arXiv:1911.03175v2 [physics.flu-dyn] 22 Jan 2020 a) Matters Surfactant Why and Bubbles Soap of Merging Bubbles Soap of Merging taevre ntikeswt utpemxm n minima. and maxima multiple sub- a with and thickness bubble in a or varies bubbles strate the between gap a where called ipesosavrigfimtikes h eta einis radially region thickens central and The thinnest thickness. the film varying a shows wimple rsuesc httefimsrae trc ahother each attract surfaces film disjoining the negative that a such and speed pressure approaching slow very a from esi h rdcino om n stu rca o many treatment for water crucial waste thus is as and such foams processes of industrial production the in cess h iudfimi eo rtcltikesvan-der-Waals thickness film critical shared the of a rupture below the to lead is forces film liquid the oti muiissc seetoye,wihafc h c the affect bubbles which of electrolytes, lescence as such impurities contain ipedfraino h iudfilms liquid the merging of the deformation affects ripple other each approach process bubbles the which separation oeue aagn osefc h l drainage film the act effect surface flows of Marangoni concentration molecules varying spatially of i in- The Additionally, presence by rheology. governed surface are ruptures. and film eventually forces foam termolecular the and of drains stability the time and drainage over that film gle omto ftelqi ls ttcsraefre,rheolo forces, surface static hydrodynamics films, and liquid the of tw formation the de- merging surface thereby the by out films of driven radially distance bridge spreads closest connecting quickly the The tension liq- at two films. occur the soap may formed connecting This bridge films. liquid uid van- a attractive entrapped create thin the sufficiently forces from is Waals sheet up gas built this Once pressure gas. the by slightly deform bubbles. fluid filmed thin the merging addressed two have of studies microscopi mechanics few and very structure foams of growth, properties the for process alescence lcrncmi:[email protected] mail: Electronic h olsec ftosa ube safnaetlpro- fundamental a is bubbles soap two of coalescence The eie h iudpoete,as h pe under speed the also properties, liquid the Besides fe h olsec ftebbls hysaeasin- a share they bubbles, the of coalescence the After hntosa ube prahec te,terfilms their other, each approach bubbles soap two When 3 h olsec ftetobblsivle h de- the involves bubbles two the of coalescence The . 9–11 arcaPfeiffer, Patricia 1) 2) 3) Singapore Singapore, 637371 f irbblsrsligi rca edii structur dendritic hig fractal sufficient a for in However resulting microbubbles shape. off circular a Raylei into a We initially heals of layer. causes takes merging acceleration gas rapid high separating the the the and spot into uniform single accelerated broug a rapidly on are is bridged bubbles rim are soap sheet two gas mechani from a fluid films by fundamental liquid a the is study bubbles imental soap two of merging The 2020) January 23 (Dated: Singapore 2 nttt o hsc,Ot o urceUiest Magdeb University Guericke von Otto Physics, for Institute iiino hsc n ple hsc,Sho fPhysical of School Physics, Applied and Physics of Division o nryEetoi ytm,SnaoeMTAlac for Alliance Singapore-MIT Systems, Electronic Energy Low hscnla oapml,wml,dml,or dimple, wimple, pimple, a to lead can This . ept h motneo h opbbl co- bubble soap the of importance the Despite . 8,9 4–6 too. , . 1 igu Zeng, Qingyun 10,13 ipe r interfaces are Ripples . 10,11 iperesults pimple A . 