Item Type Article
Authors Kiyama, Akihito;Rabbi, Rafsan;Pan, Zhao;Dutta, Som;Allen, John S;Truscott, T. T.
Citation Kiyama, A., Rabbi, R., Pan, Z., Dutta, S., Allen, J. S., & Truscott, T.
T. (2022). Morphology of bubble dynamics and sound in heated oil.
Physics of Fluids, 34(6), 062107. https://doi.org/10.1063/5.0088065 Eprint version Publisher's Version/PDF
DOI 10.1063/5.0088065
Publisher AIP Publishing
Journal Physics of Fluids
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The following article appeared in Physics of Fluids and may be found at http://doi.org/10.1063/5.0088065.
Download date 2024-01-26 18:48:32
Link to Item http://hdl.handle.net/10754/678782
Morphology of bubble dynamics and sound in heated oil
Cite as: Phys. Fluids34, 062107 (2022);doi: 10.1063/5.0088065 Submitted: 12 February 2022
.
Accepted: 21 April 2022.
Published Online: 7 June 2022
AkihitoKiyama,1 RafsanRabbi,1 ZhaoPan,2 SomDutta,1 John SAllen,3 and Tadd TTruscott1,4,a) AFFILIATIONS
1Utah State University, Mechanical & Aerospace Engineering Department, Logan, Utah 84322, USA
2Department of Mechanical and Mechatronics Engineering, University of Waterloo, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada
3University of Hawaii at Manoa, Mechanical Engineering Department, Honolulu, Hawaii 96822, USA
4Mechanical Engineering Program, Physical Science and Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Kingdom of Saudi Arabia
Note:This paper is part of the special topic, Kitchen Flows.
a)Author to whom correspondence should be addressed:[email protected]
ABSTRACT
The interaction between a heated oil bath and water droplets commonly occurs in the kitchen and has important implications for cooking, fire safety, and indoor air pollution. The interplay between the bubble dynamics in a heated oil bath, the generated sound, and the ligament- like expulsion to the surrounding air is examined. We focus on an explosion of a millimeter-sized water droplet in heated oil as a simplified case. We discuss three typical bubble types that can be classified as a function of the stand-off parameterh/R, wherehis the distance between the oil surface and bubble andRis the maximum bubble radius. Our data describe the morphology of bubble dynamics inside a heated oil bath and represent those found in the cooking pan. This paper also highlights potential applications of our findings.
VC 2022 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://
creativecommons.org/licenses/by/4.0/).https://doi.org/10.1063/5.0088065
I. INTRODUCTION
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 para- mount than achieving the perfect cooking temperature. A common household technique to estimate the oil temperature is to insert (mois- turized) chopsticks into the hot oil.1By observing the morphology of the bubbles around the chopsticks and perhaps listening to the associ- ated crackling sound, an experienced cook can roughly estimate if the oil is frying-ready.2To demonstrate the connection between the bub- ble dynamics and sound, we performed a preliminary experiment using moisturized bamboo chopsticks. As shown inFig. 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 visi- ble. The bubbles also emit sound from bursting. A synchronized microphone captures the sound as shown inFig. 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,3,4fire 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., Fanet al.5).
Manzelloet al.6experimentally studied the bubble dynamics and asso- ciated jets/ligaments formation above the surface after the water drop- let impacts onto a heated peanut oil (oil thickness d1 cm). Lan et al.7studied the vaporization upon droplet impact on a heated alco- hol surface (d5 cm), while Xuet al.8filmed the formation of a Worthington jet in a similar setting. Alchalabiet al.9visualized the vaporization process of water droplets during the crater formation in heated soybean oil (d10 cm). Marstonet al.10provided a detailed visual understanding of the jet formation from a thinner oil layer (dOð0:1Þcm). More recently, Kumaret al.11performed an impact experiment of methanol drops onto the heated mustard oil (d0:35 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,12for instance, in the distribution of bubbles in beer after pouring.13Bubble
dynamics after beer-bottle tapping14,15and a bottle-shattering after imposing an impact have also been investigated.16Recently, Poujol et al.17studied 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 Aand B). This preliminary experiment reveals three distinct types of oil- bubble morphology, which we investigate by employing a second, sim- pler 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 explo- sion of water leaked from the wet paper triggers the event. We term this event anexplosion cavity.18Second, inFig. 2(b), two vertical jets form, with the downward moving thin jet creating an extended cavity.
