Spark discharges at the interface of water and heptane: emulsification and effect on discharge probability

Spark discharges in liquid have shown great potential for use in numerous applications, such as pollutant degradation, precision micromachining, and nanomaterials production. Herein, spark discharges are initiated at the interface of two immiscible liquids, heptane and water. This leads to the formation of an emulsion via mechanisms akin to bubble dynamics and instabilities at the gas–liquid. At high discharge number, an additional mechanism contributes to emulsion formation, resulting in an increase in the number of smaller heptane droplets in water. Analyses of the current–voltage characteristics show that high probability of discharge occurrence is obtained when the electrodes are aligned with the interface. This result is correlated with the low erosion rate of the electrodes. In the case of discharges at the interface, we observed that beyond a certain number of discharges, the breakdown voltage drops; far from the interface, it increases with the discharge number. Based on 2D simulation with a Monte Carlo approach to consider various droplet distribution in water, the electric field distribution is determined. The results support the fact that the decrease in breakdown voltage may be attributed to the intensification of the E-field in water close the heptane droplet. Therefore, spark discharges generated at the interface of a heptane/water system produce an emulsion of heptane in water, which facilitates the occurrence of subsequent discharges by intensifying the electric field and reducing the breakdown voltage.


Introduction
In the past few years, research on plasma-liquid interactions has expanded significantly due to its applicability in * Author to whom any correspondence should be addressed.
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various fields, such as nanomaterials synthesis [1,2], water depollution [3][4][5], activated water production [6,7], and electrolysis [8,9], and due to its safe and environmentallyfriendly character [10].Typically, discharges generated in liquid are sustained in either streamer (i.e.∼100 µm filaments of plasma that are connected to one electrode) or spark (i.e. one intense filament connecting the two electrodes) modes.Although these discharges have been extensively investigated, they remain poorly understood, particularly in terms of the physical and chemical processes taking place at the plasma-liquid interface.Based on the numerous studies reported in the literature, several possible mechanisms of discharge ignition in liquid have been proposed, including direct ionization of liquid molecules [11], liquid-to-gas phase transition [12], and electron tunneling [13].However, no consensus has been reached so far.
Recently, discharges in liquid have been studied at or near the interface of two immiscible liquids, like water and heptane.Hamdan and Cha [14] have demonstrated that in this system, both, the probability of successful discharges (streamer mode) and the emission volume increase as the pin of the electrode approaches the interface.Moreover, when the electrical conductivity of water is higher than ∼500 µS cm −1 , the streamer transits to a spark [15].In general, discharges at the interface of two immiscible liquids have shown great potential for use in nanomaterials synthesis.For instance, streamer discharges at the interface of water/heptane lead to carbonaceous nanomaterials [16], while H:SiOC nanomaterials are produced at the water/hexamethydisilazane interface [17].Furthermore, when spark discharges are ignited in heptane in-contact with silver nitrate solution, Ag nanoparticles (5-10 nm) encapsulated in C-matrix are produced in heptane, and larger Ag particles (10-100 nm) are produced in solution [18].Considering that the discharge changes the color of the solutions from colorless to milky, it may further be concluded that an emulsion is formed.
Emulsion formation is usually investigated from the viewpoint of fluid mechanics.Researchers in this field typically study the emulsions (i.e.micrometer droplets of one liquid in another) produced by ultrasonic cavitation.Despite the complexity and multitude mechanisms implicated in this process [19,20], it is generally accepted that the emulsion is mainly produced by bubble cavitation.Considering that spark ignition in liquid also induces bubble formation with expansionimplosion dynamics [21,22], it may be concluded that under certain conditions, discharges near the interface of two immiscible liquids may lead to emulsion formation.
In this study, spark discharges ignited at or near the interface of a water/heptane mixture are investigated for emulsion formation applications.The electrical characteristics of the discharges are analyzed, and the temporal evolution of quantities of interest, such as probability of discharge occurrence, breakdown voltage, discharge current, discharge delay, etc, is assessed.The solution is also characterized, and the formation of emulsion (heptane droplets in water) is highlighted.The effect of discharge number on the droplet size distribution of the emulsion is also determined, and possible mechanisms of emulsion formation are proposed.

