Morphology of bubble dynamics and sound in heated oil

From tempura, schnitzel, samosa to French fries, deep-fried foods are gourmet favorites across cultures and times. The perfect delicious crunch depends on a multitude of factors, but none may be more paramount than achieving the perfect cooking temperature. A common household technique to estimate the oil temperature is to insert (moisturized) chopsticks into the hot oil.¹ By observing the morphology of the bubbles around the chopsticks and perhaps listening to the associated crackling sound, an experienced cook can roughly estimate if the oil is frying-ready.² To demonstrate the connection between the bubble dynamics and sound, we performed a preliminary experiment using moisturized bamboo chopsticks. As shown in Fig. 1(a), we insert a moist chopstick into a hot oil bath ( Appendix A). As the chopstick enters the oil and is heated, bubbles start to expand and become visible. The bubbles also emit sound from bursting. A synchronized microphone captures the sound as shown in Fig. 1(b). Though the cooking technique is a common knowledge, the underlying physics deserves further study.

Studies on bubble dynamics of water in heated oil are primarily motivated by food science,^3,4 fire hazards, and indoor air quality. The majority of research in this area has focused on the cavity dynamics after a droplet impact onto a heated liquid system (e.g., Fan et al.⁵). Manzello et al.⁶ experimentally studied the bubble dynamics and associated jets/ligaments formation above the surface after the water droplet impacts onto a heated peanut oil (oil thickness $δ∼1$ cm). Lan et al.⁷ studied the vaporization upon droplet impact on a heated alcohol surface (⁠$δ∼5$ cm), while Xu et al.⁸ filmed the formation of a Worthington jet in a similar setting. Alchalabi et al.⁹ visualized the vaporization process of water droplets during the crater formation in heated soybean oil (⁠$δ∼10$ cm). Marston et al.¹⁰ provided a detailed visual understanding of the jet formation from a thinner oil layer (⁠$δ∼O(0.1)$ cm). More recently, Kumar et al.¹¹ performed an impact experiment of methanol drops onto the heated mustard oil (⁠$δ∼0.35$ cm) and studied the evaporation process in detail.

Bubble dynamics in food and cooking processes is also an active research area. Carbonated beverages have been widely explored,¹² for instance, in the distribution of bubbles in beer after pouring.¹³ Bubble dynamics after beer-bottle tapping^14,15 and a bottle-shattering after imposing an impact have also been investigated.¹⁶ Recently, Poujol et al.¹⁷ studied the sound emission from a glass of champagne and showed that the bubbles at the surface rupture and emit an audible sound.

We attempted to reduce the complexity of deep-frying bulk food by dipping a moist thin piece of paper, which can be an approximate model of a two-dimensional food, into the hot oil ( Appendixes A and  B). This preliminary experiment reveals three distinct types of oil-bubble morphology, which we investigate by employing a second, simpler experimental setup (see Sec. II). First, bubble bursting occurs at the oil surface [Fig. 2(a)] followed by a hemispherical crater formed at the surface creating mist and splashes. We conjecture that an explosion of water leaked from the wet paper triggers the event. We term this event an explosion cavity.¹⁸ Second, in Fig. 2(b), two vertical jets form, with the downward moving thin jet creating an extended cavity. Similar cavity dynamics were filmed in Lan et al.,⁷ where they labeled it as a weak explosion. Xu et al.¹⁹ used a deep layer of rapeseed oil heated up to 260 °C and report a similar phenomenon. We term this event an elongated cavity. Third, a multi-step expansion and shrinkage of the cavity and the formation of numerous jets are shown in Fig. 2(c). We term this event an oscillating cavity.

We further simplify the model by reducing the dimension of the “food”: frying a droplet instead of a 2D paper sheet. We reproduced the aforementioned three cavity types in a more controlled manner, which provides a preliminary understanding of the interplay among heated liquid expulsion, bubble dynamics, and sounds. Deciphering the sound signals can lead be extended to future applications, e.g., acoustic sensing of aerosol generation as discussed in the paper.

