Laser-Induced Breakdown Spectroscopy and Shadowgraphy of Acoustically Levitated Heptane Droplets

Abstract

In this study, we examined the impact of droplet size and laser energy on droplet fragmentation and the resulting species composition due to laser irradiation of an acoustically levitated heptane droplet. Using shadowgraphy and spatially resolved laser-induced breakdown spectroscopy (LIBS), we observed two different fragmentation regimes for the conditions studied. The experiments demonstrated that low laser energy densities (<~70 mJ/mm³), designated as regime 1, resulted in a single plasma breakdown event accompanied by broadband emission and C₂ Swan bands, suggesting weak plasma formation. Conversely, high energy densities (>~70 mJ/mm³), designated as regime 2, resulted in multiple plasma breakdowns that resulted in the emission of H_α, O, and N, implying a full laser breakdown in the gaseous reactive mixture. Additionally, in regime 2, we calculated the electron density using Stark broadening of the H_α line and temperature using Boltzmann analysis of O lines at 715 nm and 777 nm. We found that the electron densities and temperatures within the air spark and heptane droplets are quite similar. The findings from this research could impact the design of spray ignition systems and may also aid in validating the modeling efforts of aerosols, droplet breakdown, and ignition.

1. Introduction

Laser ignition involves generating a spark by narrowly focusing down a high-energy laser pulse to initiate the combustion [1] of a fuel–air mixture. This technique allows for precise control over the ignition process, leading to enhanced performance and reliability (compared to traditional ignition systems). Laser ignition offers increased flexibility in timing and ignition location and may also mitigate electrode erosion, a significant concern under high-pressure conditions. Moreover, research indicates its potential to lower NOx emissions [2] and expand lean operating limits [3]. Recent advances have positioned laser spark ignition [4] as a viable alternative to conventional electric spark igniters across various applications including gas turbines [5,6], scramjet engines [7], reciprocating engines [4], and liquid rocket engines [8]. However, laser ignition has certain drawbacks including increased cost and complexity, which can vary depending on the specific application.

Research on laser ignition has largely focused on gaseous fuels; however, there is an increasing interest in extending laser ignition techniques to liquid fuel sprays [9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24], especially for aerospace applications. Igniting liquid fuels in aircraft engines presents a complex challenge, shaped by multiple parameters such as the local equivalence ratio, degree of mixing [25], condensed fuel concentration, presence of shear layers, and gas density [20]. Understanding and optimizing this process is challenging due to the interplay of these variables. A key aspect of ignition and combustion in this context is the laser-induced breakup of fuel droplets, which involves processes like vaporization, explosive boiling, and the formation of ligaments and smaller droplets. This secondary breakup or atomization is inherently stochastic and poses a challenge to analyze and comprehend the combustion processes within the spray flame [26,27]. Gebel et al. [27] studied the breakup of kerosene droplets induced by laser-generated blast waves, using Mie scattering diagnostics to analyze the droplet breakup process. They observed that small secondary droplets detached from the primary droplet, which then deformed into disk-like shapes before ultimately dispersing into an ultra-fine mist. Similarly, Kawahara et al. [28] used high-speed imaging to investigate the laser-induced ignition of isooctane–air mixtures. Their findings highlighted a microlensing effect caused by the droplets, showing how the droplet curvature altered the focal point of the incoming laser beam.

Numerous research groups have also explored the interaction between droplets and laser plasmas [29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44]. Avila et al. [32] investigated the fragmentation of levitated water droplets induced by cavitation bubbles, identifying three distinct fragmentation regimes: atomization, sheet formation, and coarse fragmentation. More recently Jagadale et al. [45] established different fragmentation regimes in diesel droplets by laser-induced bubbles using multiple femtosecond laser pulses. Rao et al. [31] investigated the laser-induced fragmentation of water and diesel droplets arranged in an array, utilizing shadowgraphy techniques. They found that droplet breakdown could occur in either a single-mode or multi-mode fashion, depending on the location of the laser focus. Bulat et al. [35] developed models to analyze the interaction between laser pulses and droplets. They identified several stages of optical breakdown in droplets, including the heating of the droplet to its boiling point, its subsequent evaporation, the formation of a vapor cloud around the droplet, the ionization of the vapor cloud leading to an electron avalanche, the emergence and expansion of micro-plasma spots, and the propagation of a shock wave within the droplet and the surrounding gas. Although most studies on droplet–laser interactions have concentrated on the fluid mechanical aspects of the phenomenon, there is a notable lack of literature addressing the effects of laser energy and droplet size on breakup dynamics and the composition of species in the breakdown region. Furthermore, crucial plasma parameters, such as electron density and temperature, which are essential for ignition and combustion processes in fuel sprays, have often not been quantified.