3 2 ellqi films liquid Real . egHuTan, Hau Beng 1 7 rfoam or 10,12 Once . the n der- A . oa- ive gy, o c 3 n lu-itrOhl Claus-Dieter and r,Mgeug316 Germany 39106, Magdeburg urg, fe coalescence. after e n ahmtclSine,NnagTcnlgclUnivers Technological Nanyang Sciences, Mathematical and ( process. play merging they hydrodynamic that the demonstrate in also part importa crucial we are bubbles, surfactants the photography While stabilize high-speed to observed. with instability out- studied an radially is and films process two ten- This the surface connecting bridge, ward. rim liquid a point-like accelerates a sion on connect films Once interferometry. two be through just revealed shape is its coalescence forms, fore dimple a Then velocity. approach low ufcatsdu oey uft ( sulfate ≥ dodecyl sodium surfactant i that potential. wire electric copper fixed a a with syringes on the held of tips wetted both nect t20-25 at ue ihtecplayrs ehdt be to method mea- rise been capillary has tension the surface with of sured coefficient their and mM 10 l smvdsol oad h rtwt rnlto stage translation a bub- with first second to- the the ( towards brought and slowly stationary are moved is they is bubbles ble way the this of Once One created diameter. gether. are in bubbles 12mm about soap to inflated two attached is bubble tip A syringe plunger. the the to on pressing by formed film flat Germany GmbH Wolf ≈ fe h otc ewe ubeadfilm remains and cascade bubble bubble a smaller between a show contact the means film after This flat a coalescence. partial with of merge which bubbles, Soap uigteiflto tnzl ftepatcsyringe plastic the of nozzle at inflation the during ta prahvlct of velocity approach an at /0,0s n luiae ihete ht ih sourc light white Ultra, dy- a Cube either The (Sugar with illuminated time and 1). (exposure frames/s camera 1/900,000s) 67,500 high-speed or Fig. a 22,500 at with and AX200) observed (Photron setup is coalescence experimental for of the material namics of supplementary film sketch (cf. soap a bubbles single two a forming the by connecting coalesce suddenly bubbles the mH Austria GmbH, ( source light herent otJc nui yigswt urcneto,Henke-Sa connection, Luer with syringes Insulin Soft-Ject 1mcoaiuao,Hlu arLbreaf Germany Laborbedarf, Saur Helmut micromanipulator, M1 eerhadTcnlg,Snaoe138602, Singapore Technology, and Research hTyo ntblt ftelqi i.A ae ie,the times, later At rim. liquid the of instability gh-Taylor 90 (GC) 99.0% h opbblsaecetdb ipn i ftesyringes the of tip dipping by created are bubbles soap The at bubbles soap two of merging the about report we Here, h ube r aeo nauosslto fteanionic the of solution aqueous an of made are bubbles The 2mW/cm ocnrtoso h ufcatteusal i pinches rim unstable the surfactant the of concentrations h hwta u otedml omto h eoiyi not is velocity the formation dimple the to due that show ttgte.Oc h iudlyr ntal separated initially layers liquid the Once together. ht h w iudfim rce.Teeyteconnecting the Thereby proceed. films liquid two the a rcs nfa omto.I h rsn exper- present the In formation. foam in process cal ◦ ) w ocnrtosaeue,nml and 5 namely used, are concentrations Two C). 2 .T vi lcrccagn ftetobubbles two the of charging electric avoid To ). rtclmclecnetain(m)71 mM 7-10 (cmc) concentration micelle critical , Wlsr wavelength laser, CW , 1 SI MRC,INC. AMERICA, USHIO W3-4Sre,Rihe Lasertechnik Roithner Series, CW532-04 noasa ouinadifltn the inflating and solution soap a into ) a) ≈ c/.Drn hsapproach this During 1cm/s. im-lrc,BioXtra Sigma-Aldrich, λ 14 = σ . 3n,intensity 532nm, S)o co- a or USA) , = 25 15 ± mN/m 2 econ- we ity, rim the ss, nt a e s - ) Merging of Soap Bubbles 2