We heated cooking oil (canola oil, Kroger brand) by using a heater, to fry a water droplet (Fig. 3). Canola oil (125 ml, approximate depth $∼4$ cm) is poured into a Pyrex beaker. We deposit a droplet of the distilled water (approximate volume < 4 μL) to a wire similar to the suspended drop method used in combustion studies (e.g., Ref. 21). We then submerge the droplet into the oil by a manual stage. The oil temperature is controlled by a heater underneath and monitored by a K-type Thermocouple, and it ranged approximately from 170 to 210 °C. The temperature range was selected based on the preliminary observations (Fig. 2), overlapping with the temperatures used for frying food. The highest temperature was set to not exceed the smoke point of canola oil (⁠$≈$ 238 °C²²). We note that in most cases for the Explosion and Elongated cavities, the droplet exploded after we placed it at a given height. Thus, the plunging speed of the droplet is assumed to be negligibly small. The Oscillating cavity cases were achieved by a droplet that slipped off of the wire, thus having a plunging speed, which is determined largely by gravity.

The literature indicates that the material property of Canola oil is dependent on temperature. The density of Canola oil at room temperature is $ρ≈913$ kg/m³ and decreases to $ρ≈807$ kg/m³ at 200 °C.²³ The surface tension also decreases from $σ≈$ 3 $×101$ mN/m at room temperature to $σ≈$ 2 $×101$ mN/m at 200° C. In the literature,²³ it is reported that viscosity decreases from 64 mPa $·$ s at room temperature to 3 mPa $·$ s at 200 °C.

A high-speed camera (Phantom, v2511) captures the bubble dynamics in the oil bath. The frame rate is 5000–20 000 f.p.s., with a spatial resolution in oil of $≈$ 0.06–0.08 mm/pixel. For a rounded glass container of oil, the image is slightly distorted, so that the horizontal distance is not reliable. We, thus, measured most of the dimensions vertically unless otherwise stated. The high-speed imaging employs a back-light method. A microphone (Earthworks Audio, QTC40, bandwidth: 3 Hz–40 kHz) measures acoustic signals (sampling rate: 40–44.1 kHz). The video and audio data acquisitions are synchronized through a National Instrument DAQ and controlled through a custom LabView script on a PC.

We assume that the mechanism for the three cavity types can be understood by considering the interaction between a single exploding bubble and the oil free-surface (Fig. 2). As summarized for a cavitation study in water,²⁴ one of the primary parameters to consider is the stand-off distance h/R. The quantity h is the distance between the free surface and a droplet before the bubble formation. R denotes the maximum bubble radius.

Explosion cavity: A room temperature water droplet increases in temperature as it approaches and enters the heated oil bath. The droplet undergoes a micro-explosion from the sudden temperature change and forms a vapor bubble. The bubble may rupture the surface if the bubble dynamic strength is significant. The overall dynamics following the surface rupture are similar to surface explosion experiments of firecrackers¹⁸ and lasers.²⁵ These literatures suggest that large splash and jet formation can occur from any large surface deformation. One can expect that h/R = 1 is the threshold for this event if the deformation of the surface associated with the bubble expansion is negligible, while it is not typically the case in our experimental data. We report that this event [see Figs. 2(a) and 4(a)] occurs when h/R is very small [typically $h/R<0.5$⁠, see Fig. 5(a)].

Elongated cavity: The droplet reacting at a slightly deeper location causes another interesting behavior. The formation of the bubble is vertically asymmetric after maximum spreading. The top of the bubble collapses faster than the bottom because it is located closer to the surface, resulting in a downward jet. The collapse of a single cavitation bubble of water in the vicinity of the free surface leads to a similar jetting phenomenon as a result of the interaction between acoustic waves and interfaces [e.g., Refs. 24, and 26–30]. This event may occur when a bubble wall approaches the oil surface sufficiently enough that it does not rupture it [i.e., $h/R≥1$⁠, see Figs. 2(b) and 4(b)].