This article is a revised and expanded version of a paper entitled “Laser-Induced Fragmentation and Spectroscopy of Acoustically Levitated Hydrocarbon Droplets [46]”, which was presented at the AIAA Aviation Forum and ASCEND, Las Vegas, 2024. In this paper, we build on those preliminary findings, providing additional analyses and new experimental results that were not included in the original conference presentation. The objective of this expanded study is to enhance our understanding of breakup dynamics by examining the combined effects of droplet size and laser pulse energy (energy per volume metric) on the laser–droplet interaction and subsequent fragmentation and species resulting from the breakdown. By employing shadowgraphy imaging, we investigate how laser energy influences droplet breakup and plasma formation. Additionally, we use LIBS [47,48,49] to understand the composition of species in the breakdown and to quantify electron density and temperature. Furthermore, we implemented spatially resolved LIBS, where we reference the image acquired from the camera to the collected emission. This allows us to determine the different locations of breakdown and infer spatially resolved plasma parameters over the entire interacting domain. The outcomes of this study can inform laser-ignited spray systems and may provide valuable insights for future experimental and modeling endeavors. The paper is structured as follows: Section 2 details the experimental setup and methodology for image and spectra acquisition, while Section 3 presents the results and ensuing discussion. Finally, Section 4 outlines the conclusions drawn from this study and lays out the plans for future research.

2. Experimental Setup and Methodology

2.1. Optical Setup

Figure 1 shows the experimental setup employed in this investigation [50]. For the laser ignition source, we utilized an Nd:YAG laser (Continuum custom system, Santa Clara, CA, USA) with a 35 ns pulse duration, operating at a repetition rate of 5 Hz with an output wavelength of 1064 nm. We used a variable attenuator, formed from a half-waveplate and polarizer, to control the laser energy (shot-to-shot energy variation of ~3%). A Galilean telescope with focal lengths of −100 mm and 200 mm expanded the laser beam by a factor of 2, resulting in a collimated beam diameter of ~25 mm. The collimated beam is then focused with a 100 mm plano-convex lens to achieve a beam waist of ~0.1 mm (based on burn paper measurement) at the droplet location (held within the levitator) with a Rayleigh range of ~5 mm.

To create a controlled environment for the study of laser breakdown on droplets, we utilized a single-axis acoustic levitator (TinyLev, Makerfabs, Berthoud, CO, USA) to suspend a single heptane (Thermo Fisher Scientific H3504, purity ≥ 96%, Denver, CO, USA) droplet in ambient air. The levitator, as described in Marzo et al. [51], uses an array of 72 ultrasonic transducers operating at 40 kHz to create a standing wave, with nodes used for trapping both liquid and solid particles. However, this setup has limitations, particularly when attempting to trap droplets smaller than ~500 μm. In this size range, the acoustic streaming force induces significant oscillations [52], causing the droplets to detach and be laterally displaced from the trapping region. We used a 3 mL syringe (BH Supplies, Temecula, CA, USA) to inject a droplet with an initial diameter of ~2 mm, allowing it to evaporate until it reached the desired diameter. To estimate the time required to reach this diameter, we applied the D² law of droplet evaporation [53]. The details of this procedure can be found in the Supplementary Materials. Additionally, we determined the droplet diameter from the image captured just before the laser hits the droplet. We used MATLAB R2022a to process the image. The pixel size was 3.3 μm which gives a pixel resolution uncertainty of 1.65 μm for the droplet diameter in each test case. We conducted experiments with three different laser energies and a range of droplet diameters as shown in

Table 1. Experimental test conditions.

Laser Energy (mJ)	Droplet Diameter Range (mm)
35	1.1 ± 0.1
80	1 ± 0.2
80	1.5 ± 0.2
100	1.1 ± 0.2

. For all the test conditions, we did not observe any visible chemiluminescence (through combustion reactions) from the laser interaction with the droplet.

