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The role of atomization in the coupling between doped droplets dynamics and their flames

The droplet and flame chemiluminescence dynamics as well as their coupling during atomization events of graphene oxide doped diesel are investigated experimentally. The tested doping concentrations are 0, 0.001, 0.005, 0.01, and 0.02% by weight. To minimize heat transfer between the droplet and its suspension mechanism, small diameter fibers are used for the droplet suspension. Separate shadowgraphy and OH* chemiluminescence measurements are performed at 4000 Hz to study the droplet and flame dynamics, respectively. The results show that both the droplet diameter squared and the flame chemiluminescence feature intermittent oscillations. The droplet diameter squared oscillations RMS is positively related to the number and intensity of the atomization events and the graphene oxide doping concentration. The probability density function of the inverse of the time separation between two consecutive atomization events and the power spectrum density of the droplet diameter squared oscillations feature dominant large probabilities and powers at about 25 Hz prior to the occurrence of the first intense atomization event. After the occurrence of the first intense atomization event, this frequency decreases to about 5 Hz for both. Although the intense atomization triggers the large amplitude oscillations at 5 Hz, it was argued that the retracting motion of the igniter induces the oscillations at 25 Hz. Our findings suggest that the atomization events are the root cause of the smaller frequency coupling between liquid fuel droplets doped with graphene oxide and their flames. This has implications for spray combustion research.

The tested doping concentrations are 0, 0.001, 0.005, 0.01, and 0.02% by weight. To minimize heat transfer between the droplet and its suspension mechanism, small diameter fibers are used for the droplet suspension. Separate shadowgraphy and OH * chemiluminescence measurements are performed at 4000 Hz to study the droplet and flame dynamics, respectively. The results show that both the droplet diameter squared and the flame chemiluminescence feature intermittent oscillations. The droplet diameter squared oscillations RMS is positively related to the number and intensity of the atomization events and the graphene oxide doping concentration. The probability density function of the inverse of the time separation between two consecutive atomization events and the power spectrum density of the droplet diameter squared oscillations feature dominant large probabilities and powers at about 25 Hz prior to the occurrence of the first intense atomization event. After the occurrence of the first intense atomization event, this frequency decreases to about 5 Hz for both.
Although the intense atomization triggers the large amplitude oscillations at 5 Hz, it was argued that the retracting motion of the igniter induces the oscillations at 25 Hz.
Our findings suggest that the atomization events are the root cause of the smaller frequency coupling between liquid fuel droplets doped with graphene oxide and their flames. This has implications for spray combustion research. a) Author to whom correspondence should be addressed: sina.kheirkhah@ubc.ca