Experimental setup
As shown in figure 1, the experimental setup is composed of two copper electrodes (0.3 mm diameter) immersed in a solution of n-heptane (20 ml) and water (60 ml) contained in a 100 ml beaker (note that the relative volume of the two liquids does not affect the reported results).Considering that the density of water (1 g cm −3 ) is greater than that of n-heptane (0.68 g cm −3 ), the latter lies on top of the former, thereby creating an interface between the two liquids.The electrodes are vertically mounted in the beaker; however, their heads are bent in such a way that they are parallel to the interface.To enable the adjustment of the interelectrode gap distance (d), one of the electrodes is connected to a micrometer positioning system.In this study, all experiments were performed at d = 100 µm; however, the distance (z) between the electrode heads and the interface was varied between −2 and +2 mm.Positive and negative z values signify electrode heads in either heptane or water, and z = 0 refers to the position wherein the electrode heads are exactly at the interface between heptane and water.
High-voltage pulses with an amplitude of 20 kV and a width of 500 ns were generated using a positive polarity power source (NSP 120-20-P-500-TG-H; Eagle Harbor Technologies), at the pulse repetition rate of 5 Hz.The voltage and current waveforms of the generated discharges were measured using a high-voltage probe (P6015A, ×1000; Tektronix) and a current monitor (6585, 0.5 V/A; Pearson), respectively, and both were displayed on an oscilloscope (MSO54, 2 GHz, 6.25 GS s −1 ; Tektronix).To measure the turbidity of the aqueous solution, white light (issued by a Thorlabs SL201L light source) was transmitted through the solution and detected by photomultiplier tube (PMT) placed on the opposite side of the beaker.The PMT voltage waveform was also recorded along with the electrical waveforms.
Finally, optical microscopy analyses were conducted to evaluate the size distribution of the emulsion.For this purpose, a sample of the processed water was collected at 1 cm below the interface using a pipette, and one drop of this sample was put between two microscope glass slides (distance = 0.3 mm) to prevent heptane emulsion evaporation and movement in the liquid during analyses.