Similar cavity dynamics were filmed in Lanet al.,7where they labeled it as a weak explosion. Xuet al.19used a deep layer of rapeseed oil heated up to 260C and report a similar phenomenon. We term this event anelongated cavity. Third, a multi-step expansion and shrinkage
FIG. 2.Three cavity types20formed by the expansion of water from a wetted paper (approximately 5 mm5 mm) near the oil surface. A piece of paper is sinking parallel to the oil–air interface (see alsoFig. 11in Appendix A). (a)Explosion cavity, the free surface explodes, and splash and droplets emerge while forming a hemispherical cra- ter. The oil temperature wasT200C and water volume was V¼15lL. (b) Elongated cavity, a bubble formed right below the surface induces a downward jet inside, leading to a stretched cavity.38The temperature wasT174C for a water volume ofV¼10lL. (c)Oscillating cav- ity, a periodic oscillation of a vapor bubble results in the surface movements, and the thin fine jets formation. The temperature wasT196C, and the water volume wasV¼20lL.
FIG. 1.(a) Images of the moisturized bamboo-chopsticks inside the hot oil at 205C. (b) Acoustic signal recorded near the surface as a function of time, andDt is a time offset corresponding to the frame rate. Dashed squares mark approximate correspondence to the images in (a) (0.1–0.6 s and 2.5–3.0 s).
of the cavity and the formation of numerous jets are shown inFig.
2(c). We term this event anoscillating 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.
II. EXPERIMENTAL METHOD
We heated cooking oil (canola oil, Kroger brand) by using a heater, to fry a water droplet (Fig. 3). Canola oil (125 ml, approximate depth4 cm) is poured into a Pyrex beaker. We deposit a droplet of the distilled water (approximate volume<4lL) 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 210C. The temperature range was selected based on the preliminary observations (Fig. 2), overlapping with the temperatures used for fry- ing food. The highest temperature was set to not exceed the smoke point of canola oil (238C22). We note that in most cases for the ExplosionandElongatedcavities, the droplet exploded after we placed it at a given height. Thus, the plunging speed of the droplet is assumed to be negligibly small. TheOscillating cavitycases 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 temper- ature isq913 kg/m3and decreases toq807 kg/m3at 200C.23 The surface tension also decreases fromr3101mN/m at room temperature tor2101mN/m at 200C. In the literature,23it is
reported that viscosity decreases from 64 mPas at room temperature to 3 mPas at 200C.
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 of0.06–0.08 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, band- width: 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.
III. MORPHOLOGY
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,24one of the primary parameters to consider is the stand-off distanceh/R. The quantityhis the distance between the free surface and a droplet before the bubble formation.Rdenotes the maxi- mum 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 firecrackers18and lasers.25These literatures suggest that large splash and jet formation can occur from any large surface deformation. One can expect thath/R¼1 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 [seeFigs. 2(a)and4(a)]
occurs whenh/Ris very small [typicallyh=R<0:5, seeFig. 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 sur- face, 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 jet- ting phenomenon as a result of the interaction between acoustic waves and interfaces [e.g., Refs.24, and26–30]. This event may occur when a bubble wall approaches the oil surface sufficiently enough that it does not rupture it [i.e.,h=R1, seeFigs. 2(b)and4(b)].
We again emphasize that the surface deformation may affect the thresholds in different cases. For instance, Liet al.31performed a cavi- tation experiment in water with an electric discharge method and filmed the elongated cavity ath=R0:8. Their numerical simulations reproduced the elongated cavity for approximately h=R¼0:5–1:5, and they reported an intermediate response between the explosion and elongated cavities ath=R¼0:25.