2 mm (a) (b)

k=0 k=0 k=5 k=5 k=5 k=0 k=0 r r 4 mm -44 µs -44 µs 44 µs 200 µm (c) 1.2 before coalescence after coalescence 0.8

[µm] 0.4 d

178 µs 311 µs 444 µs 1067 µs 1511 µs 2489 µs 0.0

-400 -300 -200 -100 0 100 200 300 400 FIG. 1. Inclined side view of two merging soap bubbles. In the r [µm] magnified view at t = 44µs fringes can be observed in the area, (d) where the bubbles touch− each other. Time t = 0 corresponds to the start of the liquid bridge formation. The dashed circle at t = 44µs surrounds the the area where the merging started. After coalescence air d air the two bubbles share one film. D air and σ = 27 2mN/m for a 5 and 10mM SDS solution, re- spectively. We± measured their kinematic viscosity using an Ubbelohde viscometer, from which we calculated the dy- FIG. 2. (a) Interference fringes in the soap film preceding the coa- namic viscosity, which is 1.01 0.02mPas for both solutions. lescence and (b) in the frame after the coalescence (frame interval ± ∆t = 44µs).(c) From the fringes the spatial varying height of the air Figure 1 is composed of selected snapshots from a high- film can be calculated and is shown before (black squares) and after speed imaging sequence showing the process of two bubbles coalescence (red circles). (d) A sketch of the overall shape of the merging. At the top of the first frame the syringe tips and dimple. Note that the vertical scale is strongly stretched. the copper wire are visible. The bottom of this frame shows a darker area that is caused by liquid draining due to grav- ity. The first snapshot (t = 44µs) is taken shortly before the bridging occurs. A weak− fringe pattern is visible just be- the measurements are performed in transmission, the shortest fore the two bubbles merge. The dashed circle at t = 44µs distance has a bright fringe. That location is indicated in Fig. indicates the point where the liquid bridge has connected the 2a with an arrow and is the zeroth order fringe (k = 0). The two films. Between t = 44µs and t = 2489µs the two bubbles distance between bright fringes of λ/2n (n is the refractive merge. A compoundbubble is formed throughthe sharing of a index of the soap solution: n = 1.33) allows converting the liquid film. The merged film will grow until the angle between line drawn in Figs. 2a and 2b into a height map of the air gap before and just after coalescence, see Fig. 2c. The position the two bubbles becomes 120 ◦. The concentric structure after t = 1067µs occurs due to thickness differences in the film. of the fringes are determined by taking the mean gray values We are concerned with the initial process of film merging. along several lines through the fringe pattern. The maximum thickness of the air film is 1.0 0.1µm. Repeating the exper- For this we first want to understand the shape of the air gap ± separating the soap films. The interference fringes forming iment 50 times we find dimple heights between 0.4µm and prior to the coalescence event are observed in Figure 2a with 1.0µm at the moment of coalescence. The overall shape of an illumination of a continuous wave laser at λ = 532nm the gap between the two films is sketched in Fig. 2d. Please wavelength. We observe in a magnified view the two films note that the vertical axis is strongly magnified. with a spatial resolution of 22µm/pixel. Unfortunately, the We now discuss the growth of the merged films starting quality of the interference pattern is affected by the imaging from the location where the two films are bridged. Figure 3a and illumination through two soap films. Nevertheless, we shows a typical example of this merging dynamics. The dim- observe concentric and mildly distorted circles where the dis- pled region just before coalescence is indicated with a blue tances between two fringes is decreasing towards the center, dotted circle and the arrow indicates the location of the liq- which is consistent with the presence of entrapped air between uid bridge. Bridging always happens on the crest of the dim- the two soap films. Figure 2b just after coalescence demon- pled region as shown in Fig. 2. We see the rim expanding strates that the two films bridge between the crests of the dim- radially from the point of contact. Interestingly, that part of ple which is the shortest distance between the two films. Since the rim which travels through the dimpled region has a dis- Merging of Soap Bubbles 3

(a) (b) (c) top view spreading rim fringes

1 mm -40 µs 0 µs 40 µs r 500 µm 1 0 µs 44 µs 89 µs side view merging point air 80 µs 160 µs 240 µs air soap film air vrim vdimple