We utilized a range of optical diagnostic techniques to investigate the interaction between the laser and droplets, as well as plasma formation [46]. For the spatial and temporal analysis of optical emissions from the laser plasma, we employed laser-induced breakdown spectroscopy (LIBS). Additionally, we used shadowgraphy to capture images of droplet fragmentation resulting from the laser interaction. To enable spatial mapping of the LIBS measurements, we integrated a periscope that allowed us to adjust the collection height and rotate the image along the horizontal laser beam, ensuring proper alignment with the vertical input slit of the spectrometer. We used a combination of lenses to achieve a magnification of 0.8 (f = 500 mm and f = 400 mm) to collect the light and couple it to a spectrograph and camera. The spectrograph (Andor Kymera 328i, Andor Technology Ltd., Belfast, Northern Ireland) employed a 100 μm slit width and a grating with 300 grooves/mm, offering a theoretical resolution of 1.01 nm. We recorded spectra using an sCMOS camera (Andor iStar, Belfast, Northern Ireland) with an intensifier gain level of 4000 and variable gate width, providing a resolution of 7.7 μm/pixel. For shadowgraphy, we collimated the light from a red LED (emitting light at 623 nm) using a lens with a focal length of 100 mm and employed a telescope (f = 200 mm and f = 75 mm) to magnify and focus the image onto an sCMOS camera (Andor iStar). The camera’s resolution was 3.5 μm/pixel. The shadowgraphy is used primarily for direct imaging of droplet breakup dynamics, but its images are also used to spatially reference the recorded LIBS spectra (relative to the initial droplet position). Some regions in the shadowgraph images (shown in the subsequent sections) at specific time delays appear saturated. While the original image is unsaturated, we adjusted the brightness of the images to show various features like the blast waves and droplet fragments.

2.2. Spatial LIBS Methodology

Figure 2 shows the method we employed to implement spatially resolved LIBS measurements (relative to the initial droplet location and surrounding gaseous regions). The overall approach was to spatially reference the 1-D spatially resolved LIBS spectra with 2-D images of the droplet from the shadowgraphy. As an illustrative example, we captured both the shadowgraph image (Figure 2a) and the raw spectral image (Figure 2c) at the same time delay and gate width, which are 1000 ns and 100 ns, respectively, in this case. In Figure 2b, we display the pixel intensity versus distance along the laser beam direction, from the 2-D shadowgraph image (using the magenta region in Figure 2a). We divide the images into a series of spatial ribbons, each 50 pixels wide (~175 μm), along the laser beam direction. We then apply a threshold intensity value (determined from multiple datasets) to differentiate between regions without a droplet (intensity > 400 [a.u]) and then assume that remaining regions do contain a droplet. We rejected the regions close to the boundary between droplet and no droplet regions where the threshold algorithm misassigned the regions as such. Furthermore, based on the pixel location, we distinguish between the laser illumination side and the shadow (laser exit) side for the regions with no droplet. The red dotted lines in Figure 2a indicate the shadow side of the droplet, the blue dotted lines represent the droplet region, and the green dotted lines denote the illumination side of the droplet. To find the corresponding location of the droplet on the spectrometer, we developed a linear transfer function that maps the location of pixels from one camera to the other (based on viewing a grid on both detectors). In Figure 2c, the red, blue, and green dotted regions represent the shadow side, droplet, and illumination side, respectively.

To generate the spectra from the spectrometer, we averaged a 50-pixel-long ribbon along the detector (spatial direction). Additionally, to account for the background (dark counts and stray scattering), we selected another ribbon from the bottom of the camera sensor (a region that did not receive any light), averaged it, and subtracted it from the main spectra. In Figure 2d, we show the variation in spectra for the droplet region and the illuminated side (there was no detectable emission on the shadow side for this case). Note that the spectrometer is also calibrated for (relative) intensity using an LS-1-CAL tungsten–halogen light source.

2.3. Electron Density Determination by Stark Broadening

We determined the electron density (n_e) by analyzing the Stark broadening of the H_α emission line at 656 nm. Traditionally, electron density estimation relied on the Stark broadening of Hydrogen Balmer lines, which show significant broadening due to the linear Stark effect. We used the Gigosos–Cardenoso model (GC) [54,55] to calculate electron density, as this model also considers collisional/Van der Waals broadening and instrumental broadening. We neglected the Natural, Resonance, and Doppler broadening (at temperatures as high as 10,000 K), as each contributed to less than 5 pm [56]. The H_α FWHM due to Stark broadening Δλ_Stark (nm) [55,56] is determined as:

$$\Delta {\mathsf{\lambda }}_{\mathrm{S}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{k}}=8.33\times {10}^{-3}{\left({\displaystyle \frac{{\mathrm{n}}_{\mathrm{e}}}{{10}^{20}}}\right)}^{{\displaystyle \frac{2}{3}}}$$

(1)

where n_e is the electron density (m⁻³).

