High-frequency acoustic droplet vaporization is initiated by resonance
HHigh-frequency acoustic droplet vaporizationis initiated by resonance
Guillaume Lajoinie ∗ , Tim Segers ∗ , and Michel Versluis Physics of Fluids Group, MESA+ Institute for Nanotechnology,Technical Medical (TechMed) Center,University of Twente, P.O. Box 217,7500 AE Enschede, The Netherlands
Abstract
Vaporization of low-boiling point droplets has numerous applications in combustion, processengineering and in recent years, in clinical medicine. However, the physical mechanisms governingthe phase conversion are only partly explained. Here, we show that an acoustic resonance canarise from the large speed of sound mismatch between a perfluorocarbon microdroplet and itssurroundings. The fundamental resonance mode obeys a unique relationship kR ∼ ∗ Both authors contributed equally to this manuscript a r X i v : . [ phy s i c s . f l u - dyn ] F e b aporization of low-boiling point droplets is omnipresent in today’s society with applica-tions in renewable energy and energy storage [1], combustion [2], intumescent fire-protectivecoatings [3], and recently in clinical medicine [4, 5]. Deterministic vaporization can be ini-tiated by heat or negative pressure, and by combinations thereof [6], which allows dropletvaporization to be triggered by laser light [7, 8], ultrasound [9], neutrons [10], and pro-tons [11]. Ultrasound-triggered phase-change of superheated nano- and microdroplets isknown as acoustic droplet vaporization (ADV) [12–15]. ADV is of great interest for medicinesince submicrometer-sized surfactant-stabilized droplets, or nanodroplets, have been shownto be able to extravasate leaky tumor vasculature thereby passively accumulating withinthe tumor [16, 17]. Upon phase change, the formed bubbles can perform therapeutic actionsuch as local drug delivery and sonoporation [18–20].The interaction of ultrasound with a low-boiling point droplet has been subject to exten-sive study aiming at understanding the underlying physical mechanisms driving nucleation.Experimentally, it has been found that a prominent peak negative pressure (PNP) nucleationthreshold exists above which the nucleation probability increases with the acoustic pressureamplitude and that this threshold, counterintuitively, lowers with an increase in ultrasoundfrequency and with a decrease in ambient pressure [9, 12, 21–30]. These observations arein line with what is predicted from both classical nucleation theory [31] and superhamonicfocusing [23, 32], and by the combination of the two [33, 34]. Superharmonic focusing re-sults from the focusing of higher harmonics with wavelengths on the order of the dropletdiameter that are generated through nonlinear propagation of the transmitted ultrasoundwave [32]. However, the required nonlinear propagation in tissue is dramatically lower fromthat in water due to the two orders of magnitude lower ratio of acoustic nonlinearity toattenuation, or Gol’dberg number [35]. This severely limits the effectivity of ADV by su-perharmonic focusing in vivo . In this Letter, a physical ADV nucleation mechanism basedon an acoustic resonance of the droplet is presented that has been overlooked until now.The theoretical resonance behavior is experimentally validated and its role in lowering thevaporization threshold is elucidated using classical nucleation theory. Resonant ADV offersan efficient approach for in vivo applications and adds to our fundamental understanding ofacoustic droplet vaporization.Here we will give the main results of the derivation; all details can be found in theSupplementary Information SI.1. The system consists of a perfluoropentane (PFP) droplet2medium 1) immersed in water (medium 0) considered to be of infinite size. We assumea purely spherical geometry. To calculate the resonance behavior we couple the pressureon the inside of the droplet interface p ( R in , t ) to the external acoustic driving pressure p A ( t ). The droplet is assumed to be small compared to the wavelength in water λ and theacoustic pressure can be considered homogeneous