I. INTRODUCTION
As doping agents, nanomaterials have been used to improve several liquid fuels combustion characteristics, such as their burning rate and emissions, see for example [1][2][3][4][5][6] . In the context of droplet combustion, it is shown that doping of liquid fuels with nanomaterials leads to the occurrence of the atomization phenomenon [5][6][7][8][9][10][11] . This changes the spatio-temporal size distribution of the droplets and their burning rate 6 , which may influence the dynamics of coupling between the droplets and the corresponding flames. Our understanding related to the characteristics of the droplet-atomization-flame coupling is limited, and this requires further investigations.
The atomization phenomenon is comprised of the nucleation and bubble growth, droplet surface rupture, ligament formation and its break up, and ejection of baby droplets 7 . Nucleation occurs at the liquid-liquid interface of multicomponent fuels with different boiling temperatures, at the liquid-solid interface of the droplet and its suspending mechanism, and/or at the nanomaterials surface 7,12 . For the latter, it is shown that the addition of carbonaceous nanomaterials to liquid fuels allows for absorption of the combustion heat at the materials surface, formation of nucleation sites, and as a result generation of bubbles at these sites 5,6 . Coalescence of the bubbles, transfer of heat from the flame to the bubbles, and the surface regression of the main droplet lead to formation of relatively large bubbles 4,5,13 . Once these large bubbles reach the droplet surface, it is ruptured, and ligaments are formed 7,14 . Finally, the ligaments break up and baby droplets are ejected 10 .
The atomization intensity is highly influenced by the concentration and the type of the doping agents. For moderate doping concentrations, the nanomaterials form a shell that is continuously ruptured during the atomization events 9 . However, for excessively large concentrations of the nanomaterials, the shell is relatively strong, which traps the bubbles, and suppresses the atomization. Mosadegh et al. 6 showed that the amount of oxygen available in the graphene oxide molecular structure can also influence the atomization phenomenon.
It was reported that partially oxidized graphene oxide features a relatively large infrared absorption which was discussed to increase the probability of the occurrence of the atom- The droplet burning rate is defined 12 as the negative of the derivative of the main droplet diameter squared (D 2 ) with respect to time (t). Mosadegh et al. 6 showed that, for graphene oxide doped ethanol droplets, variation of D 2 versus t can be treated separately for time periods before and after the first atomization event. For the time period prior to the occurrence of the first atomization event, the burning rate corresponds to the mass loss due to the droplet evaporation; and, this rate increases with increasing the thermal conductivity of the doped fuel. However, the burning rate during the atomization period features contributions from both the evaporation and ejection of the baby droplets. It was shown 6 that the burning rate during the atomization period is positively correlated with the infrared absorption of the doping agent. Mosadegh et al. 6 studied the characteristics of the baby droplets ejections and showed these occur during the second half of the droplet lifetime. It was concluded that the most expected baby droplet diameter and ejection velocity are about 50 µm and 0.5 m/s, respectively. They 6 estimated the mass of the ejected baby droplets during the atomization period, and showed that the main droplets which eject relatively large mass of the baby droplets feature relatively small evaporation mass loss. Although the influence of the nanomaterials doping on the droplet burning rate is of significant importance, it is unclear how atomization impacts the droplet and flame coupling.
Pandey et al. 10 analyzed the droplet shape deformation and the flame chemiluminescence oscillations. For ethanol mixed with water, they 10 reported that the droplets shape deformation and their flame chemiluminescence feature oscillations at about 32 and 43 Hz, respectively. They showed that the addition of nanoceria particles to the droplets decreases both of the above frequencies to 13 Hz. Their results 10 suggest that the droplet shape deformation and the flame chemiluminescence oscillations may be coupled through two mechanisms. First, the atomization events induce the droplet shape deformation. This changes the fuel vapour flux into the flame and as a result the flame chemiluminescence. Second, the atomized baby droplets are ignited as they reach the flame, and this induces alteration of the flame chemiluminescence. Although the results of Pandey et al. 10 are of significant importance as they elaborate the mechanisms of the droplet shape deformation and the flame chemiluminescence oscillations, the root cause of these oscillations is unclear, and this requires further investigations.
The first objective of the present study is to investigate if the coupling observed in Pandey et al. 10 for nanoceria doped ethanol droplets also exists for graphene oxide doped diesel droplets. Our second objective is to discover the root cause of such coupling and to investigate the effect of graphene oxide doping concentration on the above coupling.

II. EXPERIMENTAL METHODOLOGY
Details of the doped fuel preparation and tested conditions, experimental setup, diagnostics, and data reduction are presented below.

A. Doped fuel preparation and the tested conditions
Graphene oxide (GO) functionalized with octadecyl amine groups was used as the doping agent in the present study. The chemical composition of the tested GO was investigated using the Energy-Dispersive X-ray Spectroscopy. The results showed that the tested GO platelets are mainly comprised of about 80% and 20% by weight of carbon and oxygen, respectively. The GO nanomaterials were suspended in ultra-low sulphur diesel, and the suspension was sonicated for 60 min prior to each experiment. No surfactant was used during the suspension preparation. In total, five doping concentrations of 0, 0.001, 0.005, 0.01, and 0.02% (by weight) were examined, which are denoted by D, D001, D005, D01, and D02, respectively, and are presented in Table I. To assess the stability of the suspensions, their photographs were acquired. The photographs corresponding to neat diesel, D001, D005, D01, and D02 are presented in the first to fifth columns of Fig. 1, respectively. The images presented in Figs. 1(a) and (b) correspond to those collected immediately after preparation of the fuel as well as 5 months later.
As can be seen, the doped fuels were stable and no sedimentation was observed during the above period.
The Scanning Electron Microscopy (SEM) was performed to study the morphology of the GO.
the suspension mechanism 16 . A plasma-assisted igniter (item 2) was mounted on a linear actuator plunger (item 3 in Fig. 4(b)) for ignition. For repeatability purposes, separate experiments were performed to ensure that the igniter arc is always formed at 1 mm below the droplet. The igniter operated for about 400 ms and was retracted using the actuator immediately after the operation period ended.
Separate high-speed shadowgraphy and OH * chemiluminescence techniques were employed to study the droplet and flame dynamics. These diagnostics are shown in Figs. 4(b) and (c), respectively. The acquisition frequency for both techniques was set to 4000 Hz. filter was installed on the UV lens to facilitate collecting flame chemiluminescence near the wavelength of the OH * emission at 308 nm. The intensifier gate was set to 90 µs, and the pixel resolution of the chemiluminescence measurements was 23 µm/pixel. All diagnostics were controlled and synchronized using an NI PCIe 6361 data acquisition board (item 7).