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.32Disturbances on the surface, such as a floating bubble or any curvature, may cause liquid jetting (see experiments in a tube33or on an armored droplet34). Note that we do FIG. 3.A schematic of the experimental set-up. Position of a water droplet is
adjusted by a manual stage. Bubble dynamics are recorded by a high-speed cam- era with a synchronized microphone for the audio signals. The oil temperature before and after the droplet reaction is measured by a thermocouple.
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 cavitymay occur when a bubble explodes far from the free surface [i.e.,h=R>1, seeFigs. 2(c) and4(c)]. The acoustic wave attenuates and does not affect the surface ash=R1.
IV. ANALYSIS A. Regime map
Figure 5(a)summarizes the experimental results with respect toh andR, categorizing the three transition regimes. The explosion cavities are visible ath=R<1 as expected. Elongated cavities largely range
betweenh=R¼0:5–1:5 similar to Liet 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 inFig. 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.
B. Explosion cavity
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 (t¼0.05 ms). The bubble then expands (t¼0.30 ms), leading to the rupture of the oil surface (t¼0.30–0.80 ms). In the early stage of the rupture, the rapid expansion of the bubble forms an aerosol of the heated oil (t¼0.8 ms, marked by a dashed square). The droplets are comparable to the (or even smaller than) camera resolution. Their approximate radius is smaller than 50lm associated with some motion blur. Their speed reaches UOð10Þ m/s. A splash rises to open a crater to the air (t0:80–2 ms) and forms a bubble at the sur- face (t5–17:5 ms). The speed of the splash sheet is less than 10 m/s, and the associated droplets have a relatively large size (several pixels, Oð100Þlm, marked by a dashed square att¼5 ms). The crater keeps its hemispherical shape until its bottom moves upward (t17:5 ms).
This surface rupture is a unique phenomenon (see alsoAppendix C) and characterizes the following fluid dynamics including aerosol formation. Figure 6(b)shows the depth of craterdas a function of time. Thedvalue increases rapidly in the early stage and then slows down. The dvalue is compared with a power-lawd/t0:39 (inset), corresponding to an experimental value from a firecracker explosion at a water surface.18While 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 thed 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 FIG. 4.Illustrations for the three different cavity dynamics.20(a)Explosion cavity,
(b)elongated cavity, and (c)oscillating cavity.
FIG. 5.(a) Cavity types plotted as a function ofhandR. The solid line showsh=R¼1, and the dash-dotted lines representh=R¼0:5 and 1.5.31(b) Cavity types plotted as a function ofh/Rand temperature. The emergence of regimes is nearly independent of temperature. The cavity positioning (bothRandh) is rather important. The same lines and legend in (b) are used for (a). The error bars represent the estimated uncertainty for the image analysis.
[marked by a circle inFig. 6(c)] was achieved att¼0.5–0.8 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 inFig. 6(d), where we obtain a peak frequency of1.4 kHz.
C. Elongated cavity
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 (t¼2–10 ms) as observed in the cavitation experiments near the free surface.26We 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 of1:7 m/s from a linear fit to the data inFig. 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 inFig. 7(e), where we obtain a peak fre- quency of1.4 kHz. The linear frequency of the bubble36can be esti- mated by
fm¼ 1 2pR
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3cDP
q þ2ð3c 1Þr qR s
; (1)
where the maximum radius of the bubbleR5:55 mm, the poly- tropic gas constantc¼1:4, and the pressure differenceDP¼Patm
Pv84 kPa. The oil density and surface tension at 200C are
assumed to beq807 kg/m3andr2102mN/m, respectively.23 Thus, fm0:6 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 fre- quency 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 (t¼2 ms). A daughter liquid jet forms inside the bubble, and a daughter droplet emerges in the oil (t¼10–14 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 oscil- lating cavity in time as highlighted in the discussion section and Fig. 9(a)(Multimedia view).