around the droplet. Integration of the themomentum equation in water then gives: p ( R out , t ) = ( p atm + p A ( t )) + ρ (cid:18) R ¨ R + 32 ˙ R (cid:19) , (1)with p ( R out , t ) the pressure on the outside of the droplet interface. p atm is the atmosphericpressure, R ( t ) is the droplet radius, and its overdots represent the interface velocity andacceleration, respectively. The pressure jump across the interface is expressed using thenormal stress balance: p ( R in , t ) − p ( R out , t ) = 4( µ − µ ) ˙ RR + 2 σR , (2)with µ i the viscosity of medium i . While in the analogous derivation of the Rayleigh-Plessetequation for bubbles the equation is closed by the highly compressible and uniform gaspressure [36], here we need to evaluate the complete acoustic pressure distribution withinthe droplet. A classical acoustic derivation of the particle velocity v leads to the well-knownspherical Bessel equation: x ∂ v∂x + 2 x ∂v∂x + ( x − v = 0 . (3)Here, x = k r , with k = ω/c the wavenumber, c the speed of sound in the droplet, and r the radial coordinate. Avoiding the unphysical divergence at r = 0, the solution to Eq. (3)is a spherical Bessel function of the first kind: v ( r, t ) = f ( t ) j ( x ) = f ( t ) sin x − x cos xx . (4)Writing X = k R , the boundary condition at the droplet interface v ( R, t ) = ˙ R yields: v ( r, t ) = ˙ R j ( x ) j ( X ) . (5)The pressure distribution is then found by inserting Eq. (5) in the mass conservation andcompressibility equation and using the Bessel function recurrence relation j (cid:48) ( x ) = j ( x ) − j ( x ) /x : ∂p∂t = − β (cid:18) ∂v∂r + 2 vr (cid:19) = − ρ k c ˙ R j ( x ) j ( X ) , (6)3here β = 1 /ρ c is the compressibility of the droplet. Note that, owing to the j ( x ) = sinx/x sinc term, the pressure amplitude will always be maximum in the center of thedroplet. Integrating Eq. (6) for small oscillation amplitudes ( R = R (1 + (cid:15) ), (cid:15) (cid:28)
1) with R the resting radius and X = k R , with the initial boundary condition p ( r,
0) = p atm +2 σ/R at t = 0 and evaluating in r = R yields: p ( R in , t ) = ( p atm + 2 σ/R ) − ρ k c j ( X ) j ( X ) ( R − R ) . (7)Note that this approximation only holds when j ( X ) is not near its zero-crossing. Combin-ing Eqs. (1), (2) and (7) now gives the droplet dynamics equation: ρ (cid:18) R ¨ R + 32 ˙ R (cid:19) = − ρ k c j ( X ) j ( X ) R (cid:32) − R R + ˙ Rc (cid:33) − µ − µ ) ˙ RR − σ (cid:18) R − R (cid:19) − p A ( t ) . (8)The reradiated pressure scattered by the droplet induces a compression of the surroundingmedium. The effect of acoustic reradiation on the droplet dynamics can be expressed by anadditional pressure term Rc ∂p∂t at r = R [37], effectively adding a damping term to the set ofequations. The above equations can also be extended to include the acoustic interaction witha rigid wall through the addition of a pressure term ρ ∂∂t (cid:16) R ˙ R d (cid:17) representing the reflectedscattering, with d the distance to the wall [38]. For a droplet at the wall, d = R , and theleft-hand side of Eq. 8 takes the form ρ (cid:16) R ¨ R + 2 ˙ R (cid:17) , see SI.2. Equation (8) can be solvednumerically to obtain the resonance behavior of the system. The pressure in the center ofthe droplet can be obtained by re-evaluating Eq. (6) in r = 0 instead of r = R : p drop = ( p atm + 2 σ/R ) − ρ k c ( R − R ) j ( X ) . (9)Linearization of Eq. (8) gives a relation between the angular eigenfrequency of the droplet ω and its resting radius: ρ ( ω R ) = ρ ω R c c ω R − cot ( ω R c ) + 2 σR . (10)Using a first-order expansion cot ( z ) (cid:39) /z − z/ O ( z ) and by neglecting the interfacialtension term, Eq. (10) reduces to a simple classical form: f (cid:39) πR (cid:115) ρ c ρ , (11)4 b p d r o p / p A radius (μm)
52 201.5234