Results
Before delving in the results, it is important to note that the repetition rate of 5 Hz is chosen to avoid the contribution of large bubble formed close to the electrodes.In addition, at this frequency, the oscilloscope can acquire all the current and voltage waveforms for post-processing.The repetition rate may have influence on the reported results, particularly at higher rate (higher than hundreds of Hz); the influence of this parameter (and others) is beyond the scope of this study and will be investigated separately.
The typical current and voltage waveforms presented in figure 2 show an abrupt voltage drop followed by current spikes, which is characteristic of in-liquid spark discharges [23].Considering that the waveforms recorded at different z values are analogous, they are not presented here.However, quantities of interest are provided below.
The thousands of discharge waveforms recorded herein were processed using a previously developed algorithm (a  detailed description can be found in [24]) in order to identify the failed and occurred discharges.Quantities of interest, such as breakdown voltage, discharge delay, current spike maximum, injected charge, and injected energy, were also extracted from the voltage and current waveforms of the occurred discharges.By counting the number of occurred breakdowns in 100 successive pulses, the probability of discharge occurrence was calculated.In addition to the electrical discharge waveforms, the algorithm was used to analyze the PMT signal and determine the transmission percentage of the liquid relative to the first signal recorded when the water was perfectly clear.
Figure 3 shows the variation of discharge probability as a function of discharge number for various values of z (0, ±1, and ±2 mm).In all cases, the probability of successful discharge is 1 at discharge number <1000.Beyond 1000 discharges, the probability decreases, and it even reaches zero when the electrodes are above or below the interface.The decrease is mainly due to the effect of electrode erosion in modifying the geometry of the electrode tips and increasing the gap distance between them.At z = ±2 mm, the discharge probability starts decreasing after ∼2000 discharges, and it quickly drops to zero after 3000-4000 discharges.Meanwhile, at z = +1 and −1 mm, the decrease in discharge probability starts after ∼1000 and ∼3000 discharges, respectively, and zero probability is reached after ∼4000 discharges in both cases.When discharge is ignited exactly at the interface (z = 0), the probability remains 1 up to ∼4000 discharges, then it decreases to about 75% after 5000 discharges, the point at which the experiment was stopped.As mentioned earlier, the decrease in discharge probability is mainly due to the erosion of electrodes, which in turn depends on the solution in which the discharge is ignited [24].The increase of the gap distance due to erosion is estimated in each configuration, and we found that the gap increases from 100 µm to ∼400, 300, and 200 µm after discharges in water, heptane, and at the interface, respectively.In fact, the erosion induces not only an increase of the gap distance but also a modification of the electrode shape, thus, an alteration of the electric field in the gap.However, as the discharge produces impacts at the surface of the electrode, the morphology of this latter is rough and exhibits many micro-/nano-asperities that can enhance the electric field and lead to breakdown; the influence of discharges-induced electrode modification has been investigated in [24].The high erosion found in water can be related not only to physical erosion, but also to chemical erosion by the reactive species produced such as O, OH, etc.Although these species are also formed at the interface (confirmed by optical emission spectroscopy, not shown here), the low erosion rate may be related to the bubble dynamics at the interface (see discussion).
The profiles of breakdown voltage are presented in figure 4(a) for various conditions (z = 0, ±1, and ±2 mm).The solid curves correspond to the averages of 200 values, whereas the shaded areas correspond to the 90% intervals.The trends observed at z = ±1 and ±2 mm are similar, with initial breakdown voltages of 16-19 kV for a pre-set voltage  plateau value of 20 kV.This indicates that, at these conditions, the initial discharges occur in the rising period of the plateau.As the number of discharges increases, the breakdown voltage increases until it reaches the pulse plateau value (20 kV) after ∼1000 discharges.The increase in breakdown voltage signifies that the discharges occur later on during the pulse.This is confirmed by the discharge delay data presented in figure 4(c).At z = 0, a distinct trend is observed, particularly after 100 discharges.Indeed, instead of a continuous increase, a significant drop in breakdown voltage from ∼16 to 12 kV is detected as the number of discharges increases from ∼100 to 170.Afterwards, the breakdown voltage increases monotonously to reach the pulse plateau value after ∼2000 discharges.The discharge delay profile also exhibits a significant decrease from ∼50 to 30 ns after ∼100 discharges, followed by a monotonous increase beyond ∼170 discharges.The evolution of discharge current profiles (figure 4(b)) are similar to that of breakdown voltage profile, with values of 70-80 A at z = ±1 and ±2 mm and ∼60 A at z = 0.The profile of this latter also shows a decrease by ∼10 A when the number of discharges increases from ∼100 to 170.Afterwards, the discharge current increases monotonously to reach ∼70 A after ∼2000 discharges; a value comparable to the other z-conditions.Overall, the trends of the data (discharge probability, breakdown voltage, discharge current, and discharge delay) recorded at z = 0 indicate that certain phenomena occurring at the interface facilitate discharge occurrence and reduce the breakdown voltage.
Inspired by the voltage-current plots performed by Rond et al [12], Bourbeau et al [24], and Höft and Huiskamp [25], similar plots are performed for the discharges studied here, and the plots are shown as supplementary material (figure S1).The results indicate a linear variation of the breakdown voltage as a function of the current.However, because the discharge evolves with time, three regions are identified.In water (Z = −2 mm), region 1 represents the initial few hundred discharges and exhibits a slope (i.e. a resistance) of ∼300 Ω.These discharges occur in the rising period of the high voltage pulse.Region 2 represents the discharges occurred in the plateau period of the pulse (i.e.constant voltage) and, thus, it manifests as a plateau in the voltage-current plot.Finally, region 3 represents the discharges occurred in the falling period of the pulse and exhibits a slope of ∼260 Ω.To explain the meaning of the measured slope, we must consider that the discharge current peak is delayed by ∼7 ns relative to the breakdown voltage.Therefore, the slope of the linear fit of the voltage-current datapoints represents an average resistance of the medium filling the gap during the 7 ns period (transient period leading to breakdown).In this period, the gap resistance decreases significantly, e.g. from ∼10 6 Ω in distilled water to a few