280 µs 340 µs 400 µs 133 µs 222 µs 1067 µs t

FIG. 3. Spreading of the merged films during the coalescence of two soap bubbles (a) with a concentration of [SDS]=5 mM and (b) with [SDS]=10 mM. The dark circle (blue dotted) in the first snapshot represents the fringe pattern. The films merge at t = 0 in (a) at the location indicated by the arrow and in (b) at the lower left side of the fringes. In (b) at t = 44 and 89 µs the smooth rim and the liquid bridge indicated with a blue circle and a red cross, respectively. The modulated rim that connects the two films propagates fastest through the dimpled region. (c) Sketch of the spreading rim from top and in side view. The rim propagates faster within the regime of the dimple (dashed blue circle) due to the higher curvature. In the side view the region which is already merged consists only of a singe film, whereas still two separate films exist ahead of the rim. torted and fuzzy front, while the part that travels outside is tia with the pressure gradient from surface tension, i.e. smooth and circular. Figure 3b shows a similar case with the only difference that the concentration of surfactant was dou- Du 1 2σ G = = ∇p 2 , (1) bled to [SDS]=10mM. The liquid bridge forms on the lower Dt −ρH ≈−ρH D left part of the dimpled region, again on a crest and the rim spreads circularly. In contrast the rim traveling through the where u is the velocity of the fluid particle in the rim, ρH is dimpled region reveals an instability or modulation with a the density of the liquid and ∇p the pressure gradient. The length scale of 44µm at t = 89µs after bridging. Small dark latter we estimate with the Laplace pressure in the cylindrical structures pinch-off from the modulated rim leaving behind rim of cross-section D and radius of curvature of D/2. In- 3≈ 3 radial streaks. These streaks of round objects emanate from serting suitable values for σ = 0.025N/m, ρ = 10 kg/m and 6 the slower parts of the modulated rim. Even after the rim has D = 1.6 10− m we obtain a high values for the acceleration · 7 2 t µ with G = 2 10 m/s . While viscosity counteracts this ac- left the field of view at = 1067 s in Fig. 3b, radial pointing · structures remain on the merged film. Figure 3c sketches the celeration we nevertheless expect this acceleration to act until process of film merging within the dimple (right) and outside viscosity has diffused. This picture has been confirmed with the dimple (left). The part of the rim with a radial modulation Volume of Fluid simulations in axisymmetry (cf. supplemen- has a non-uniform radial velocity. As a consequence the two tary material for details to the simulations). Figure 4 depicts a films cannot merge simultaneously at a distance r from the liq- simulation result for the parameters similar to the experiment uid bridge. Instead pockets of gas become entrapped during and accounting for viscous and compressible effects (solver their merging. This is consisted with the observation that the Interfoam from the OpenFOAM framework). Within 0.5µs round objects in Fig. 3b are formed between the slowest trav- the rim accelerates from 0 to a velocity of about 4.0m/s. eling parts and the fastest parts of the rim. Connecting these Now we argue that this extreme acceleration of the rim clues we suggest that the objects are microscopic bubbles en- from the liquid into the gas phase destabilizes the rim due 16,17 trapped by the non-homogeneousmerging of film. A close-up to the Rayleigh-Taylor instability . The most amplified 18 of the structured process is depicted in Fig. 3b at t = 44 and wavelength is √3λc with λc = pσ/(GρH ), see Ref. . Typ- 89 µs where the rim traveling to the left is marked with a blue ical experimental values lie between 44 µm (as in Fig. 3b at circle centered around the location of the liquid bridge (red t = 89µs) and 150 µm. Since the rim expands and hence the cross). Comparing the radius of the circle and the radius of length-scale of the instability, the most unstable mode (i. e. the modulated rim, it is clearly visible that the velocity in the how many lobes the rim has as a result of the instability) is dimpled regime is higher, i.e. 3.0 0.2m/s, whereas the ve- taken as a quantitative measure. We obtain values for the un- locity of the smooth rim is 2.5 0.2m/s.± The difference in the stable mode between 12 (as in Fig. 3a) and 44. Perturbations velocity can be attributed to the± varying curvature of the of the below a critical wavelength λc are stabilized by surface ten- 18 soap film inside and outside the dimple. Outside the two free sion. The critical wavelength can be calculated as soap films separate more rapidly than within the dimple. λc = pσ/G(ρH ρL), (2) −

