized fast-response thermocouples cannot be used. Acknowledgments Research was carried out within the framework of the development program of the National Research Tomsk Polytechnic University (project VIU–ISHFVP–184/2018). Nomenclature a – thermal diffusivity coefficient, m2/s; Cp – heat capacity, J/(kg∙°С); dh – metal tube outer diameter, mm; mR – current mass of Rhodamine B in the droplet, μg; n – number of measurement points; Rd – initial water droplet radius, mm; Rd* – current water droplet radius, mm; Se – droplet surface area, m2; Sh – droplet-holder contact area, m2; t – time, s; T* – current average temperature of the droplet, °С; Tstat* – droplet average temperature after reaching the stationary temperature mode, °С; T0 – initial average temperature of the droplet, °С; Ta – air flow temperature, °С; Td – temperature in the center of the droplet, °С; TPLIF – results of PLIF measurements, °С; TTherm – results of thermocouple measurements, °С; Ua – air velocity, m/s; - 15 -

Vd – initial droplet volume, μl; Vd* – current droplet volume (Vd*=4/3π Rd*3), μl; We – mass rate of water evaporation, kg/(m2s); WR – instantaneous release rate of Rhodamine B, μg/s; WRe – instantaneous specific rate of Rhodamine B evaporation from the droplet surface, μg/(mm2s); WRh – instantaneous specific rate of Rhodamine B sedimentation onto the holder, μg/(mm2s). Greek  – Rhodamine B luminous intensity, count; * – current Rhodamine B luminous intensity, count; stat* – Rhodamine B luminous intensity after reaching the stationary temperature mode, count; aver – Rhodamine B average luminous intensity at the droplet temperature stabilization stage (aver=(stat(1)*+ stat(2)*+…+ stat(n)*)/n), count; max – Rhodamine B maximum luminous intensity at the droplet rapid evaporation stage, count; 0 – Rhodamine B initial luminous intensity, count; γin – initial volume concentration of Rhodamine B in the droplet, μg/l; γ* – current volume concentration of Rhodamine B in the droplet, μg/l; γstat* – volume concentration of Rhodamine B in the droplet after reaching the stationary temperature mode, μg/l; ΔmR – Rhodamine B mass change in the droplet per Δt time period, μg; Δt – time period, s; ΔT – PLIF measurement error, °С; ΔTPLIF – deviation of PLIF measurements from thermocouple measurement, °С; Δ – Rhodamine B luminous intensity maximum deviation on the droplet rapid evaporation stage, %; λ – thermal conductivity coefficient, W/(m∙°С); ρ – density, kg/m3; χ – dynamic range, count/°С. References 1. D.B. Spalding, Some fundamentals of combustion, Butterworth’s, London, 1955. 2. N.A. Fuchs, Evaporation and Droplet growth in Gaseous Media, Pergamon Press, London, 1959. 3. W.E. Ranz, W.R. Marshall, Evaporation from Drops, Chem. Eng. Prog. 48 (1952) 141–146, 173– 180. 4. M.C. Yuen, L.W. Chen, Heat-transfer measurements of evaporating liquid droplets, Int. J. Heat Mass Transfer 21 (1978) 537–542. https://doi.org/10.1016/0017-9310(78)90049-2.

- 16 -

5. M. Renksizbulut, M.C. Yuen, Numerical study of droplet evaporation in a high-temperature stream, J. Heat Transfer 105 (1983) 389–397. doi:10.1115/1.3245591. 6. V.I. Terekhov, V.V. Shishkin, N.E. Terekhov, K.Ch. Bi, Heat and mass transfer in disperse and porous media experimental and numerical investigations of nonstationary evaporation of liquid droplets, J. Eng. Phys. Thermophys. 83 (2010) 883–890. https://doi.org/10.1007/s10891-010-04107. 7. S.S. Sazhin, A.E. Elwardany, P.A. Krutitskii, G. Castanet, F. Lemoine, E.M. Sazhina, M.R. Heikal, A simplified model for bi-component droplet heating and evaporation, Int. J. Heat Mass Transfer 53 (2010) 4495–4505. https://doi.org/10.1016/j.ijheatmasstransfer.2010.06.044. 8. S. Tonini, G.E. Cossali, A novel formulation of multi-component drop evaporation models for spray