50 MHz100 MHz 25 MHz 10 MHz radius (μm) f R [ M H z ] droplet at a rigid wall bubble in free fielddroplet in free field FIG. 1: (a) Calculated theoretical resonance curves for different driving frequencies. (b) Calculatedresonance frequency f R as a function of size: droplet in free-field (red), droplet at a rigid wall (black)and bubble in free-field (blue). with f = ω / π the eigenfrequency of the droplet. The same approach leads to an expressionfor the damping of the system in canonical form: δ = ω R c + 2( µ − µ ) ρ ω R . (12)As a result of the negligible contribution of viscous damping, which is three orders of mag-nitude smaller than the first term in Eq. (12), this then further reduces to: δ (cid:39) c c (cid:114) ρ ρ . (13)For a droplet at the wall the linearization simply adds a prefactor (cid:112) / ODE45 solver in Matlab and are displayed in Fig. 1(a). The physical parameters for PFPand water that were used for the calculations are listed in SI.3 and were extracted from[39–41]. The resonance frequency f R is plotted against the droplet size in Fig. 1(b) for a5roplet in free-field and for a droplet against a rigid wall. Two direct results from theseplots are that (1), unlike superharmonic focusing, the acoustic resonance strength has verylittle dependency on droplet size (see also SI.4) and (2), the resonance is expected to havea high quality factor and a frequency about 50 times higher than that of free gas bubbles,see the corresponding Minnaert bubble resonance frequency f M = 3 . µ mMHz /R plottedin Fig. 1(b) [36].Owing to the high eigenfrequencies expected, the response of PFP droplets was mea-sured experimentally at frequencies of 19.6 and 45.4 MHz. The droplets were resting onthe piezoelectric substrate on which surface acoustic waves (SAW) were generated using aninterdigitized transducer (IDT), see Fig. 2(a). In contact with water, the SAW generates alongitudinal bulk acoustic wave at the Rayleigh angle θ R ≈ ◦ [42–44], see Fig. 2(b). Theuse of a SAW device prevents any nonlinear propagation in the bulk of the medium, leavinga purely sinusoidal excitation. Straight electrode IDTs with a single aluminum electrodepair per wavelength (60 pairs, thickness of 750 nm, aperture of 1 cm) were fabricated on a128 ◦ rotated Y-cut X-propagating lithium niobate (LiNbO , Roditi, United Kingdom) waferusing standard soft lithography techniques. The IDTs were actuated by a 50-cycle sinu-soidal ultrasound pulse generated by a waveform generator (model 8026, Tabor Electronics)connected to a 50 dB linear power amplifier (350L, E&I). A sound absorbing silicone rub-ber (PDMS, Dow Corning) was placed both below and above the end of the piezoelectricsubstrate to reduce acoustic reflections.A perfluoropentane (PFP) droplet emulsion was prepared as in [15]. Its size distributionwas measured using a Coulter counter, see Fig. 2(c). The suspension was loaded by capillarysuction in a chamber that was approximately 100 µ m in height. The chamber was locateddirectly above the piezoelectric substrate, open at the front end to allow for a direct couplingbetween the SAW and the liquid, and closed above using a microscope cover slip (24 mmlength), see details in Fig. 2(b).Droplet vaporization was imaged using an inverted microscope (Olympus BX-FM)equipped with a 20 × magnification objective (Olympus SLMPlan N) coupled to the Bran-daris 128 ultra high-speed camera [45, 46] operated at 15 million frames per second (Mfps)to record the time and location of droplet nucleation. The imaging resolution was 0.29 µ mper pixel. The field of view (FOV) was positioned close to the meniscus of the liquid, atthe front end of the chamber, to minimize interference caused by acoustic reflections from6 ab c radius (µm) c o u n t λ θR λ4 Xe flash light objectivebeam-splitterCCD cameraBrandaris 128acoustic absorberelectrodes cover glassPFP dropletsLiNbO3FOV