ohms.The difference between the slope values in regions 1 and 3 can thus be correlated to the ignition mode.Indeed, the discharges in region 1 (occurred during the voltage rise period) maybe ignited by a direct ionization of the liquid, whereas those in region 3 (occurred during the voltage fall period) may be ignited with the assistant of nano-/microbubbles produced by local Joule heating close the pin.As compared to the values reported by Höft and Huiskamp [25] (140-144 Ω) and Rond et al [12] (150 Ω), our values are almost twice.This difference can be explained by different ionization mode as the pulse widths are different (pulse width of few µs in [12,25] vs. 500 ns here) and/or by the technical characteristics of the pulsers.Similar trends are observed at z = 0 (at the interface) and +2 mm (in heptane).However, in the former case, one notes a transition in region 1 in the interval of 500-1000 discharges (higher slope).Such a transition can be correlated to the formation of emulsion.Before and after this interval, the data align on linear profiles with similar slope of ∼360 Ω; the slope in region 3 is ∼320 Ω.In the case of Z = +2 mm, except the initial few data, one measures a slope of 200 and 300 Ω in regions 1 and 3, respectively.The difference values between slopes measured in water and heptane can be related to the nature of the liquid [24].
The electrical characteristics are also processed to determine the variation of injected energy and charge as a function of discharge number.The data are presented as supplementary data (figure S2(a)).Overall, the profiles are very similar to the breakdown voltages, with initial values of 18-22 mJ depending on z-condition.At z = 0, a drop of the energy from ∼19 to 15 mJ is observed when the number of discharges increases from ∼100 to 170.The trend of injected energy is expected as it depends on the breakdown voltage, discharge current, and discharge delay.As for the injected charge (figure S2(b)), the general trends are similar for the conditions of at z = ±1 and ±2 mm: we measure initially ∼10 µC and a continuous decrease to ∼2 µC after 3000-4000 discharges.This decrease is mainly related to the discharge delay, as the discharges occur later in the pulse towards these discharge numbers.At z = 0, the initial value (∼10 µC) is also comparable to the other z-conditions, but when the number of discharges increases from ∼100 to 170, a slight increase of the charge (by ∼1 µC) is measured.This increase is also related to the discharge delay (figure 4(c)), as these discharges occur earlier in the pulse.At this stage, it is worth noting that the erosion induced by discharges also modifies the discharge characteristics such as injected energy or charge.Although we believe that such modification is not significant (see [23]), further investigations are required to separately address the influence of each parameter (gap distance, voltage magnitude, pulse width, frequency, etc) on the discharge characteristics (energy, charge, etc) as well as on the emulsion properties.
Interestingly, the water turns turbid and milky during plasma processing, as shown in figure 5(a) and in the video provided as supplementary material.The evolution of water turbidity as a function of discharge number was monitored by detecting the transmittance of white light through the aqueous solution using a PMT.Based on the results illustrated in figure 5(b), the evolution profiles recorded at z = ±1 and ±2 mm are similar, with no significant variation detected during the first ∼1000 discharges.A gradual decrease to ∼80%-90% transmittance is observed during subsequent discharges.At z = 0, a different trend is seen, with transmittance values decreasing after the 10th discharge.Initially, in the interval of 10-1000 discharges, a gradual decrease to ∼70% transmittance is detected; however, the rate of decrease increases later on, and ∼20% transmittance is reached after 5000 discharges.Overall, the transmittance data displayed in figure 5 indicate that plasma processing at or near the interface of heptane/water leads to the formation of an emulsion of heptane in the aqueous solution.
Figures 6(a)-(c) depict typical optical microscopy images of the emulsions obtained after processing with 50, 500, and 5000 discharges, respectively, at z = 0 (several images were recorded for a given discharge number, as detailed in table 1 in supplementary material).These images clearly show spherical droplets with variable size and density, and the number of droplets (i.e.surface density) increases with increasing number of discharges.For instance, the images acquired after processing with 50 and 5000 discharges show ∼20 and ∼2000 droplets, respectively.Statistical analysis was used to determine the size distribution of droplets in each image, as shown in figures 6(d)-(f).Overall, similar droplet sizes are obtained after 50, 500, and 5000 discharges, and the droplet diameter varies between ∼2 and 40 µm.At low discharge number, the probability density is ∼0.1 and 0.02 for droplet's size <10 µm and >10 µm, respectively.At higher discharge number, the distribution becomes slightly narrower.Moreover, the probability density of droplets of various sizes increases with increasing number of discharge due to the formation of more droplets.
Droplet sizes in an emulsion are typically reported in terms of the mean diameter d 10 and the Sauter mean diameter d 32 .
The former is the conventional mean defined by the sum of the droplet diameters divided by their number.Meanwhile, the latter is defined by equation ( 1) [26]: Herein, both diameters, d 10 and d 32 , were determined for the droplets in each image, and the variation of these two values as a function of discharge number is presented in figure 7. The figure also shows the profiles of the averaged d 10 and d 32 corresponding to different images recorded at a given discharge number.Based on these profiles, d 10 and d 32 vary in the range of 7-10 and 8-22 µm, respectively.The values of d 10 and d 32 corresponding to 50 discharges are obviously larger than those obtained at higher discharge numbers, which suggests that relative contributions of the formation mechanisms vary depending on the discharge.A priori, the initial discharges produce both, large and small droplets.Comparatively, the subsequent discharges produce more droplets with smaller size, probably by another mechanism, as presented in the discussion section.
In addition to d 10 and d 32 , the volume fraction (ϕ ) of each emulsion, i.e. the ratio between the volume of heptane droplets and water volume, was determined using the following equation: where d i is the droplet diameter determined by statistical analysis, and V total is the total volume of the imaged area calculated as the product of the surface area and the gap between the two microscope supports (300 µm).As shown in figure 8, ϕ increases with increasing discharge number (N), and the data can be fitted by a power equation ( 3): This indicates that almost the same volume of emulsion is produced by different discharges.This could be due to the nearly constant energy of these discharges (the lowest and highest energy are ∼15 and 20 mJ, respectively); this parameter will be assessed in a future parametric study.