The FWHM for Van der Waals broadening, $\Delta {\mathsf{\lambda }}_{\mathrm{v}\mathrm{d} \mathrm{W}\mathrm{a}\mathrm{a}\mathrm{l}\mathrm{s}}$, of H_α is calculated (in nm) as [55,56]:

$$\Delta {\mathsf{\lambda }}_{\mathrm{v}\mathrm{d} \mathrm{W}\mathrm{a}\mathrm{a}\mathrm{l}\mathrm{s}}=0.1\times {\displaystyle \frac{\mathrm{p}}{{\left(\frac{{\mathrm{T}}_{\mathrm{g}}}{300}\right)}^{0.7}}}$$

(2)

where p is the pressure (bar) and T_g is the gas temperature (K). We measured the instrumental broadening of the spectrometer with a He:Ne laser at 543 nm by fitting a Lorentzian function as 0.48 nm (in rough agreement with the calculation based on grating and monochromator parameters).

In Figure 3, we show the method used to fit the H_α line using a Lorentzian profile in MATLAB with an open source peakfit [57] code. Furthermore, we obtained the electron density based on assuming that the resulting lineshape is Lorentzian-broadened with contributions from only Stark, Van der Waals, and instrumental broadening as follows [35]:

$$\Delta {\mathsf{\lambda }}_{\mathrm{S}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{k}}=\Delta {\mathsf{\lambda }}_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{d}}-\Delta {\mathsf{\lambda }}_{\mathrm{v}\mathrm{d} \mathrm{W}\mathrm{a}\mathrm{a}\mathrm{l}\mathrm{s}}-\Delta {\mathsf{\lambda }}_{\mathrm{i}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{u}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{a}\mathrm{l}}$$

(3)

where the uncertainty in electron density measurements is estimated based on the method discussed in Van der Horst et al. [56] and found as ~±25% with the fitting error contributing the most.

In addition to determining the electron density, we utilized optical emission spectra to measure the plasma gas temperature. Assuming the plasma is in Local Thermodynamic Equilibrium (LTE), we employed the Boltzmann method to estimate the plasma temperature using the atomic oxygen lines at 715 nm and 777 nm. We chose these lines based on their strengths and upper-level energy spacing. The plasma temperature is found as [13]:

$$\mathrm{k}\mathrm{T}={\displaystyle \frac{{\mathrm{E}}^{\prime }-\mathrm{E}}{\ln \left(\frac{\mathrm{I}{\mathrm{g}}^{\prime }{\mathrm{A}}^{\prime }{\nu }^{\prime }}{{\mathrm{I}}^{\prime }\mathrm{g}\mathrm{A}\nu }\right)}}$$

(4)

where I is the total emitted line intensity (wavelength-integrated), ν is the line center frequency, g is the statistical weight, E is the transition upper-level energy, and A is the Einstein coefficient for spontaneous emission (for two lines ′ and unprimed). While deviations from LTE can occur, the high electron densities, electron temperatures, and short time scales associated with laser-induced breakdown plasmas typically support the LTE assumption, especially in the core region of the plasma [13,58].

In Figure 4, we illustrate the curve fitting of both the O lines with a Voigt profile using the peakfit [57] code to calculate the total intensities. The uncertainty is estimated based on the method given in El-Rabii et al. [13] and is about 30%, with the uncertainty in Einstein coefficients and measured areas contributing the most.