D. Oscillating cavity
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 t0:1 ms. The bubble growth shows a multi-step explosion during the formation stage until t3 ms [see alsoFig. 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 FIG. 6.(a) High-speed images of the explosion cavity at the approximate temperature of 203C. Black arrows point to the water droplet on the wire (i) and a vapor bubble formed on the droplet surface (ii). Squares highlight the aerosols observed att¼0.80 ms andt¼5 ms. (b) A depth of cavitydas a function of time. The inset shows the fitting withd/t0:39reported in the literature.18(c) The acoustic signals recorded above the beaker as a function of time,Dtcorresponds to the camera frame rate (0.05 ms). The cir- cle shows a peak acoustic amplitude when the crater opens up to the air. (d) The power spectrum for the acoustic signals, where the fundamental frequency (1:4 kHz) is marked by a dashed line. Multimedia view:https://doi.org/10.1063/5.0088065.1
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 inFig. 10(a)(the third frame from the left). Recently, a simi- lar type of jet was reported to have formed due to Rayleigh–Taylor instability upon bubble oscillation.37The 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 bub- ble then breaks up into numerous bubbles, and the overall oscillation is attenuated (stage 3).
The audio signalsp(V) recorded by using a microphone are shown inFig. 8(c). In this case, the time offset was aboutDt0.05 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 inFigs. 8(a) and8(b). In stage 2, a significantly large sound was detected. It attenu- ates in time and leads to stage 3 (not shown). In stage 3, the main bubble is disintegrated into several small bubbles. Applying the spectrum analy- sis to the acoustic signal for the first 5 ms in stage 2 [Fig. 8(d)], we found the fundamental frequency peak at0.8 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 agree- ment indicates that the periodic oscillation of the bubble dominates the sound generation. In the spectrum analysis, the second harmonic fre- quency of1.6 kHz was observed and is also visible inFig. 8(c).
V. DISCUSSION
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 inFig. 6(c)has the fun- damental frequency of1.4 kHz [Fig. 6(d)], which is similar to that for the elongation cavity reported in Fig. 7(e). Considering the fre- quencies 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 inFigs.
6(c)and7(d)is similar to each other, the location of the microphone forFig. 7(d)(6 cm from the oil surface) was much closer to the oil surface when compared to that forFig. 6(c)(16 cm from the oil sur- face). The high-speed video observations suggest that it is likely related FIG. 7.(a) High-speed images of the elongated cavity at the approximate temperature of 195C.20White arrows point to the water droplet at the beginning (i), a wave front propagating on the expanding bubble (ii), and daughter jet and droplet formed on the cavity (iii). (b) The projected area of the cavity,A, as a function of time. (c) The height of the jetHjas a function of time. The adopted linear fitting shows the approximate jet speed (1:7 m/s). (d) The acoustic signal as a function of time. (e) The power spectrum for the acoustic signals, where the fundamental frequency (1:4 kHz) is marked by a dashed line. Multimedia view:https://doi.org/10.1063/5.0088065.2
to the size of the crater/bubble. As shown inFig. 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 inFig. 5(a).
The maximum radiusRof 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 theRvalue, pos- sibly because it undergoes the multi-step explosion, leading to the for- mation 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 ath8 mm and led to the vio- lent 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 fre- quency for the elongated cavity was1.5 kHz [Fig. 9(c)], which is per- haps related to the initial dynamics of the bubble, whereas the fundamental frequency for the oscillating cavity (1.1 kHz) is domi- nated by the bubble oscillation [Fig. 9(d)]. The second harmonic fre- quency 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 inFig. 9(b)] can also be an indicator.
Related to the oscillating cavity, we show two with different levels of surface disturbance. As discussed inFig. 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 sur- face 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 bub- bles 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.