We now address the mechanism destabilizing the rim’s cir- where ρH and ρL are the densities of the heavier (water) and cular shape. For this we estimate the acceleration G of rim lighter (air) fluids, respectively. Since ρH ρL, we can ne- ≫ due to surface tension σ. Ignoring viscosity we balance iner- glect ρL in equation (2). Merging of Soap Bubbles 4

10 The applied potential on the bubbles ensures reproducible results, however, a simple connection between the bubbles (i.e. a wire to exchange electric charges) yields the same re- 5

[µm] sults. In experiments without this potential, a deformation of r the rim is only observed by chance. We speculate that the bubbles are charged by inflating them. A similar effect was 0 15 10-3 10-2 10-1 100 investigated by Choi et al. , who observed that droplets be- 5.0 come charged during conventional pipetting. The closure of the distorted rim depends strongly on the SDS concentration: with increasing amount of SDS more bub- 2.5 ble pinch-off events are seen. However, when reaching the [m/s]

u critical micelle concentration, a further increase of the bub- ble formation does not occur. The detachment of tiny soap 0 bubbles from the rim is only possible, because more surface 10-3 10-2 10-1 100 7 active molecules are available than necessary for the current 5.0 X 10 surface. So the excess molecules can be used to create and stabilize a new surface in a much shorter time, which leads to ] 2 the pearling of the droplets. The pearling is more pronounced 2.5 directly after the formation of the liquid bridge than further [m/s away from the bridging point, since the distance of the films G increases with distance from the bridging point and thus the 0 closure dynamics slows down. 10-3 10-2 10-1 100 t [µs] The measured wavelength of the indentation agrees with an impulsively acting Rayleigh-Taylor instability and growth by radial expansion. The high acceleration of the liquid within FIG. 4. Numerical simulations of the development of the rim radius over time (top row) and reaches a velocity of 4.0m/s (center row). the first 50ns after the coalescence, which is confirmed by The rim accelerates within 0.5µs to a velocity of 4.0 m/s, i. e. that simulations, induces the instability. Since the instability al- results in an acceleration of 5 107 m/s2 (bottom row). Dimple height: ready occurs during bridging the instability timescale is con- 1.6 µm, film thickness: 5.5 µm.· sistent with the claim that the acceleration of the liquid is caus- ing the instability25–27. Structures similar to those described in the current work The acceleration G governs the dominant wavelength at the were already found in similar systems at the receding rim of rim, which strongly depends on the dimple height. With an bursting fluid films28,29 or during the impact of a droplet on 7 2 30 acceleration of G = 2 10 m/s λc is 0.7 µm. a fluid surface . Another work was provided by Thoraval et The instability already· occurs during≈ bridging, and thus a al., who investigated an impacting droplet on a liquid layer diameter of the liquid bridge of 7 µm with the initial wave- and found a formation of bubble rings in the impact region31. length of λc/√3 = 0.4µm would lead to a wavelength of Despite these structures look similar to those described in the 44 µm at a circumference of the rim of 2.4mm. Thus, λc current work, the mechanism of their formation differs. 0.7µm seems an appropriate value. ≈ In this work the coalescence of soap bubbles is studied. The Rayleigh-Taylor instability leads to a pearling of tiny Prior to their coalescence the bubbles form a dimple and en- soap bubbles from the rim if the indentation is sufficiently trap a tiny volumeof air. Upon merging,the rim of the spread- large. The indentation leads locally to a higher curvature of ing film is accelerated for a brief moment, simulations predict the rim and thus a higher propagation velocity of the highly less than 1µs. During that time a Rayleigh-Taylor instability curved parts. The curvature decreases due to the reunion of sets in resulting in an instability of the rim front. The velocity the water columns and thus the velocity decreases. The rim of the rim is higher in the area of the dimple, due to a higher becomes smooth after the propagation through the dimpled curvature in that regime and hence the velocity of the rim is area and remains circular. faster. Depending on the surfactant concentration the entrap- Upon the approach of two merging bubbles a dimple is ment of gas pockets is possible with increasing SDS concen- formed between them. This is a general phenomenon when tration. However above the cmc no further effect of the SDS bubbles or droplets approach either each other19–21 or a concentration on the instability of the rim is observed. substrate22–24. The computed height of the dimple calculated See supplementarymaterial for a sketch of the experimental using the Bragg equation agrees very well with the height in setup, details and snapshots of the simulations. other experiments23,24. The distance between the bubbles is The Deutsche Forschungsgemeinschaft, DFG, is acknowl- shortest at the rim of the dimple and the film thickness at edged for support within project DA 2108/1-1. this point decreases, such that attractive van-der-Waals forces become important and lead to a rapid decrease of the film 1B. B. Ferguson, C. Hinkle, and D. J. Wilson, “Foam Sep- 5,20 thickness . The point where the coalescence of the bubbles aration of Lead(II) and Cadmium(II) from Waste Water,” occurs is randomly distributed over the rim of the dimple. Separation Science 9, 125–145 (1974). Merging of Soap Bubbles 5