3. Results and Discussion

3.1. Shadowgraphy of Laser-Induced Droplet Fragmentation

The fragmentation of droplets induced by a laser pulse is influenced by factors such as laser pulse energy, duration, and focusing conditions as well as the intrinsic droplet characteristics such as size, composition, and density [31,59]. When the laser is focused within the droplet, part of its energy is scattered and reflected while the droplet absorbs (and potentially refocuses) the remainder. This absorbed energy partly initiates plasma formation, causing droplet expansion and fragmentation, while the rest dissipates into a blast wave. In some cases, plasma formation events occur at multiple locations within or around the droplet [59]. Bulat et al. [35] proposed that the fundamental mechanism behind laser-induced droplet breakdown is the explosive evaporation of the droplet. As the laser penetrates the droplet’s core, it heats the droplet intensely, exceeding the saturation vapor temperature at the given conditions and creates an internal vapor cavity, or cavitation bubble, within the droplet. Subsequent laser pulse absorption increases the pressure within this cavity, generating plasma and initiating a blast wave. This expanding blast wave leads to thermal ionization of the surrounding (cavitation) gas and droplet species along its path. The resultant free electrons cause further ionization, continuing the breakdown process and culminating in rapid vaporization. Consequently, the droplet undergoes destruction through jetting or explosion. While Bulat et al. [35] do not specify the droplet size and laser energy required for this type of breakdown, several studies [7,31,32] experimentally verified this mechanism of droplet breakdown in water droplets at diameters of 3–4 mm with small laser energies (~2 mJ).

Figure 5 illustrates the optical breakdown of a heptane droplet, ~1.5 mm in diameter, induced by a laser pulse at 80 mJ, captured at various time delays from the laser pulse. Although each image represents a separate experiment, the sequence is highly repeatable, allowing the panels to depict the temporal progression of droplet irradiation. At these laser and focusing conditions, we also observe optical breakdown in air (without the presence of the heptane droplet). In the image shown at t = 100 ns (relative to the time of the laser illumination), we observe a strong luminous (plasma) region within the droplet, proximate to the droplet–air interface on the “shadow” (downstream laser) side. This luminous region may be indicative of a cavitation bubble, likely consisting of heptane vapor, and suggests plasma breakdown primarily occurs at this location. At 400 ns, owing to rapid ionization and heating, the bubble/luminous region grows in size, engulfing the droplet. The plasma formation inside the droplet generates a blast wave (labeled forward plume) that propels the droplet fragments (as seen at 1000 ns) towards the shadow side of the droplet, implying non-uniform spatial energy deposition.

The time scale for cavitation formation and bubble growth can be determined from the Rayleigh–Plesset equation [60]:

$${\mathrm{t}}_{\mathrm{c}\mathrm{a}\mathrm{v}}={\displaystyle \frac{{\mathrm{R}}_0}{\sqrt{{\mathrm{P}}_{\mathrm{L}\mathrm{a}\mathrm{s}\mathrm{e}\mathrm{r}}/\mathsf{\rho }}}}$$

(5)

where R₀ is the initial bubble radius (considered to be on the order of the beam waist) and ρ is the heptane density. The pressure inside the bubble after laser energy deposition, P_Laser, comes from the rapid conversion of the absorbed energy into heat, which causes localized vaporization and a vapor bubble to form. This pressure can be estimated from the energy density in the region affected by the laser. A rough estimate of the pressure rise inside the bubble can be obtained by assuming that the energy density is approximately equal to the work done by the expanding bubble:

$${\mathrm{P}}_{\mathrm{L}\mathrm{a}\mathrm{s}\mathrm{e}\mathrm{r}}={\displaystyle \frac{{\mathrm{E}}_{\mathrm{L}\mathrm{a}\mathrm{s}\mathrm{e}\mathrm{r}}}{3{\mathrm{V}}_{\mathrm{L}\mathrm{a}\mathrm{s}\mathrm{e}\mathrm{r}}}}$$

(6)

where the factor 1/3 is a consequence of averaging over the three spatial dimensions for energy distribution into the bubble, E_Laser is the laser energy, and V_Laser is the initial volume of the spark. The substitution of the laser parameters yields the characteristic time scale for the bubble development as ~30 ns (prior to explosion), which agrees with our empirical observations presented in Figure 5.

Additionally, at later delays (10 μs and 1 ms), the droplet undergoes catastrophic fragmentation, disintegrating into smaller fragments. Overall, when the laser passes through the droplet, the front side (entrance) appears to undergo a relatively weaker disturbance, while the exit experiences intense energy buildup and eventual fragmentation. Hsieh et al. [36] noted this type of fragmentation in water droplets in an argon atmosphere with a 532 nm laser, and several other studies [31,32,59] also documented this in diesel [31] and biodiesel droplets [45].