VI. CONCLUSION
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 visu- alized 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, wherehand Rare the locations of the water droplet and the maximum radius of the bub- ble (Fig. 5). Within the parameter space tested, the emergence of FIG. 8.(a) High-speed images of the oscillating cavity at the approximate temperature of 197C. (b) The projected area of the cavity,A, as a function of time. Dashed line splits bubble dynamics into two regimes. (c) The acoustic signals as a function of time. (d) The power spectrum for the acoustic signals, where the fundamental frequency (0:8 kHz) is marked by a dashed line. The inset shows the spectrum for the projected areaAshown in (b). The fundamental frequency was0:8 kHz. Multimedia view:
https://doi.org/10.1063/5.0088065.3
regimes is nearly temperature independent, suggesting that the stand-off parameterh/Rlargely determines how the bubble behaves and how the heated oil is expelled. Typical high-speed images of cra- ter/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 inFig. 4. The oscillating cavity is espe- cially 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 gener- ation or oil spattering is a potential application.
FIG. 10.(a) High-speed images of the oscillating cavity with at least one air bub- ble on the oil surface.20The oil tempera- ture was203C. A jet forms from the bubble at t¼4.8 ms. (b) High-speed images of the oscillating cavity without noticeable surface disturbance. The oil temperature was197C. The jet forma- tion is not visible, and the bubble dimin- ishes att¼20 ms.
FIG. 9.(a) High-speed images of the elongated cavity followed by the oscillating cavity at the approximate temperature of 197C. The first bubble forms on the droplet surface (i), leading to a weakly elongated cavity. A daughter droplet forms on the cavity wall (ii). The secondary bubble then forms (iii), subsequently oscillating violently. (b) The acous- tic signals as a function of time. Squares correspond to the signals used for spectrum analysis in (c) and (d). (c) The spectrum for the elongated cavity regime where the funda- mental frequency was approximately 1.5 kHz. (d) The spectrum for the oscillating cavity regime where the fundamental frequency was approximately 1.1 kHz. Multimedia view:
https://doi.org/10.1063/5.0088065.4
ACKNOWLEDGMENTS
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.
AUTHOR DECLARATIONS Conflict of Interest
The authors have no conflicts to disclose.
DATA AVAILABILITY
The data that support the findings of this study are available from the corresponding author upon reasonable request.
APPENDIX A: PRELIMINARY EXPERIMENTS
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 12shows 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 (0–20lL) and hot oil tem- perature (150–210C). 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 distin- guishable 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 situa- tions including bubble–bubble interaction is needed, where this manu- script provides a fundamental understanding.
APPENDIX B: FRYING A BATTER DROPLET
Figure 14shows 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 (t¼4 ms). In contrast, a batter droplet continuously forms bubbles at its surface, and large cavity dynamics were not observed.
FIG. 12.Bubble formation from the chop- stick at approximately 152C (a), 179C (b), and 210C (c).20
FIG. 11.The set-up for preliminary experiment with the chopstick (a) and wet paper (b).
APPENDIX C: RUPTURING PROCESS OF THE FREE SURFACE
The surface rupture upon theexplosion cavityis a unique phenome- non, thus worth observing in a detail.Figure 15shows the detailed view of the free surface rupture process; the first 0.55 ms for the data that were presented inFig. 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 pos- sibly 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 whent0:3 ms as commented in the paper.
FIG. 13.Multi cavities found in the paper set up, where a piece of paper was held by a paperclip. The designated oil temper- ature was 200C. Water volume used was 200lL. The time offsetDtwas set at the timing for the camera trigger. An explosion cavityaccompanied by a splash was filmed at 40 ms. A transition between theelongatedandoscillating cav- itieswas observed at70–80 ms. A thick jet was formed after these cavity dynam- ics. Anelongated cavitywas also found in the same experiment while forming a thin jet and droplets to the air at380–400 ms. Multimedia view: https://doi.org/
10.1063/5.0088065.5
FIG. 14.Bubble formation from a droplet of water (a) and batter fluid (b). The oil temperature was approximately 194C (a) and 205C (b).
FIG. 15.Detailed view of free surface explosion shown inFig. 6(a). The very left panel showst¼0 ms. The time interval between frames is 0.05 ms. A square denotes the dome that changing its curvature. An arrow marks the sheet surface pattern.