2A. K. Brown, A. Kaul, and J. Varley, “Continuous foaming for protein 16Y. Zhou, “Rayleigh–Taylor and Richtmyer–Meshkov instability induced recovery: Part II. Selective recovery of proteins from binary mixtures,” flow, turbulence, and mixing. I,” Physics Reports 720-722, 1 – 136 (2017). Biotechnol. Bioeng. 62, 291–300 (1999). 17Y. Zhou, “Rayleigh–taylor and richtmyer–meshkov instability induced 3R. G. Horn, L. A. D. Castillo, and S. Ohnishi, “Coalescence flow, turbulence, and mixing. ii,” Physics Reports 723-725, 1 – 160 (2017), map for bubbles in surfactant-free aqueous electrolyte solutions,” rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbu- Adv. Colloid Interface Sci. 168, 85 – 92 (2011). lence, and mixing. II. 4R. R. Dagastine, R. Manica, S. L. Carnie, D. Y. C. Chan, G. W. Stevens, 18D. Sharp, “An overview of Rayleigh-Taylor instability,” and F. Grieser, “Dynamic forces between two deformable oil droplets in Physica D 12, 3 – 18 (1984). water,” Science 313, 210–213 (2006). 19E. Klaseboer, J. Chevaillier, C. Gourdon, and O. Masbernat, “Film drainage 5R. Manica, J. N. Connor, S. L. Carnie, R. G. Horn, and D. Y. C. Chan, “Dy- between colliding drops at constant approach velocity: Experiments and namics of interactions involving deformable drops: Hydrodynamic dim- modeling,” J. Colloid Interface Sci. 229, 274 – 285 (2000). pling under attractive and repulsive electrical double layer interactions,” 20R. Manica, E. Klaseboer, and D. Y. C. Chan, “Dynamic interactions be- Langmuir 23, 626–637 (2007). tween drops – a critical assessment,” Soft Matter 4, 1613–1616 (2008). 6R. Manica, J. N. Connor, R. R. Dagastine, S. L. Carnie, R. G. Horn, and 21B. Liu, R. Manica, X. Zhang, A. Bussonnière, Z. Xu, G. Xie, and Q. Liu, D. Y. C. Chan, “Hydrodynamic forces involving deformable interfaces at “Dynamic interaction between a millimeter-sized bubble and surface mi- nanometer separations,” Phys. Fluids 20, 032101 (2008). crobubbles in water,” Langmuir 34, 11667–11675 (2018). 7S. I. Karakashev and A. V. Nguyen, “Effect of sodium dode- 22L. R. Fisher, E. E. Mitchell, D. Hewitt, J. Ralston, and J. Wolfe, “The cyl sulphate and dodecanol mixtures on foam film drainage: Ex- drainage of a thin aqueous film between a solid surface and an approaching amining influence of surface rheology and intermolecular forces,” gas bubble,” Colloids and Surfaces 52, 163 – 174 (1991). Colloids Surf. A 293, 229 – 240 (2007). 23R. C. A. van der Veen, T. Tran, D. Lohse, and C. Sun, “Direct measure- 8C. L. Henry and V. Craig, “Ion-specific influence of electrolytes on bubble ments of air layer profiles under impacting droplets using high-speed color coalescence in nonaqueous solvents,” Langmuir 24, 7979–85 (2008). interferometry,” Phys. Rev. E 85, 026315 (2012). 