Figure 6 depicts an optical breakdown due to a heptane droplet with a diameter of ~1 mm, induced by a laser pulse of 80 mJ, again captured at various time delays relative to the laser pulse. In comparison to the larger diameter (1.5 mm) case, at early time delays (100 ns panel), we observe a prominent luminous (plasma) region on the illumination side (upstream side), as well as within the droplet, closer to the droplet–air interface on the shadow side. This may be indicative of two distinct breakdown events, contrasting with the single event observed in the case of the larger droplet. The plasma breakdown on the illuminated side appears to originate from the gas phase adjacent to the droplet, potentially incorporating the vapors from the droplet, and may not have formed from the cavitation/vapor bubble route as described by Bulat et al. [35]. The second breakdown site, a weaker event occurring at the shadow side of the droplet, can be attributed to the droplet’s ability to refocus [28] some of the laser energy. However, this results in a significantly weaker breakdown and blast, as much of the energy has already been expended in the initial breakdown. Furthermore, we observe blast waves generated from the two breakdowns, with a stronger blast wave on the illumination side and a weaker one on the shadow side of the droplet. In addition to these blast waves, two jets, labeled as backward and forward plumes, are evident on both the illuminated and shadow sides of the droplet. These plumes show the expulsion of droplet fragments propelled outward from the droplet. Eickmans et al. [59] noted this type of fragmentation in water droplets with a 1064 nm laser at different intensities.

If the energy deposited by the laser pulse is large relative to the volume of the droplet, the droplet may not have time to undergo cavitation and instead, it will disintegrate due to rapid phase transition or explosive boiling. This is supported by the experimental observation shown in Figure 5 and Figure 6. For a fixed laser energy of 80 mJ, we observed quite different droplet fragmentation regimes based on the droplet size. In the case of the 1.5 mm droplet, plasma emission is observed inside of the droplet and the droplet seems to maintain its structural integrity during the emission process for a relatively long time (~1 us), thus supporting the idea that cavitation has led to the formation of plasma within the droplet. However, when the droplet size is reduced to 1 mm, plasma emission is accompanied by droplet fragmentation almost instantaneously (images at 100 ns already show droplet fragmentation). It is posited that as the volumetric energy absorbed in the droplet increases, the droplet undergoes almost instantaneous disintegration without cavitation.

Figure 7a,b provide a comparison of droplet breakup dynamics for a droplet of 1 mm diameter but at two different laser energies of 80 mJ and 35 mJ, respectively. Note that we do not detect an optical breakdown in air at 35 mJ. Despite the substantial difference in laser energy, the droplet fragmentation at 35 mJ closely resembles that observed at 80 mJ with a larger droplet diameter of 1.5 mm (Figure 6). In both cases, a single blast wave originates from a single breakdown event occurring at the droplet–air interface on the shadow side, resulting in a forward plume.

The results so far indicate that the energy coupled into the droplet affects the breakup dynamics and energy distribution within the droplet. It is also worth noting that there may exist other fragmentation regimes beyond those examined in this study, that could result in different modes of optical breakdown within the droplet. Some research groups [35,36,59] have identified a lower energy regime where breakdown predominantly occurs near the shadow side of the droplet, with the remaining laser pulse sustaining breakdown growth that results in a blast wave. On the other hand, a higher energy regime [36,59] is also observed, characterized by multiple breakdowns on both the illuminated and shadow sides of the droplet.

3.2. LIBS of Laser-Induced Droplet Fragmentation

Figure 8 shows single-shot LIBS spectra of air plasma over a range of 500–800 nm at various time delays relative to the laser pulse. We focused the laser using the same configuration as is employed for droplets with pulse energy of 80 mJ in this case. These data, collected in the absence of droplets, serve as a benchmark for the diagnostic system and will be crucial for subsequent comparisons with spectra acquired when droplets are present. At the earlier time delays, we notice a high background contribution from bremsstrahlung emission (also known as free–free transitions) which decreases significantly with time [13]. The plot labels the atomic lines of N II at 648 nm and 661 nm, H_α at 656 nm, O I at 715 nm, 777 nm, and 794 nm, and N I at 746 nm [61]. These lines are a result of the laser breakdown of ambient air, with N and O originating from the dissociation of molecular nitrogen and oxygen, respectively, while H_α comes from the dissociation of naturally occurring water vapor in air [45]. These air plasma spectra are consistent with measurements from other researchers at similar conditions [13].