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Table 1. Thermal and physical properties of the holders. nichrome wire (N80CR20)

metal tube (steel X6CrNiMoTi 17-12-2)

T, °C

Cp, J/(kg∙°С)

λ, W/(m∙°С)

ρ, kg/m3

a∙106, m2/s

Cp, J/(kg∙°С)

λ, W/(m∙°С)

ρ, kg/m3

a∙106, m2/s

20 100 200 300 400 500 600

440 450 460 460 460 460 460

13.6 13.8 15.6 17.2 18.9 20.7 22.6

8400 8400 8400 8400 8400 8400 8400

3.68 3.65 4.04 4.45 4.89 5.36 5.85

504 510 538 562 588 627 753

15 16 22 23 24 26 30

7900 7870 7830 7790 7750 7700 7660

3.77 3.99 5.22 5.25 5.27 5.39 5.20

Table 2. Rhodamine B evaporation rate WRe and sedimentation rate WRh. WRh, μg/(mm2s)

type of holder metal tube (0.8 mm), steel X6CrNiMoTi 17-12-2

2.6910-4

metal tube (0.6 mm), steel X6CrNiMoTi 17-12-2

2.6410-4

nichrome wire (0.2 mm)

1.5810-4

- 20 -

WRe, μg/(mm2s)

0.7310-4

60

T (C)

50 40 30 20 10

1,000

2,000

3,000

 brightness counts

4,000

Fig. 1. Calibration curve [23] (for γin≈1,000 μg/l).

Ø105 mm Ø100 mm

Water Droplet

Thermocouple (type S)

Quartz Cylinder 10 mm Hole

Motorized Manipulator

Droplet Holder

10 mm Hole

NI 9213

Analog Input Device Optical Mirror

PC

Laser Beam Beam Optics Synchronizer

Light Filter (600-10 nm)

Nd:YAG Laser (532 nm)

CCD Camera Fig. 2. Scheme of the experimental setup (top view).

- 21 -

USB Status Trig ge r Rec ord in g Hi gh-Spe ed

PTU-X Powe r

Fig. 3. Holders used in experiments (also given are the formulas for droplet surface area – Se and dropletto-holder contact area – Sh).

Fig. 4. Frames of the evaporating water droplet at different moments of time for Vd≈15 μl, Rd≈1.53 mm, Ta≈300 °C, Ua≈3 m/s, γin≈3,000 μg/l (additionally shown is the average droplet brightness, i.e. ).

- 22 -

 brightness counts

40,000

in500 g/l

in1,000 g/l

35,000

in2,000 g/l

in3,000 g/l

30,000

in10,000 g/l

25,000 20,000 15,000 10,000 5,000 0

0

10

20

t (s

30

40

Fig. 5. Rhodamine B fluorescence variations in the water droplet (Vd≈15 μl, Rd≈1.53 mm) during its evaporation for various initial dye concentrations at Ta≈300 °C, Ua≈3 m/s. 14,000

Rd1.33 mm Rd1.53 mm

17,500

 brightness counts

 brightness counts

20,000

Rd1.69 mm

15,000 12,500 10,000 7,500

* - Droplet Lifetime

5,000 0

10

20

t (s

*30

40

12,000

Ta100 C

Ta200 C

Ta300 C

Ta400 C

Ta500 C

10,000 8,000

stat*

6,000

* *50

0.6

0.7

a

0.9

1.0

b 15,000

 brightness counts

0.8

Rd*/Rd

Ua3 m/s Ua4 m/s

12,500

Ua5 m/s

10,000 7,500

* - Droplet Lifetime

5,000 0

10

20

t (s

30

* * *50

40

c Fig. 6. Rhodamine B fluorescence variation in the evaporating water droplet: a – for different initial droplet size (at Ta≈300 °C, Ua≈3 m/s, γin≈3,000 μg/l); b – for different air flow temperature (at Vd≈15 μl, Rd≈1.53 mm, Ua≈3 m/s, γin≈3,000 μg/l); c – for different air flow velocity (at Vd≈15 μl, Rd≈1.53 mm, Ta≈300 °C, γin≈3,000 μg/l).