We again emphasize that the surface deformation may affect the thresholds in different cases. For instance, Li et al.³¹ performed a cavitation experiment in water with an electric discharge method and filmed the elongated cavity at $h/R≈0.8$⁠. Their numerical simulations reproduced the elongated cavity for approximately $h/R=0.5–1.5$⁠, and they reported an intermediate response between the explosion and elongated cavities at $h/R=0.25$⁠.

Oscillating cavity: The bubble maintains a relatively spherical shape while oscillating and initiates free surface vibrations. The rapid expansion of the bubble generates acoustic pressure waves that result in the vibration of the free surface.³² Disturbances on the surface, such as a floating bubble or any curvature, may cause liquid jetting (see experiments in a tube³³ or on an armored droplet³⁴). Note that we do not expect the formation of the large upward jet in the other two cases because the disturbance considered is small relative to the crater found in the explosion cavity. Oscillating cavity may occur when a bubble explodes far from the free surface [i.e., $h/R>1$⁠, see Figs. 2(c) and 4(c)]. The acoustic wave attenuates and does not affect the surface as $h/R≫1$⁠.

Figure 5(a) summarizes the experimental results with respect to h and R, categorizing the three transition regimes. The explosion cavities are visible at $h/R<1$ as expected. Elongated cavities largely range between $h/R=0.5–1.5$ similar to Li et al.³¹ (see also dashed lines). The oscillating cavity data are located where $h/R>1.5$⁠. The same data are plotted in terms of the oil temperature in Fig. 5(b), revealing that all three regimes are present at nearly the same temperatures, and that h/R is the primary driving difference between the cavity types within the experimental condition tested. Recently, the dynamics of a laser-induced cavitation bubble of water near the free surface were studied in detail,³⁵ where both the splash/jet and bubble dynamics were determined by the stand-off distance, which was consistent with our results.

Figure 6(a) shows a typical behavior of the explosion cavity (Multimedia view). A water droplet on a wire is heated up and forms a bubble (t = 0.05 ms). The bubble then expands (t = 0.30 ms), leading to the rupture of the oil surface (t = 0.30–0.80 ms). In the early stage of the rupture, the rapid expansion of the bubble forms an aerosol of the heated oil (t = 0.8 ms, marked by a dashed square). The droplets are comparable to the (or even smaller than) camera resolution. Their approximate radius is smaller than $50 μ$m associated with some motion blur. Their speed reaches $U∼O(10)$ m/s. A splash rises to open a crater to the air (⁠$t∼0.80–2$ ms) and forms a bubble at the surface (⁠$t∼5–17.5$ ms). The speed of the splash sheet is less than 10 m/s, and the associated droplets have a relatively large size (several pixels, $O(100) μ$m, marked by a dashed square at t = 5 ms). The crater keeps its hemispherical shape until its bottom moves upward (⁠$t∼17.5$ ms).

This surface rupture is a unique phenomenon (see also  Appendix C) and characterizes the following fluid dynamics including aerosol formation. Figure 6(b) shows the depth of crater d as a function of time. The d value increases rapidly in the early stage and then slows down. The d value is compared with a power-law $d∝t0.39$ (inset), corresponding to an experimental value from a firecracker explosion at a water surface.¹⁸ While the best fit for our data was slightly smaller (0.28), a power-law relationship is observed. The viscosity of oil might play a role, but we have not tested the effect experimentally. As the d value reaches the maximum, the cavity flattens and the bagging splash dome shows a curved shape. The overall trend of acoustic signals also agrees with the bubble/crater dynamics [Fig. 6(c)]. The sound level p(V) was relatively small in the bubble formation stage. The peak value [marked by a circle in Fig. 6(c)] was achieved at t = 0.5–0.8 ms, which agrees with the bubble rupture and aerosol ejection times [Fig. 6(a)]. This suggests that the explosion is the primary source of the audible sound. Once the dome is fully closed, sound above the noise floor was not measured (5–20 ms). The power spectrum for the first 5 ms is shown in Fig. 6(d), where we obtain a peak frequency of $≈$1.4 kHz.