C. Data reduction
To estimate the droplet diameter, a procedure similar to that of Hicks et al. 21 , Dietrich et al. 22 , and Ghamari and Ratner 5 was followed. First, the droplet edges were obtained using the shadowgraphy technique. For a representative droplet, these edges are shown by the red color data points in Fig. 5. Then, an ellipse with the major and minor diameters of a and b was fit to the droplet edges, see the yellow ellipse in Fig. 5. Finally, the droplet equivalent diameter was calculated using D = (ab 2 ) 1/3 . A Cartesian coordinate system was used to analyze the droplet dynamics. The x-axis is positioned on the wire centerline, and the y-axis is normal to the x-axis. The origin of the coordinate system was fixed and was selected such that x = 0 pertains to the center of the ellipse at t = 0.
It was not necessary to pre-process the shadowgraphy images for droplet dynamics analysis. However, the chemiluminescence images were pre-processed prior to their analyses.
All acquired chemiluminescence images were subtracted by the background image (averaged for 200 chemiluminescence images before the droplet ignition) and were normalized for the spatially dependent sensitivity of the imaging equipment, similar to our past work 6,23,24 that utilized the same diagnostics. To minimize the electronics noise, a 7×7 pixels 2 window median-based filter was applied to the chemiluminescence images.

III. RESULTS AND DISCUSSIONS
The results are grouped into two subsections. First, the droplet diameter squared and the flame chemiluminescence oscillations as well as the atomization events characteristics are discussed. Then, in the second subsection, the coupling between the above parameters is elaborated.

A. Characteristics of the droplets, flames, and atomization events
Variations of the droplet diameter squared (D 2 ) versus time is presented in Fig. 6 Fig. 7(b). A sliding window size identical to that used for obtaining the droplet diameter squared fluctuations was used for It is hypothesized that the similarity between the characteristics of the droplet diameter squared and the flame chemiluminescence oscillations (presented in Figs. 6-8) is not coincidental, and it is due to the occurrence of the atomization events. In order to characterize these events as well as to assess the above hypothesis, the D 2 time series, similar to that shown in Fig. 6(a), are used. Analysis of the D 2 data as well as the shadowgraphy images shows that the beginning and the end of an atomization event correspond to a relatively large variation in the D 2 values, as evident in Figs. 6(c-e). Here, the atomization intensity (I a ) is defined as I a = D 2 i /D 2 e , with D 2 i and D 2 e being the droplet diameter squared immediately at the beginning and at the end of an atomization event, respectively. The droplet diameter squared primarily changes due to the atomization and evaporation. Analysis of D 2 data suggests that the smallest value of D 2 that can be detected is 1 mm 2 (see the red dashed line in Fig. 6(a)) due to the presence of the droplet suspension mechanism; the maximum duration of an atomization event is ∼30 ms; and that |dD 2 /dt| features a maximum of 1.5 mm 2 /s in the absence of atomization. This means that the percentile change in the droplet diameter squared due to evaporation features a maximum of about (1.5 mm 2 /s × 0.03 s)/1 mm 2 ≈ 5%. As a result, events with I a 1.05 during time periods smaller than 30 ms are expected to correspond to the atomization. Indeed, using the shadowgraphy images, this was confirmed that D 2 i is larger than D 2 e by at least 5% during an atomization event. The values of I a were obtained for the 12 repeats of all tested conditions, the Probability Density Function (P DF ) of this parameter normalized by the corresponding maximum was obtained, and the results are presented in Fig. 9(a).
In the figure, the PDF was calculated for several temporal bins, aiming to highlight how the intensity of atomization change during time. As can be seen, I a can become as large as about 3; and, the atomization events mostly occur towards the end of the droplet lifetime.  The relation between the atomization events and the droplet diameter squared RMS was investigated statistically. Figure 10(a) presents variation of D 2 rms versus both the mean atomization intensity (I a ) as well as the number of the atomization events (N a ) for all tested conditions and their repeats. For clarity purposes, variation of D 2 rms averaged for all repeats of each tested condition (denoted by D 2 rms ) versus the mean atomization intensity also averaged for the repeats of each tested condition (I a ) is presented in Fig. 10(b). Variation of D 2 rms versus the number of the atomization events averaged for the repeats of each tested condition (N a ) is presented in Fig. 10(c). The lengths of the error bars in Figs. 10