- 23 -

Parabola y = A + B*x + C*x^2 0.89627 ± 7.18722 0.02382 ± 0.00473 -7.78164E-7 ± 4.217 77E-7

Model Equation A B C

T C

 count/C

200 180 160 140 120 100 80 60 40 20 0

3.0

Model Equation a

2.7

b

Exp3P2 y =exp(a+b*x+c*x^2) 1.05248 ± 0.09435 -2.63034E-5 ± 6.74 368E-5 -5.32007E-9 ± 6.46 603E-9

c

2.4 2.1 1.8 1.5

0

2,500

5,000

in (g/l

1.2

7,500 10,000

0

2,500

5,000

in (g/l

a

7,500 10,000

b

Fig. 7. PLIF measurement dynamic range (a) and error (b) versus initial Rhodamine B concentration (data

 brightness counts

from Fig. 5 was used for calculations). 14,000 12,000 10,000 8,000 6,000 4,000

0

10

20

30

40

0

10

20

30

40

30

40

t (s

Rd mm

1.6 1.2 0.8 0.4

Td C

0.0

Stage:

80 70 60 50 40 30 20 10 0

t (s

Thermocouple (TTherm) PLIF (TPLIF)

TPLIF=TPLIF-TTherm 0

I

10

20

II

III

t (s

a - 24 -

IV

b Fig. 8. Typical stages of water droplet heating/evaporation (a) and corresponding temperature fields obtained by the traditional PLIF measurement technique (b) (for Vd≈15 μl, Rd≈1.53 mm, Ta≈300 °C, Ua≈3 m/s, γin≈3,000 μg/l).

- 25 -

20,000 15,000

15,000

Ideal (2nd Case) *=in

10,000

Real (3rd Case) *=(experimental)

* (g/l

20,000

in (g/l

Ideal (1st Case) *=f(Vd)

25,000

5,000

0

10

t (s

20

0

30

Parabola y = A + B*x + C*x^2 2204.86138 ± 256.00085 2.79148 ± 0.14353 -1.05936E-4 ± 1.25937E

A B C

5,000

in3,000 g/l

0

Model Equation

10,000

2,500 5,000 7,500 10,000

stat* (count

a

b

Fig. 9. a – Rhodamine B concentration variation (γ*) during droplet heating and evaporation for the three described cases (for Vd≈15 μl, Rd≈1.53 mm, Ta≈300 °C, Ua≈3 m/s, γin≈3,000 μg/l); b – Rhodamine B concentration (γin) versus luminous intensity (stat*) (for Vd≈15 μl, Rd≈1.53 mm, Ta≈300 °C). Ta100 C Ta200 C

 (%

25

Ta300 C Ta400 C

20

15

Ta500 C

0.015

0.018

0.021

0.024

0.027

2

We (kg/(m s) Fig. 10. Maximum deviation of Rhodamine B luminous intensity (Δ) versus mass evaporation rate of water (We) (for Vd≈15 μl, Rd≈1.53 mm, Ta=100-500 °C, Ua≈3 m/s, γin≈3,000 μg/l).

25,000

* (g/l

20,000

Metal Tube (0.8 mm) Metal Tube (0.6 mm) Nichrome Wire (0.2 mm)

15,000 10,000 5,000 0 0.2

0.4

0.6

Rd*/Rd

0.8

1.0

Fig. 11. Rhodamine B fluorophore concentration variation (γ*) during droplet heating and evaporation for three different holder types (for Vd≈15 μl, Rd≈1.53 mm, Ta≈300 °C, Ua≈3 m/s, γin≈3,000 μg/l). - 26 -

0.004

0.005

Rd1.53 mm

0.004

Rd1.68 mm

WR (g/s

WR (g/s

0.003

Rd1.33 mm

0.002 0.001 0.000 0.4

0.5

0.6

0.7

Rd*/Rd

0.8

0.003 0.002 0.001 0.000 0.4

0.9

Metal Tube (0.8 mm) Metal Tube (0.6 mm) Nichrome Wire (0.2 mm)

0.5

0.6

0.7

Rd*/Rd

a

0.8

0.9

b

Fig. 12. Instantaneous Rhodamine B release rate WR corresponding to several initial droplet sizes (a) (0.6 mm diameter metal tube holder, Ta≈300 °C, Ua≈3 m/s, γin≈3,000 μg/l) as well as three different holder types (b) (for Vd≈15 μl, Rd≈1.53 mm, Ta≈300 °C, Ua≈3 m/s, γin≈3,000 μg/l).