9V. V. Yaminsky, S. Ohnishi, E. A. Vogler, and R. G. Horn, “Stabil- 24M. H. W. Hendrix, R. Manica, E. Klaseboer, D. Y. C. Chan, and ity of Aqueous Films between Bubbles. Part 1. The Effect of Speed on C.-D. Ohl, “Spatiotemporal evolution of thin liquid films during im- Bubble Coalescence in Purified Water and Simple Electrolyte Solutions,” pact of water bubbles on glass on a micrometer to nanometer scale,” Langmuir 26, 8061–8074 (2010). Phys. Rev. Lett. 108, 247803 (2012). 10D. Y. C. Chan, E. Klaseboer, and R. Manica, “Film drainage 25R. D. Richtmyer, “Taylor instability in shock acceleration of compressible and coalescence between deformable drops and bubbles,” fluids,” Commun. Pure Appl. Mathematik 13, 297–319 (1960). Soft Matter 7, 2235–2264 (2011). 26J. Ding, J. Li, R. Sun, Z. Zhai, and X. Luo, “Convergent Richt- 11 S. C. Ozan and H. A. Jakobsen, “On the effect of the myer–Meshkov instability of a heavy gas layer with perturbed outer in- approach velocity on the coalescence of fluid particles,” terface,” J. Fluid Mech. 878, 277–291 (2019). Int. J. Multiph. Flow 119, 223 – 236 (2019). 27Y. Zhou, T. T. Clark, D. S. Clark, S. Gail Glendinning, M. Aaron Skinner, 12 D. Valkovska, K. Danov, and I. Ivanov, “Surfactants role on the deforma- C. M. Huntington, O. A. Hurricane, A. M. Dimits, and B. A. Remington, tion of colliding small bubbles,” Colloids Surf. A 156, 547 – 566 (1999). “Turbulent mixing and transition criteria of flows induced by hydrodynamic 13 L. Y. Clasohm, J. N. Connor, O. I. Vinogradova, and R. G. instabilities,” Physics of Plasmas 26, 080901 (2019). Horn, “The "wimple": Rippled deformation of a fluid drop caused 28É. Reyssat and D. Quéré, “Bursting of a fluid film in a viscous environ- by hydrodynamic and surface forces during thin film drainage,” ment,” Europhys. Lett. 76, 236–242 (2006). Langmuir 21, 8243–8249 (2005). 29H. Lhuissier and E. Villermaux, “Soap films burst like flapping flags,” 14 G. Pucci, D. M. Harris, and J. W. M. Bush, “Partial coalescence of soap Phys. Rev. Lett. 103, 054501 (2009). bubbles,” Phys. Fluids 27, 061704 (2015). 30S. T. Thoroddsen, M.-J. Thoraval, K. Takehara, and T. G. Etoh, 15 D. Choi, H. Lee, I. S. Kang, G. Lim, D. S. Kim, K. H. Kang, et al., “Sponta- “Micro-bubble morphologies following drop impacts onto a pool surface,” neous electrical charging of droplets by conventional pipetting,” Scientific J. Fluid Mech. 708, 469–479 (2012). reports 3, 2037 (2013). 31M.-J. Thoraval, K. Takehara, T. G. Etoh, and S. T. Thoroddsen, “Drop impact entrapment of bubble rings,” J. Fluid Mech. 724, 234–258 (2013).