Discussion
Emulsions are usually produced by ultrasonic cavitation in a medium containing two liquids [20,27].The acoustic field forms bubbles that undergo a series of expansion-implosion events (oscillations) near the interface [22].Under the action of the Kelvin impulse, the bubble implodes asymmetrically towards the denser liquid [28], thereby creating a strong shear flow at the interface.This produces instabilities that lead to interface distortion and the formation of small droplets of one liquid in the other, i.e. an emulsion.Depending on the interfacial tension of the two liquids, among other parameters, variable properties of the emulsion may be achieved.In the present study, discharges were generated at or near the interface of a water/heptane system, resulting in the formation of a heptane emulsion in water.Notably, many more droplets are produced when the electrodes are aligned with the interface.Based on the available literature, an acoustic field is produced upon the ignition of spark discharges in liquid, resulting in the formation of bubbles.Beyond the plasma phase (∼1 µs), bubbles with high pressure (tens to hundreds of bars) and high temperature are formed, and they oscillate over a few hundred microseconds [22].Although the expansion phase produces a well-defined interface, instabilities (such as Kelvin impulse [28], Rayleigh-Taylor [20], etc) are observed during the implosion phase.As in the case of ultrasonic cavitation, the shear flow of implosion is directed towards water, resulting in the formation of a heptane emulsion.Note that we did not observe the formation of emulsion in heptane but only millimeter droplets of water that are ejected into heptane; however, these droplets rapidly fall to the interface and mix with water after relaxation by coalescence.We believe that this finding can be explained by the dynamics of the bubble at the interface.Indeed, the discharge produces a half-bubble that grows in heptane and another half-bubble that grows in water.The difference between densities (0.68 for heptane vs. 1 g cm −3 for water) will lead to asynchronized half-bubble dynamics, resulting in the production of a heptane emulsion in water, with no water emulsion in heptane.Further investigation is needed, e.g. by fast imaging of the bubble dynamics.
The droplet size distribution of an emulsion is usually described by a lognormal distribution, particularly when the formation process is dominated by a single mechanism [29].Herein, it was found that the data acquired at low discharge number (i.e.<100) is well fitted by a lognormal distribution (figure S3 in supplementary material), but at high discharge number, two lognormal distributions are needed to obtain a satisfactory fit (figure 9(a)).Figure 9(b) and table 2 in supplementary material present the fit parameters (σ, median, and amplitude) and correlation coefficients corresponding to the fitted curves obtained at different discharge numbers.
As shown in figure 9, the first distribution, lognormal 1, fits droplets with diameters up to ∼20 µm.Comparatively, the second distribution, lognormal 2, is narrower, and it fits the 5-10 µm droplets.Notably, the contribution of lognormal 2 to the total fit increases with increasing discharge number.Overall, the results suggest that two mechanisms are implicated in emulsion formation, and that the relative contributions of these mechanisms vary depending on the number of ignited discharges.At low discharge number, droplets are formed by the expansion-implosion dynamics of the discharge-induced bubble.The size distribution of droplets formed via this mechanism is well fitted by lognormal 1.Although the expansionimplosion mechanism occurs for every discharge, another mechanism contributes to emulsion formation at high discharge number.This second mechanism may be related to the effect of the discharge in emitting an acoustic field, including a shock wave [22].Based on previous studies [22,26,30,31], the acoustic field induces excitation (i.e.expansionimplosion) of the bubbles originating from anterior bubble residue or dilute gas in liquid.When this phenomenon is produced near a droplet or near the interface, smaller droplets are expected to be produced.In addition, energetic shock waves can destabilize the heptane droplets in water and break them down into smaller droplets [32].This mechanism agrees well with the lognormal 2 fit of the distribution data acquired at high discharge number.In the case of low discharge number, the number of produced droplets/bubbles is low.Therefore, the contribution of the second mechanism linked to the acoustic field in the production of smaller droplets is most likely low.Its contribution is expected to increase progressively with the discharge number, i.e. with the number of droplets/bubbles produced by previous discharges near the interface.This assumption needs further validation, e.g. by optical imaging, as in [32].The formation of a heptane emulsion in water induces a variation in the breakdown voltage of the discharge, particularly that produced at the interface (z = 0).Since the dielectric permittivity of heptane is much smaller than that of water (∼2 vs. 80), the emulsion may be considered as a discontinuous medium, wherein the electric field distribution is strongly modified.Knowing that ⃗ E = − ⃗ ∇ (V), the modification of the E-field was quantified by numerically solving the Laplace equation, ⃗ ∇ .(ε ⃗ ∇V) = 0, using 2D simulation [32].A Monte Carlo approach was adopted to simulate the emulsion of spherical heptane droplets in water.The diameter of simulated droplets was randomly assigned based on the single lognormal distribution recorded experimentally, with d = 7 µm and σ = 0.56 corresponding to the first few hundred discharges.Simulations of the electric field distribution were done on a 750 µm × 750 µm uniform Cartesian grid, subdivided into an array of 1000 × 1000 elements, using a python solver.As shown in figure 10, the symmetry axis of the electrodes was exactly aligned with the heptane/water interface.