The elongated cavity occurs when a droplet explodes under the surface and does not rupture the surface [Fig. 7(a), Multimedia view]. A vertical jet emerges to the air while generating a downward jet inside the bubble (⁠$t=2–10$ ms) as observed in the cavitation experiments near the free surface.²⁶ We assumed that the oil surface was initially smooth (i.e., no floating bubbles). This period corresponds to the expansion of the bubble before the jet impinges on the bottom side [Fig. 7(b)]. The vertical upward jet, whose tip size is approximately 2 mm, has an approximate jet speed of $≈1.7$ m/s from a linear fit to the data in Fig. 7(c). A synchronized microphone captured the peak sound at 1 ms, which decays in time [Fig. 7(d)]. The power spectrum for the first 10 ms is shown in Fig. 7(e), where we obtain a peak frequency of $≈$1.4 kHz. The linear frequency of the bubble³⁶ can be estimated by

where the maximum radius of the bubble $R∼5.55$ mm, the polytropic gas constant $γ=1.4$⁠, and the pressure difference $ΔP=Patm−Pv≈84$ kPa. The oil density and surface tension at 200 °C are assumed to be $ρ≈807$ kg/m³ and $σ≈2×102$ mN/m, respectively.²³ Thus, $fm∼0.6$ kHz, which is smaller than the measured value of 1.4 kHz, suggesting that the acoustic emission is dominated by the rapid expansion in approximately 1 ms rather than the elongation of the bubble [Fig. 7(b)]. We note that the non-spherical dynamics of the bubble may affect the approximations, and it is possible that a smaller bubble somewhere out of the camera is the source of the higher frequency in this case. In addition, the sound signal oscillates with a smaller amplitude (10–30 ms) perhaps due to the bubble persistence.

Interestingly, we sometimes observed a generation of daughter droplets. In Fig. 7(a) (Multimedia view), a propagating wave front travels on the bubble surface (t = 2 ms). A daughter liquid jet forms inside the bubble, and a daughter droplet emerges in the oil (⁠$t=10–14$ ms). A formation of daughter droplet has also been observed when the droplet impacts a heated oil bath (e.g., Ref. 19). The daughter droplet can sink and then evaporate at a deeper location. We observed one elongated cavity case that was followed by an oscillating cavity in time as highlighted in the discussion section and Fig. 9(a) (Multimedia view).

Figure 8(a) shows the typical behavior of the oscillating cavity (Multimedia view). In this case, a water droplet slipped off the wire and reached $≈$11 mm below the oil surface. The droplet forms a gas bubble, where it becomes apparent at $t≥0.1$ ms. The bubble growth shows a multi-step explosion during the formation stage until $t≈$ 3 ms [see also Fig. 8(b), stage 1], perhaps due to the relatively large size of the droplet (⁠$∼1.1$ mm). Then, the bubble undergoes a periodic oscillation (stage 2). A thin jet emerges from the small air pockets near the wires at the surface when the volumetric acceleration is initiated. The formation of the jet from a free surface air bubble can also be observed in Fig. 10(a) (the third frame from the left). Recently, a similar type of jet was reported to have formed due to Rayleigh–Taylor instability upon bubble oscillation.³⁷ The air bubbles at the surface are perhaps produced when the wire is submerged. As we performed the experiments consecutively, the residual bubbles from the previous run are also possible sources of the bubbles on the free surface. The bubble oscillation duration is 10 ms, and the projected bubble size nearly reaches the maximum value at the same moment (⁠$≈$13 ms). The bubble then breaks up into numerous bubbles, and the overall oscillation is attenuated (stage 3).

The audio signals p(V) recorded by using a microphone are shown in Fig. 8(c). In this case, the time offset was about $Δt∼$ 0.05 ms. The plot is also classified into three stages. In stage 1, the gradual oscillation of sound reflects the multi-step explosion of a bubble found in Figs. 8(a) and 8(b). In stage 2, a significantly large sound was detected. It attenuates in time and leads to stage 3 (not shown). In stage 3, the main bubble is disintegrated into several small bubbles. Applying the spectrum analysis to the acoustic signal for the first 5 ms in stage 2 [Fig. 8(d)], we found the fundamental frequency peak at $≈$0.8 kHz. This value agrees with that found in spectrum for the projected bubble size data (⁠$≈$0.8 kHz, see inset). We note that the resolution for this analysis for the inset is not high due to the limited frame rate (20 000 fps). The reasonable agreement indicates that the periodic oscillation of the bubble dominates the sound generation. In the spectrum analysis, the second harmonic frequency of $≈$1.6 kHz was observed and is also visible in Fig. 8(c).