Figure 9a,b show the time-resolved LIBS spectra over the spectral range of 500–800 nm following laser irradiation of a heptane droplet with laser pulse energy of 80 mJ at diameters of ~1.5 mm and ~1 mm, respectively. The spectra are representative of all spatially integrated light from the droplets, as found by averaging across all pixel (spatial) rows showing luminosity (we discuss the spatial variation in the spectra in the subsequent section). In the ~1.5 mm case (Figure 9a), we note C₂ Swan bands at ~516 nm, ~563 nm, and ~600 nm, but no discernible atomic lines. The C₂ molecular bands are superimposed on a significant continuum emission that reduces with time. Eickmans et al. [59] also noted continuum emission from the laser breakdown of water droplets. The plasma inside the droplet is optically dense (electron density ~10¹⁸ cm⁻³) such that the emission from the atomic species (internal to the droplet) is absorbed by the electrons. This radiation is then re-emitted by the electrons via bremsstrahlung emission [62]. As discussed in the previous section, under these conditions, we observe only a single breakdown event and a single blast wave due to the reduced energy distributed among the heptane molecules. This indicates that the energy is insufficient to dissociate the heptane into atoms, but it can lead to the formation of C₂ through the multi-photon dissociation [63] of heptane.

In the ~1 mm case (Figure 9b), we notice significant continuum emission at earlier delays compared to later times, superimposed on the atomic lines of H_α, N, and O. The H_α (656 nm) emissions may be due to a combination of dissociation of the heptane (C₇H₁₆) molecule (liquid phase but also vaporized in air region adjacent to droplet) and partly from the dissociation of ambient water vapor. The atomic O and N lines originate from the dissociation (and excitation) of the oxygen and nitrogen molecules in the air surrounding the droplet.

These findings indicate that the breakup dynamics of the droplet are significantly influenced by the ratio of laser energy to the droplet’s volume. Therefore, we propose an energy density metric, expressed volumetrically as energy per unit volume, to classify the cases into the two observed regimes based on the experiments we conducted at different laser energies (35 mJ, 80 mJ, 100 mJ) and droplet diameters (0.7–1.7 mm). Figure 10 shows the impact of energy density on the type of breakdown or regime. Here we define regime 1 as the scenario where we observe only one breakdown (within the droplet) and its corresponding blast wave, and regime 2 as the scenario with multiple breakdowns and blast waves. Furthermore, in terms of spectra, regime 1 shows primarily C₂ bands but not atomic lines, while regime 2 shows atomic lines of H_α, O, and N. We observe that regime 1 is present for energy density <~70 mJ/mm³, while regime 2 occurs when the energy density exceeds that value. A transitional regime is observed for energy densities in the range of ~60–80 mJ/mm³ (which may also be due to experiments with slight misalignments between the laser and droplet).

In addition to the reported regimes, other types of fragmentation are also noted in the literature [32,33,45,59]. Alternatively, the droplet mass could be used in place of droplet volume to develop this metric. Building on this approach, a dimensionless number could be formulated to account for factors such as droplet density, specific heat/latent heat of vaporization (to account for varying droplet compositions), initial droplet temperature, and ambient pressure, providing a predictive tool for determining the fragmentation regime.

3.3. Plasma Parameters of Heptane Droplet

The obtained droplet spectra can be analyzed to infer electron density and temperature. As a means to validate our methods, we first perform such a study for laser plasmas formed in air (no droplet present). Figure 11a,b present the electron density and temperature measurements of the air plasma at a laser energy of 80 mJ at various time delays compared to two related studies in the literature [13,64]. Since El-Rabii et al. [13] conducted their study with a 355 nm laser (34 mJ), and Boguszko et al. [64] conducted their study with a 532 nm laser (180 mJ), we do not expect to exactly match their values; however, our observed values show similar magnitudes and trends. We observe a reduction in electron density with time in all, owing primarily to plasma recombination [26]. We also observe that the temperature decreases with time because of the rapid expansion and cooling of the plasma after plasma initiation, including radiative losses and collisional processes [26].

Figure 12a,b depict the spatially resolved electron density and gas temperature measurements in heptane droplets of diameter ~1 mm (regime 2) at various time delays for the illumination side. The data are for a laser energy of 80 mJ and we compare them with results from the air spark. We are unable to conduct a similar analysis for the regime 1 scenario due to the absence of spectral lines and the droplet region in regime 2 owing to the low signal-to-noise ratio of the H_α at 656 nm. The electron density in the air plasma and on the illuminated side of the droplet are comparable, with the exception of early times. Similarly, the temperature of the air plasma closely matches that of the illuminated side of the droplet. Despite differences in species composition between air and heptane, the plasma parameters, including electron density and temperature, remain remarkably similar. This could be possibly because the ionization energies of heptane [65] (~10 eV), nitrogen [66] (~15 eV), and oxygen [67] (~12 eV) in air are in the same order of magnitude. As a result, the laser energy needed to generate free electrons and heat them to high temperatures is comparable in both media, resulting in similar electron densities and temperatures.