The E-field distributions obtained at 15 kV electrical potential (value near the breakdown voltage recorded at the beginning of the experiment) and 100 µm inter-electrode gap are presented in figure 11.In the current electrode configuration, where the electrode surface is assumed to be flat, the E-field lines are parallel to the interface.Therefore, the discontinuity of ε at the water-heptane interface does not significantly influence the E-field values (∼2 × 10 8 V m −1 ), as the normal component can be neglected.However, figure 11(b) clearly shows that the presence of heptane droplets in water produces domains with high E-field.For instance, the highest field obtained without emulsion is ∼2 × 10 8 V m −1 , compared to ∼10 9 V m −1 with emulsion.This intensification is due to the spherical geometry of the droplet as some regions exhibit significant normal component of the E-field and, therefore, an intensification occurs.Such intensification of the E-field facilitates the breakdown, which explains the reduced breakdown voltage values recorded at z = 0 (interface) compared to z = ±1 or ±2.
The number of droplets in the simulated emulsions was varied between 5 and 500.For each investigated number, the Monte Carlo approach was adopted to account for the hazardness of heptane droplet position in water.This approach is based on the simulation of hundreds of configurations, wherein the droplet positions and diameters are randomly assigned without altering the droplet size distribution.The maximum Efield was determined for each configuration and is presented in figure 12.For a given number, each data point corresponds to a single simulation.Clearly, the maximum E-field increases with increasing number of heptane droplets in water, from 2 × 10 8 V m −1 in the absence of an emulsion to ∼10 9 V m −1 in the presence of 500 droplets.This may be attributed to the increase in heptane/water interface area, where the dielectric permittivity is discontinuous.Overall, it may be concluded that after a few hundred discharges, the number of heptane droplets in water increases sufficiently (more than a hundred) so that the E-field is appreciably intensified, thereby reducing the breakdown voltage.
As detailed above, the results obtained herein provide a plausible explanation for the drop in breakdown voltage at z = 0. Briefly, when a spark discharge is initiated at the interface of heptane and water, it generates oscillating (expansionimplosion) bubbles whose dynamic induces strong chaotic shear flow, resulting in the introduction of heptane droplets into water (i.e.emulsion formation).Considering the difference between the dielectric permittivities of water and heptane, the presence of heptane droplets in water alters the Efield configuration and intensifies its magnitude, particularly at high discharge numbers, where the density of heptane droplets is large.Knowing that the E-field is the main element governing the ignition of spark discharges, it is expected that the droplet-induced intensification of the E-field near the interface will lead to a drop in breakdown voltage.Despite the reduced voltage, the energy of the discharge remains high (the lowest is ∼15 mJ while the highest is ∼20 mJ), and thus, the production of oscillating bubbles and heptane droplets in water continues to occur.Beyond a certain number of discharges, the breakdown voltage goes back up due to the effect of dischargeinduced electrode erosion in increasing the gap between the two electrodes.When the electrodes are far from the interface, the oscillating bubbles do not significantly disturb the interface, and thus, no emulsion is produced and no intensification of the electric field occurs.Consequently, the discharges at z = ±1 and ±2 stop much earlier than at z = 0 due to electrode erosion.
Finally, it is worth noting that spark discharges in liquid produce nanoparticles and micro-/nano-bubbles that may remain in liquid for long time.Therefore, the presence of these discontinuities may also influence the discharge occurrence,  in a similar way to the droplets.However, such nanoparticles and micro-/nano-bubbles are produced in every z conditions and not only at the interface, although the interface can be considered as a trap for these particles and/or bubbles.To discriminate their contribution, we performed discharges at z = 0 to produce emulsion in a beaker.Then, without modifying the electrode conditions, the beaker was adjusted vertically to produced discharges in heptane or in emulsion, far from the interface.The results clearly showed that the probability of discharge occurrence in emulsion is much higher than that in heptane (∼90% vs. 10%).The beaker was also replaced by another one that contains water or heptane and, here also, the probability of discharge occurrence at the interface heptaneemulsion was much higher.