FIG. 2: (a) Schematic of the experimental setup. The vaporization of PFP droplets is imaged usingthe Brandaris 128 ultra-high speed camera. (b) A SAW device generates a longitudinal pressurewave in the fluid at the Rayleigh angle θ R . (c) Typical size distribution of the droplets used in thisstudy. the top of the chamber. Three successive high-speed recordings of 128 frames each were ac-quired at an interval of 100 ms. Droplets were vaporized during the second recording and thefirst frames of the third recording were used to image the bubbles formed. The high-speedimaging frames were processed with an automated image analysis procedure programmedin Matlab (The MathWorks, Natick, MA). All experiments were performed at 20 ◦ C.Figure 3 shows an image sequence of the vaporization of PFP droplets driven at frequen-cies of 19.6 MHz (a) and 45.4 MHz (b). The droplets that underwent nucleation are markedby the red-dotted circles. At 19.6 MHz, the nucleated bubbles grow rapidly due to rectifiedheat transfer under acoustic forcing [47]. The bubble size subsequently decreased withinmicroseconds after the ultrasound driving was stopped. ADV at 45.4 MHz is less violentthan at 19.6 MHz. In particular, the bubbles that nucleated inside the droplets were much7 ac d r a d i u s ( µ m ) P N P P N P r a d i u s ( µ m ) n u m b e r n u m b e r FIG. 3: Vaporization of PFP droplets driven at 19.6 MHz (a) and 45.4 MHz (b) imaged at 15 Mfps.The nucleated droplets are marked by the red dotted circles. Stable bubbles are formed from allnucleated droplets as can be observed from the image captured 100 ms later. Number of nucleationevents over time and the corresponding radius of the droplet at a driving frequency of 19.6 MHz(c) and 45.4 MHz (d). smaller at 45.4 MHz. Note that every nucleation site produced a stable bubble at bothdriving frequencies, as can be observed from the images captured after 100 ms, i.e. none ofthe nucleated bubbles were observed to recondense [48].Figures 3(c,d) show a total of 217 individual nucleation events for a driving frequency of19.6 MHz and 120 individual nucleation events for a frequency of 45.4 MHz, represented asthe droplet radius versus the time at which nucleation occurs. The number of droplets thatnucleated is shown in the red histogram. The normalized PNP of the driving pulse thatresults from the superposition of waves transmitted by the 60 electrode pairs is shown in thetop panels of Figs. 3(c,d). Since the electrode pairs are spaced by 1 wavelength, the typical8urface wave has a triangular shape originating from 50 superimposed waves. The pressureprofile was experimentally verified by optical hydrophone recordings with one end of theLiNbO substrate submerged in water. The bubbles are thus more likely to nucleate at themaximum PNP, namely at the end of the 50 cycle IDT driving pulse. Note the presenceof a second event of vaporizations in Fig. 3(d) where a small number of droplets nucleatedafter the primary wave had passed, most probably a result of an internal reflection in theIDT device. Also, the absence of structure in the data presented in Figs. 3(c,d) suggeststhat there is no size dependency on the timing of the vaporization.The proportion of droplets activated by the ultrasound wave with respect to the totalnumber of droplets present in each separate bin is shown in the histograms displayed inFigs. 4(a,b) for the driving frequencies of 19.6 MHz and 45.4 MHz, respectively. The reso-nance curves calculated from the proposed theory are displayed in Figs. 4(c,d) (red lines).The theoretical resonance peaks in Fig. 4(c,d) are corrected for the presence of a rigid walland closely match the experimental peaks in Figs. 4(a,b).Numerical simulations were performed on the basis of the geometry of Fig. 2(b) to providefurther insight in the resonance behavior. The simulations were axisymmetric and computedon a GPU using k-wave, an open source Matlab toolbox for time domain ultrasound simula-tions in complex media [49], see SI.5. The grid size was 0.30 µ m at a frequency of 19.6 MHzand 0.15 µ m at a frequency of 45.4 MHz. The results are plotted in Figs. 4(c,d)(blacklines). The resulting pressure field in and around the droplet is displayed in the snapshotof Fig. 4(e), taken at t = 375 ns, i.e after 17 cycles of ultrasound, see also SupplementaryVideo. The amplification factor of the first resonance, as well as its location, is in verygood agreement with the theoretical model, although the simulated amplification is ∼ µ m. Thishigher mode appears to have a smaller effect on the ADV threshold despite the large pressureamplification (factor 10) found in simulation. This is most likely a limitation of the presentrigid numerical simulation since higher order non-axisymmetric modes can induce dropletdeformation, which may have a significant impact on the pressure distribution within thedroplet.The statistical increase in the number of vaporization events as a function of the nega-9 -2-1012 axial position (μm)-4 -2 20 4 r a d i a l p o s i t i o n ( μ m ) radius (μm)0 2.5 5 7.5 10 d r o p l e t s v a p o r i z e d ( % ) a bc d theorysimulation d r o p l e t s v a p o r i z e d ( % ) e f applied voltage (mV)0 200 400 600 n u c l e a t i o n r a t e ( μ s - ) with resonancewithout resonancedata theorysimulation p d r o p / p A radius (μm)0 2.5 5 7.5 10radius (μm)0 2.5 5 7.5 10radius (μm)0 2.5 5 7.5 10 p / p A p d r o p / p A FIG. 4: Resonant vaporization detected at a frequency of 19.6 MHz (a) and 45.4 MHz (b). Calcu-lated and simulated size-dependent pressure amplification factor within the droplet at a frequencyof 19.6 MHz (c) and 45.4 MHz (d). (e) Snapshot of the simulated pressure field for a 2.7 µ m radiusdroplet resonant at a frequency of 45.4 MHz. (f) Droplet activation probability with and withoutthe resonance effect where ’data’ represents the experimental droplet activation probability. tive acoustic pressure amplitude was investigated by varying the amplitude of the 50-cycleultrasound pulses at a frequency of 19.6 MHz. The envelop of the pressure wave, depicted inthe top panels of Fig. 3c and d, combined with the measured timing of the event, were used10o determine the voltage at which each droplet vaporized. The resulting nucleation rate isdisplayed in Fig. 4(f) (open circles). Classical nucleation theory [50, 51] dictates that thenucleation rate is a function of the surface tension of the liquid σ PFP (cid:39)
10 mN/m [41], ofthe ambient temperature T amb = 293 K and of the ambient pressure:Γ ∝ e − π k B T amb σ ( p v − p atm − p drop cos ( ωt )) . (14)Here, p v is the vapor pressure of the liquid and k B is the Boltzmann constant. The va-por pressure of PFP can be estimated using Antoine’s law and ranges from 65 kPa at atemperature of 15 ◦ C to 95 kPa at 25 ◦ C. As a result, and considering the large peak neg-ative pressures typically required to induce cavitation, ( p v − p atm ) /p drop (cid:28)
1. With thissimplification, Eq. (14) can be volume-integrated during the negative pressure phase of theultrasound cycle to determine the average nucleation rate: < Γ > ∝ (cid:90) R r − erf p ( r ) (cid:115) πσ k B T amb dr, (15)see details provided in SI.6. At resonance the pressure amplification factor due to theresonance effect p drop /p A (cid:39)
3, see Figs. 4(c,d). When the SAW devices are driven withintheir linear range, the acoustic pressure is proportional to the driving voltage. Since thedroplet concentration is contained in the prefactor, this expression can be used to fit theexperimental data and provide an estimate of the local acoustic driving pressure, which isthe only free parameter in Eq. (15). The least-squares fit is shown in Fig. 4(f) and gives p A /V (cid:39)
40 MPa/V, leading to an acoustic pressure at the droplet location of ∼
20 MPa foran excitation voltage of 500 mV. Note that these numbers only constitute a rough estimatesince, on the one hand, classical nucleation theory is known to overestimate the peak negativepressures required for cavitation [50] and, on the other hand, the range of data available forfitting is limited. It should also be noted that this pressure is of the same order as thosetypically used for ADV. Interestingly, nucleation theory as presented in Eq. (15) allows topredict the importance of the resonance effect by calculating the average nucleation ratewithout resonance, namely for p drop /p A = 1 (with the same prefactor), see Fig. 4(f) (blueline). Thus, it is clear that a pressure amplification factor of 3 has a dramatic effect ondroplet vaporization behavior. 