0.004

0.005

Rd1.53 mm

0.004

Rd1.68 mm

WR (g/s

WR (g/s

0.003

Rd1.33 mm

WR=f(Se)

0.002 0.001 0.000

5

10

15

Se (mm2)

20

0.003 0.002 0.001 0.000 1.0

25

Metal Tube (0.8 mm) Metal Tube (0.6 mm) Nichrome Wire (0.2 mm)

1.5

2.0

2.5

Sh (mm2)

3.0

3.5

Fig. 13. Instantaneous Rhodamine B release rate WR corresponding to several initial droplet sizes (a) versus Se (0.6 mm diameter metal tube holder, Ta≈300 °C, γin≈3,000 μg/l) as well as three different holder types (b) versus Sh (for Vd≈15 μl, Rd≈1.53 mm, Ta≈300 °C, Ua≈3 m/s, γin≈3,000 μg/l).

- 27 -

1.0

0.9

0.9

0.8

0.8

K=aver/*

K=aver/*

1.0

in500 g/l

0.7

in1,000 g/l in2,000 g/l

0.6

0.7

Cubic Model Equation y = A + B*x + C*x^2 + D*x^3 0.98495 ± 0.00975 A 0.00656 ± 0.0028 B -0.00101 ± 2.16179E-4 C 1.44255E-5 ± 4.56012E-6 D

0.6

in3,000 g/l in10,000 g/l

0.5

0

10

20

0.5

30

t (s

0

10

a

20

30

t (s

b

Fig. 14 Adjusting factor K during the droplet heating and evaporation (for Vd≈15 μl, Rd≈1.53 mm, Ta≈300

1.0

0.9

0.9

0.8

0.8

Ta100 C

0.7

Ta200 C

0.6

Ta300 C Ta400 C

0.5 0.4

10

20

t (s

30

40

K (t25 s)

0.02

0.7 0.01

0.6 0.5

Ta500 C

0

0.03

50

0.4

We (kg/(m2s))

1.0

K=aver/*

K=aver/*

°C, Ua≈3 m/s): a – for various γin; b – resulting approximation curve.

We

100

200

a

300

Ta (C

400

500

0.00

b

Fig. 15 Adjusting factor K during droplet heating and evaporation (for Vd≈15 μl, Rd≈1.53 mm, Ua≈3 m/s, γin≈3,000 μg/l): a – for various Ta; b – comparison of K (25 s after the droplet introduction into the air flow) and the mass water evaporation rate We (using the data from [23]).

- 28 -

a

80 70 60 50 40 30 20 10 0

Thermocouple (TTherm)

5

PLIF (TPLIF)

4 3 2 1

TPLIF=TPLIF-TTherm 0

5

10

15

t (s

20

25

30

TPLIF C

Td C

b

0

c Fig. 16. Water droplet temperature field during its rapid evaporation: a – without the adjusting factor; b – after the recalculation of Rhodamine B fluorescence using the adjusting factor K; c – combined temperature trends obtained with the thermocouple measurement and PLIF technique, with the adjusting factor applied (for Vd≈15 μl, Rd≈1.53 mm, Ta≈300 °C, Ua≈3 m/s, γin≈3,000 μg/l). Measuring the temperature of a rapidly evaporating water droplet by Planar Laser Induced Fluorescence Highlights - 29 -



Limitations for temperature measurement of evaporating droplet are determined



Four distinct stages of droplet evaporation are described



Rhodamine B fluorophore evaporation and sedimentation rates are established



Rhodamine B fluorescence varies nonlinearly during rapid droplet evaporation



An adjusting factor is used for noncontact measurement correction

- 30 -