Conclusion
This study investigates emulsion formation by spark discharges ignited at or near the interface of a heptane/water system, as well as the effect of the emulsion on discharge probability.Microscopy analyses reveal that emulsions are formed only when the electrodes are aligned with the interface, and the number of heptane droplets water increases with increasing number of discharges.At low discharge number, the droplet size distribution is fitted by one lognormal function that is consistent with bubble cavitation mechanism.Based on this mechanism, the discharges induce the formation of oscillating bubbles near the interface.The expansion-implosion dynamics of these bubbles destabilizes the interface and promotes the migration of heptane droplets into water, i.e. emulsion formation.At high discharge number, another mechanism is implicated in the emulsification process, as evidenced by the two lognormal fits of size distribution data.In addition to bubble generation, the discharge most likely emits an acoustic field that excites bubbles near the interface and near heptane droplets (induced by prior discharges), resulting in the formation of smaller droplets.Interestingly, the breakdown voltage of discharges at the interface (z = 0) decreases beyond ∼100 discharges, then it increases after ∼200 discharges, unlike the breakdown voltage of discharges in water or in heptane, which exhibits a monotonous increase.To explain such discrepancy, 2D Monte Carlo simulations of the E-field distribution were conducted at varying discharge number.The obtained results demonstrate that when an emulsion is formed, the electric field is intensified at the droplet-water interface, resulting in reduced breakdown voltage.This effect becomes more important at higher discharge numbers due to the formation of a larger number of heptane droplets in water.However, with repeated discharge, electrode erosion becomes important, and the gap distance between the electrodes increases, thereby increasing the breakdown voltage.Electrode erosion depends on the position of the electrode regarding the interface, with higher and lower rate respectively in water and at interface.This behavior can explain the high probability of discharge occurrence at the interface.However, it cannot be explained by injected energy or charge, as they are comparable, but rather by the nature of produced reactive species as well as by bubble implosion dynamics.Further investigations are needed, particularly optical diagnostics and fast imaging.