REFERENCES
1“Some other methods are also known and used. Some of them appear in the online resources and even comic books (e.g., isbn: 978-4-06-300319-2).”
2C. Schinharl, S. Dickhaut, and K. Lane,Basic Asian: Everything You Need for Yin and Yang in the Kitchen(Silverback Books, 2003), p. 26.
3B. Farkas and L. Hubbard, “Analysis of convective heat transfer during immer- sion frying,”Drying Technol.18, 1269–1285 (2000).
4S. Asokapandian, G. J. Swamy, and H. Hajjul, “Deep fat frying of foods: A criti- cal review on process and product parameters,”Crit. Rev. Food Sci. Nutr.60, 3400–3413 (2020).
5X. Fan, C. Wang, F. Guo, B. Chen, and M. Li, “Water droplet impact on high- temperature peanut oil surface: The effects of droplet diameter and oil temper- ature,”Int. J. Therm. Sci.159, 106601 (2021).
6S. L. Manzello, J. C. Yang, and T. C. Journal, “On the interaction of a liquid droplet with a pool of hot cooking oil,”Fire Saf. J.38, 651–659 (2003).
7M. Lan, X. Wang, P. Zhu, and P. Chen, “Experimental study on the dynamic process of a water drop with additives impact upon hot liquid fuel surfaces,” in Energy Procedia(University of Science and Technology of China, Hefei, China, 2015), pp. 173–176.
8M. Xu, C. Wang, and S. Lu, “Experimental study of a droplet impacting on a burning fuel liquid surface,”Exp. Therm. Fluid Sci.74, 347–353 (2016).
9M. A. Alchalabi, N. Kouraytem, E. Q. Li, and S. T. Thoroddsen, “Vortex- induced vapor explosion during drop impact on a superheated pool,”Exp.
Therm. Fluid Sci.87, 60–68 (2017).
10J. O. Marston and C. Li, “Jet dynamics during vaporization of water drops in hot oil films,”Exp. Therm. Fluid Sci.109, 109873 (2019).
11R. Kumar, Lokesh, and A. K. Das, “Fluidics of an immiscible drop impact onto a hot oil film,”Phys. Fluids34, 012108 (2022).
12Y. Zhang and Z. Xu, “‘Fizzics’ of bubble growth in beer and champagne,”
Elements4, 47–49 (2008).
13T. Watamura, F. Iwatsubo, K. Sugiyama, K. Yamamoto, Y. Yotsumoto, and T.
Shiono, “Bubble cascade in Guinness beer is caused by gravity current insta- bility,”Sci. Rep.9, 5718–5719 (2019).
14J. Rodrıguez-Rodrıguez, A. Casado-Chacon, and D. Fuster, “Physics of beer tapping,”Phys. Rev. Lett.113, 214501 (2014).
15V. Manticˇ-Lugo, A. Cayron, P. T. Brun, and F. Gallaire, “Beer tapping:
Dynamics of bubbles after impact,”J. Phys.656, 012029 (2015).
16Z. Pan, A. Kiyama, Y. Tagawa, D. J. Daily, S. L. Thomson, R. Hurd, and T. T.
Truscott, “Cavitation onset caused by acceleration,”Proc. Nat. Acad. Sci.114, 8470–8474 (2017).
17M. Poujol, R. Wunenburger, F. Ollivier, A. Antkowiak, and J. Pierre, “Sound of effervescence,”Phys. Rev. Fluids6, 013604 (2021).
18A. Benusiglio, D. Quere, and C. Clanet, “Explosions at the water surface,”
J. Fluid Mech.752, 123–139 (2014).
19M. J. Xu, J. Q. Zhang, C. P. Wu, C. H. Li, X. Chen, and S. X. Lu, “Collision dynamics of a single water droplet impinging on a high-temperature pool of oil,”Acta Mech.229, 1567–1577 (2018).