3.4. Spatial LIBS of Heptane Droplet

Figure 13a,b show representative spatially resolved spectra at a laser energy of 80 mJ and at droplet diameters of ~1.5 mm and ~1 mm, respectively. Using the spatial referencing scheme discussed in Section 2.2, we obtain spectra corresponding to the droplet region and illumination (upstream) side. Even though we see a blast wave propagating from the shadow side of the droplet in both the regimes, we do not note any emission lines or continuum in this region. In the ~1.5 mm scenario, we observe C₂ bands at 516 nm and 563 nm in the droplet region, while the illumination side is devoid of any atomic or molecular bands. However, in the ~1 mm scenario, we note the atomic lines of H_α and N in both the illumination and droplet regions. This supports our earlier hypothesis about there being a single breakdown at ~1.5 mm (regime 1) and two breakdowns at ~1 mm (regime 2).

Figure 14 shows the spatial variation in electron density for an air plasma formed from focusing a laser at 80 mJ at 1 μs from the laser. The shadowgraphy image shown in the inset highlights the characteristic tear drop shape of an air plasma with the broader waist oriented in the laser direction. While the electron density variation in Figure 14 is based on a single-shot measurement, it is representative of similar spectra observed at this time interval in other instances as well. The electron density remains consistent over the length of the plasma since air is relatively homogeneous. Additionally, the constant electron density may also imply that laser energy is distributed uniformly along the plasma. The signal-to-noise ratio for the O 715 line was so low that we were unable to make spatially resolved temperature measurements for air plasma and droplet breakdown [45].

Figure 15 shows the spatial variation in electron density in the event of a breakdown of a 1 mm heptane droplet at a laser energy of 80 mJ, 1 μs after the laser deposition. The shadowgraphy image shown in the inset shows the different regions in the droplet breakdown. We observe electron density only in the illumination side. Unlike air plasma, in the droplet case, we notice spatial variation in electron density. The electron density is higher in the center of the illumination side and tapers off on both sides. While the air is relatively homogeneous, when the laser hits a droplet, there are abrupt morphological changes. The laser–pulse interaction with the denser liquid (droplet) regions create more localized energy deposition which can rapidly vaporize and ionize the droplet and lead to a spatial variation in the electron density over the length of the plasma.

4. Conclusions

In the present study, we investigated the influence of droplet size, laser energy, and their cumulative effect on droplet fragmentation and species composition during the laser irradiation of heptane droplets in an acoustic levitator. We utilized shadowgraphy and spatially resolved LIBS diagnostics to achieve our research goals. Our experiments revealed that higher energy densities (>~70 mJ/mm³), designated as regime 2, led to multiple breakdowns located near the droplet–air interfaces on both the illumination and shadow sides of the droplet, with spectra displaying atomic lines of H_α, O, and N. Conversely, at lower energy densities (<~70 mJ/mm³), designated as regime 1, we noted a single breakdown event characterized by a spectrum featuring only C₂ bands and no atomic lines. These findings indicate that droplet breakup dynamics are significantly influenced by the ratio of the laser energy to the droplet’s volume. At a lower laser energy density, the energy distributed among the heptane molecules within the droplet is reduced, resulting in fewer breakdown events compared to conditions involving a higher energy density. This difference in energy distribution affects both the frequency of breakdowns and the chemical composition of the species resulting from these events. Moreover, we determined the electron density using Stark broadening of the H_α line and temperature using the Boltzmann method for regime 2 (i.e., high laser energy densities). The electron density and temperature of the air spark and heptane droplets are quite comparable. While there is minimal spatial variation in electron density along the plasma length in air, droplets exhibit a higher electron density in the center of the illumination side.

The energy density metric developed in this work can be expanded into a dimensionless number that incorporates droplet composition, density, and laser parameters such as wavelength and pulse width, to predict droplet fragmentation regimes. This metric could then be applied to determine the laser energy and pulse configurations necessary for consistent and efficient ignition in sprays. Additionally, the data presented here can serve to validate models of aerosols, droplet breakdown [35], and ignition [36].