Figure 1 .
Figure 1.Scheme of the experimental setup.

Figure 2 .
Figure 2. Typical current-voltage waveforms of a spark discharge at the water/heptane interface (z = 0).

Figure 3 .
Figure 3. Probability of discharge occurrence as a function of discharge number at z = 0, ±1, ±2 mm.

Figure 4 .
Figure 4. Variation of the (a) breakdown voltage, (b) discharge current, and (c) discharge delay as a function of discharge number at z = 0, ±1, ±2 mm.The solid lines represent the mean values of 200 data points, and the shaded areas correspond to the 90% intervals.

Figure 5 .
Figure 5. (a) Photographs of the heptane/water system before and after plasma processing.(b) Evolution profiles of water transmittance during plasma processing for different conditions of z.

Figure 6 .
Figure 6.Microscopy images of the emulsion recorded after processing with (a) 50, (b) 500, and (c) 5000 discharges, and the corresponding (d)-(f) experimental droplet diameter distributions with mean d 10 and d 32 diameters.

Figure 7 .
Figure 7. Mean d 10 and d 32 diameters for each recorded image (dots), and effective mean diameters (solid lines), as a function of discharge number.

Figure 8 .
Figure 8. Variation of volume fraction ϕ as a function of number of discharges.

Figure 9 .
Figure 9. (a) Fit of the experimental droplet size distribution data by two lognormal distributions.(b) Fit parameters and R 2 values of the fit at different discharge numbers.

Figure 10 .
Figure 10.Simulated geometry of the emulsion.Black, gray, and white colors correspond to the electrodes, water, and heptane, respectively.

Figure 12 .
Figure 12.Variation of maximum electric field as a function of droplet number.Red dots, black lines, and blue shaded areas correspond to individual simulations, mean values, and 90% of the data points.