20A. Kiyama, R. Rabbi, Z. Pan, S. Dutta, J. Allen, and T. Truscott, “Listen to your tempura!” inGallery of Fluid Motion(Online Video, 2021), V0087.
21G.-B. Chen, Y.-H. Li, C.-H. Lan, H.-T. Lin, and Y.-C. Chao, “Micro-explosion and burning characteristics of a single droplet of pyrolytic oil from castor seeds,”Appl. Therm. Eng.114, 1053–1063 (2017).
22H. R. Katragadda, A. Fullana, S. Sidhu, and A. A. Carbonell-Barrachina,
“Emissions of volatile aldehydes from heated cooking oils,”Food Chem.120, 59–65 (2010).
23S. N. Sahasrabudhe, V. Rodriguez-Martinez, M. O’Meara, and B. E. Farkas,
“Density, viscosity, and surface tension of five vegetable oils at elevated tempera- tures: Measurement and modeling,”Int. J. Food Prop.20, 1965–1981 (2017).
24O. Supponen, D. Obreschkow, M. Tinguely, P. Kobel, N. Dorsaz, and M.
Farhat, “Scaling laws for jets of single cavitation bubbles,”J. Fluid Mech.802, 263–293 (2016).
25J. O. Marston, M. M. Mansoor, S. T. Thoroddsen, and T. T. Truscott, “The effect of ambient pressure on ejecta sheets from free-surface ablation,”Exp.
Fluids57, 1–10 (2016).
26G. L. Chahine, “Interaction between an oscillating bubble and a free surface,”
J. Fluids Eng.99, 709–709 (1977).
27J. R. Blake and D. C. Gibson, “Growth and collapse of a vapour cavity near a free surface,”J. Fluid Mech.111, 123 (1981).
28O. Supponen, D. Obreschkow, P. Kobel, and M. Farhat, “Detailed jet dynamics in a collapsing bubble,”J. Phys.656, 012038 (2015).
29P. Koukouvinis, M. Gavaises, O. Supponen, and M. Farhat, “Simulation of bub- ble expansion and collapse in the vicinity of a free surface,”Phys. Fluids28, 052103 (2016).
30A. Kiyama, T. Shimazaki, J. M. Gordillo, and Y. Tagawa, “Direction of the microjet produced by the collapse of a cavitation bubble located in a corner of a wall and a free surface,”Phys. Rev. Fluids6, 083601 (2021).
31T. Li, A.-M. Zhang, S.-P. Wang, S. Li, and W.-T. Liu, “Bubble interactions and bursting behaviors near a free surface,”Phys. Fluids31, 042104 (2019).
32A. Kiyama, Y. Tagawa, K. Ando, and M. Kameda, “Effects of a water hammer and cavitation on jet formation in a test tube,”J. Fluid Mech.787, 224–236 (2016).
33S. Brown and P. R. Williams, “Bubble collapse and liquid jet formation in non- Newtonian liquids,”AICHE J.45, 2653–2656 (1999).
34J. O. Marston and S. T. Thoroddsen, “Laser-induced micro-jetting from armored droplets,”Exp. Fluids56, 1–10 (2015).
35J. Rossello, H. Reese, and C. Ohl, “Dynamics of pulsed laser-induced cavities on a liquid–gas interface: From a conical splash to a ‘bullet’ jet,”J. Fluid Mech.
939, A35 (2022).
36C. Brennen,Cavitation and Bubble Dynamics(Oxford Univ Press, 1995).
37Q. Zeng, S. R. Gonzalez-Avila, S. T. Voorde, and C.-D. Ohl, “Jetting of viscous droplets from cavitation-induced Rayleigh–Taylor instability,”J. Fluid Mech.
846, 916–943 (2018).
38W. Bouwhuis, X. Huang, C. U. Chan, P. E. Frommhold, C.-D. Ohl, D. Lohse, J.
H. Snoeijer, and D. van der Meer, “Impact of a high-speed train of microdrops on a liquid pool,”J. Fluid Mech.792, 850–868 (2016).