B. The coupling between the droplets, flames, and atomization events
For a representative test condition of D01, the variation of D 2 versus time is presented in Fig. 11(a). Overlaid on the figure are the solid circular data points that correspond to the atomization events, which are highlighted for I a ≥ 1.05. These data points are also colorcoded based on the value of I a , i.e. dark blue corresponds to intense atomization events.
As can be seen, generally, large intensity atomization events occur towards the end of the droplet lifetime, which confirms the results presented in Fig. 9(a).
It is of interest to investigate if there exists a relation between the intensity of the atomization events and the time separation between two consecutive atomization event, referred to as ∆t a . In order to study this, the atomization events were categorized using a threshold value of I a = 1.4, and the PDF of 1/∆t a was calculated. For the representative test condition of D01, the PDFs of 1/∆t a for atomization events with 1.05 ≤ I a < 1.4 and I a ≥ 1.4 are presented in Figs. 11(b) and (c), respectively. The results in Fig. 11(c) suggest that, for  quencies were calculated using the area-weighted average of the probability density function for P DF > 0.5 × max{P DF }. The results presented in Figs. 11(a-c) suggest that, for this tested condition, atomization event with large intensities occur less frequently and towards the end of the droplet lifetime.
The results in Fig. 11(a) as well as the atomization intensity were used to identify the moments corresponding to the first time at which I a = 1.05 and 1.4. These are referred to as t(I a = 1.05) and t(I a = 1.4). Results in Figs. 11(d) and (e) present the power spectrum densities (PSD) of the droplet diameter squared oscillations for t(I a = 1.05) ≤ t < t(I a = 1.4) and t ≥ t(I a = 1.4), respectively. As can be seen, during the the time period that the atomization events are not intense, the PSD of the droplet diameter squared oscillations feature a dominant frequency near 25 Hz, which is similar to that reported in Fig. 11(b).
However, for the rest of the droplet lifetime (corresponding to intense atomization events) the droplet diameter squared oscillations feature a dominant frequency near 5 Hz, which is similar to that reported in Fig. 11(c). The above argument suggests a causality relation between the atomization events and the droplet diameter squared oscillations.
It is noted that the amplitude of the PSD presented in Fig. 11(e) and at f ≈ 5 Hz is about one order of magnitude larger than that for the PSD presented in Fig. 11(d) at f ≈ 25 Hz.
As discussed in Appendix A, the oscillations at 25 Hz are also present prior to the occurrence the first atomization event, are due to the droplet vibrations along the vertical axis, and are originally induced as a result of the retracting motion of the igniter.
It is of interest to confirm if the observations presented in Fig. 11 hold for all tested conditions. Following the above discussions, the PDF of 1/∆t a was estimated for I a ≥ I * a , with I * a being a threshold atomization intensity value. For all tested conditions, the most probable value of 1/∆t a for several values of 1.05 ≤ I * a ≤ 1.4 were obtained, averaged for 12 repeats of each test condition, and presented in Fig. 12. The results in the figure confirm that the frequency of occurrence of the intense atomization events decrease as I * a increases, and this is consistent for all tested conditions.   conditions. The power spectrum densities were then averaged and presented in Fig. 15(f).
The PSDs in the figure were stepped for clarity purposes. As can be seen, for all tested conditions, the droplets move at a frequency of about 25 Hz. As discussed in Section III, this frequency is appreciably larger than that associated with the droplet diameter squared oscillations, flame chemiluminescence oscillations, and the atomization events. The above argument suggests that the root cause of the coupling is not due to the droplet oscillations.
However, the retracting motion of the igniter is the root cause of the 25 Hz oscillations prior to the occurrence of the first intense atomization event.