11n conclusion, it was shown that efficient vaporization can be achieved by driving phase-change PFP droplets at their fundamental resonance frequency. Good agreement was foundbetween the modeled size-dependent pressure amplification within the droplet and the mea-sured size dependent vaporization probability. Resonance-induced vaporization is a newphenomenon, with important impact on potential ADV strategies and on the understandingon previous experimental observations. In addition, this work shows the potential of usingmonodisperse phase-change agents driven by a matching resonance frequency to boost theefficiency of ADV.We thank James Friend for stimulating discussions. This work was funded byNanoNextNL, a micro and nanotechnology consortium of the Government of the Netherlandsand 130 partners. [1] M. Delgado, A. L´azaro, J. Mazo, and B. Zalba, Renew. Sust. Energ. Rev. , 253 (2012).[2] S. Zhang, Y. Shen, L. Wang, J. Chen, and Y. Lu, Appl. Energ. , 876 (2019).[3] J. Alongi, Z. Han, and S. Bourbigot, Progress in Polymer Science , 28 (2015).[4] K. E. Wilson, T. Y. Wang, and J. K. Willmann, J. Nucl. Med. , 1851 (2013).[5] P. S. Sheeran and P. A. Dayton, Curr. Pharm. Des. , 2152 (2012).[6] V. Vinogradov, P. Pavlov, and V. Baidakov, J. Chem. Phys. , 234508 (2008).[7] J. D. Dove, P. A. Mountford, T. W. Murray, and M. A. Borden, Biomed. Opt. Express ,4417 (2014).[8] G. Lajoinie, M. Visscher, E. Blazejewski, G. Veldhuis, and M. Versluis, Photoacoustics p.100185 (2020).[9] O. D. Kripfgans, J. B. Fowlkes, D. L. Miller, O. P. Eldevik, and P. L. Carson, UltrasoundMed. Biol. , 1177 (2000).[10] M. Greenspan and C. E. Tschiegg, J. Res. Natl. Bur. Stand., Sect. C , 299 (1967).[11] B. Carlier, S. V. Heymans, S. Nooijens, Y. Toumia, M. Ingram, G. Paradossi, E. d’Agostino,U. Himmelreich, J. D’hooge, K. Van Den Abeele, et al., Phys. Med. Biol. , 065013 (2020).[12] R. Williams, C. Wright, E. Cherin, N. Reznik, M. Lee, I. Gorelikov, F. S. Foster, N. Matsuura,and P. N. Burns, Ultrasound Med. Biol. , 475 (2013).[13] O. Couture, P. D. Bevan, E. Cherin, K. Cheung, P. N. Burns, and F. S. Foster, Ultrasound ed. Biol. , 73 (2006).[14] P. Sheeran, S. Luois, L. Mullin, T. Matsunaga, and P. A. Dayton, Biomaterials , 3262(2012).[15] N. Reznik, M. Seo, R. Williams, E. Bolewska-Pedyczak, M. Lee, N. Matsuura, J. Gariepy,F. S. Foster, and P. N. Burns, Phys. Med. Biol. , 7205 (2012).[16] N. Y. Rapoport, Z. Gao, and A. Kennedy, J. Natl. Cancer Inst. , 1095 (2007).[17] P. Mohan and N. Rapoport, Mol. Pharm. , 1959 (2010).[18] S. M. Fix, A. Novell, Y. Yun, P. A. Dayton, and C. B. Arena, J. Ther. Ultrasound , 7 (2017).[19] M. N. Adan, M. L. Fabiilli, C. G. Wilson, and O. D. Kripfgans, in (IEEE, 2012), pp. 448–450.[20] M. L. Fabiilli, K. J. Haworth, I. E. Sebastian, O. D. Kripfgans, P. L. Carson, and J. B. Fowlkes,Ultrasound Med. Biol. , 1364 (2010).[21] T. Giesecke and K. Hynynen, Ultrasound Med. Biol. , 1359 (2003).[22] K. C. Schad and K. Hynynen, Phys. Med. Biol. , 4933 (2010).[23] M. Aliabouzar, K. N. Kumar, and K. Sarkar, J. Acoust. Soc. Am. , 1105 (2019).[24] W. Kao, S. Kang, and C. Yeh, in (2014), pp. 1790–1793.[25] J. D. Rojas, M. A. Borden, and P. A. Dayton, Ultrasound Med. Biol. , 968 (2019), ISSN0301-5629.[26] S. Lin, G. Zhang, C. H. Leow, and M.-X. Tang, Phys. Med. Biol. , 6884 (2017).[27] X. Lu, X. Dong, S. Natla, O. D. Kripfgans, J. B. Fowlkes, X. Wang, R. Franceschi, A. J.Putnam, and M. L. Fabiilli, Ultrasound Med. Biol. , 2471 (2019).[28] R. Chattaraj, G. Goldscheitter, A. Yildirim, and A. P. Goodwin, RSC Adv. , 111318 (2016).[29] S. Capece, F. Domenici, F. Brasili, L. Oddo, B. Cerroni, A. Bedini, F. Bordi, E. Chiessi, andG. Paradossi, Phys. Chem. Chem. Phys. , 8378 (2016).[30] G. Zhang, S. Lin, C. H. Leow, K. T. Pang, J. Hernandez-Gil, N. J. Long, R. Eckersley,T. Matsunaga, and M.-X. Tang, Ultrasound Med. Biol. , 1131 (2019).[31] S. Raut, M. Khairalseed, A. Honari, S. R. Sirsi, and K. Hoyt, J. Acoust. Soc. Am. , 3457(2019).[32] O. Shpak, M. Verweij, H. J. Vos, N. de Jong, D. Lohse, and M. Versluis, Proc. Natl. Acad.Sci. U.S.A. , 1697 (2014).[33] C. J. Miles, C. R. Doering, and O. D. Kripfgans, J. Appl. Phys. , 034903 (2016).
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