We observed each cavity leads to different flow behaviors. Both explosion and elongation cavities occur near the oil surface. The acoustic signal for the explosion cavity shown in Fig. 6(c) has the fundamental frequency of $≈$1.4 kHz [Fig. 6(d)], which is similar to that for the elongation cavity reported in Fig. 7(e). Considering the frequencies and timing of sound generation, in both cases, the early stage (i.e., expansion stage) of crater/bubble dynamics dominates the sound generation. One of the possible differences between the two cases is perhaps the magnitude of the sound. While the sound level in Figs. 6(c) and 7(d) is similar to each other, the location of the microphone for Fig. 7(d) (⁠$≈$6 cm from the oil surface) was much closer to the oil surface when compared to that for Fig. 6(c) (⁠$≈$16 cm from the oil surface). The high-speed video observations suggest that it is likely related to the size of the crater/bubble. As shown in Fig. 7(a), an elongated cavity tends to be accompanied by a bigger daughter droplet(s) (Multimedia view), indicating that only a small portion of the water droplet contributes to forming a bubble. It is also visible in Fig. 5(a). The maximum radius R of the elongated cavity tends to be smaller than that of the oscillating cavity, consistent with our conjecture. The oscillating cavity shows a relatively small variation in the R value, possibly because it undergoes the multi-step explosion, leading to the formation of a gas bubble.

The generation of daughter droplets may lead to more complex fluid behavior. Figure 9(a) shows the elongated cavity followed by an oscillating cavity (Multimedia view). In this case, the elongation of the first cavity was quite small, and it forms a daughter droplet under the cavity. The daughter droplet exploded at $h≈8$ mm and led to the violent oscillation under the surface, while the bubble still persisted near the oil surface. A relatively large curvature on the oil surface assisted the formation of a thick jet. The synchronized audio data [Fig. 9(b)] capture the acoustic signature for both cavities. The fundamental frequency for the elongated cavity was $≈$ 1.5 kHz [Fig. 9(c)], which is perhaps related to the initial dynamics of the bubble, whereas the fundamental frequency for the oscillating cavity (⁠$≈$1.1 kHz) is dominated by the bubble oscillation [Fig. 9(d)]. The second harmonic frequency was $≈$ 2.0 kHz for the oscillating cavity [Fig. 9(d)]. This example demonstrates the coexistence of multiple cavities and their nonlinear response that may be possible inside a cooking pan where the heated oil expulsion can occur. In addition to the magnitude of the acoustic signal, its duration and decay speed [marked in Fig. 9(b)] can also be an indicator.

Related to the oscillating cavity, we show two with different levels of surface disturbance. As discussed in Fig. 4(c), it is clear that a jet forms from the air bubble at the oil surface [Fig. 10(a)]. In contrast, a surface without any noticeable disturbance does not form jets instead vibrates [Fig. 10(b)]. This demonstrates that the disturbance of the surface triggers the oil expulsion. One such disturbance corresponds to a common occurrence in the pan during cooking. This suggests that, unlike the other two regimes, the heated oil can be expelled from numerous gas bubbles. In other words, the rapid explosion of the bubbles on the oil surface is not necessarily requisite to eject the heated oil to the air.

As observed, each cavity has a distinct acoustic feature, which might be used for future applications. One of the possible applications of this research is the acoustic sensing of the heated oil expulsion. Detecting a high-frequency noise from the explosion cavity might help us monitor the generation of small droplets (aerosols). In addition, classifying three regimes may result in an understanding of larger droplets and thus may be beneficial to improving safety for cooking and preventing unanticipated fires.

We place a water droplet at different depths in hot oil to form a bubble from water vapor expansion, to reproduce cavity dynamics found in our preliminary experiment (Fig. 2). Our experiment visualized that the expulsion of heated oil from the cooking pan, which we experience in our daily life, is a result of the coupling of different mechanisms. In our experiment, we used a wire to hold a droplet until it explodes, enabling us to restrict the droplet movement, unlike other existed experiments that employ falling droplets. Cavity dynamics were classified based on the established findings in cavitation research. The transition between cavity types was described by the stand-off parameter h/R, where h and R are the locations of the water droplet and the maximum radius of the bubble (Fig. 5). Within the parameter space tested, the emergence of regimes is nearly temperature independent, suggesting that the stand-off parameter h/R largely determines how the bubble behaves and how the heated oil is expelled. Typical high-speed images of crater/bubble formation process as well as the expelled ligaments and associated sound signals for each cavity type were reported (Secs. IV B–IV D). Each cavity ejects heated oil into the air by different mechanisms as illustrated in Fig. 4. The oscillating cavity is especially violent, and its acoustic signal shows the non-linear response of the bubble. The acoustic signal characteristics (i.e., magnitude, fundamental frequency, and duration) for each cavity are potentially distinguishable, implying that the acoustic sensing of aerosol generation or oil spattering is a potential application.

J.S.A. acknowledges partial support from Office of Naval Research-Red Hill (Grant No. ONR N00014-20-1-2651). A.K. is a Japan Society for the Promotion of Science Overseas Research Fellow.

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

We have conducted two preliminary experiments (Fig. 11) briefly described in the manuscript.

In the bamboo chopstick experiments [Fig. 11(a)], we first rinsed the chopsticks with running water and gently wiped with a paper towel. The chopsticks were then left to sit in distilled water for several seconds to absorb some of the water and then wiped off with a paper towel. They were placed in the oil and as soon as they entered the oil, bubbles start forming. Figure 12 shows high-speed images of the bubble formation from the same chopstick at different temperatures. We note that the population of bubbles is highly dependent on the amount of water in the chopsticks. For example, chopsticks that were not soaked in water before the experiment induced much fewer bubbles. The chopstick material also influences the results as bubbles were not observed for metal chopsticks.

We modeled fried foods by using a small piece of paper (approximately 5 mm by 5 mm) moisturizing with distilled water [Fig. 11(b)]. We varied the water volume (0–20 μL) and hot oil temperature (150–210 °C). The piece of paper is connected to an adjustable stage for vertical movement. Bubble dynamics depend on both the water volume and temperature. We observed three distinguishable cavity dynamics during the heating process of the wet paper, which became the focus of this manuscript (Fig. 2). We note that these cavities may coexist in the frying process (see Fig. 13). For such a moisture-rich environment, further investigation of complicated situations including bubble–bubble interaction is needed, where this manuscript provides a fundamental understanding.

Figure 14 shows an example of bubble formation from a water droplet (a) and batter droplet (b), which is a mixture of water, all purpose flour (gold medal), and an egg. Droplets are placed on the tip. A water droplet explodes and exhibits an elongated cavity-like response. We could observe the formation of vertical jets and wavy surface texture. The formation of a daughter droplet is also observed (t = 4 ms). In contrast, a batter droplet continuously forms bubbles at its surface, and large cavity dynamics were not observed.

The surface rupture upon the explosion cavity is a unique phenomenon, thus worth observing in a detail. Figure 15 shows the detailed view of the free surface rupture process; the first 0.55 ms for the data that were presented in Fig. 6(a) where the time interval between images is set at 0.05 ms. In the seventh frame from the left (0.3 ms), the curvature of the dome top changes when compared to the one frame before (marked by a dotted square), suggesting that the dome is about to rupture. In the next frame (the eighth from the left, 0.35 ms), a wavy structure appeared on the sheet surface, implying that the contraction of the sheet occurred possibly due to the bubble expansion or rupturing (marked by an arrow). The structure becomes more visible as time proceeds. Based on these observations, we assumed that the rupture started when $t≥0.3$ ms as commented in the paper.