Tomita AtomizationwithUS 2014

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Jet atomization and cavitation induced by interactions between focused ultrasound and

a water surfacea)

Y. Tomita

Citation: Physics of Fluids (1994-present) 26, 097105 (2014); doi: 10.1063/1.4895902

View online: http://dx.doi.org/10.1063/1.4895902

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PHYSICS OF FLUIDS 26, 097105 (2014)

Jet atomization and cavitation induced by interactionsbetween focused ultrasound and a water surfacea)

Y. Tomitab)

Faculty of Education, Hokkaido University of Education, Hakodate,

Hokkaido 040-8567, Japan

(Received 8 January 2014; accepted 25 August 2014; published online 23 September 2014)

Atomization of a jet produced by the interaction of 1 MHz focused ultrasound with

a water surface was investigated using high-speed photography. Viewing various

aspects of jet behavior, threshold conditions were obtained necessary for water surface

elevation and jet breakup, including drop separation and spray formation. In addition,

the position of drop atomization, where a single drop separates from the tip of a jet

without spraying, showed good correlation with the jet Weber number. For a set of

specified conditions, multiple beaded water masses were formed, moving upwards

to produce a vigorous jet. Cavitation phenomena occurred near the center of the

primary drop-shaped water mass produced at the leading part of the jet; this was

accompanied by fine droplets at the neck between the primary and secondary drop-shaped water masses, due to the collapse of capillary waves. C 2014 AIP Publishing

LLC.[http://dx.doi.org/10.1063/1.4895902]

I. INTRODUCTION

Atomization induced by ultrasound (US) has been studied for a very long time. 1, 2 Atomization

results in an enormous increase in total surface area, yielding advantages that include the promotion

of chemical reactions and an increase in the efficiency of fuel combustion. Small droplets, formed

by nebulizers and vaporizers, have been used for many years as a means to deliver drugs by

inhalation. Recently, mist spraying has achieved temperature reductions of 2 C3 C, compared

with the surrounding air temperature.3 More recently, it has been reported that fine droplets proved

useful for mass spectrometry of complex bio-molecules in solution.4

To date, numerous studies have been published concerning jet atomization achieved using

either vibration or US. For instance, Jameset al.5 utilized a low-frequency vibration to study droplet

ejection numerically, and elucidated that droplet ejection was due to a pinch-off phenomenon

involving detachment from a main drop that was initially positioned on the surface of the vibrating

solid wall. Vibration-induced drop atomization has also been investigated by Vukasinovic et al.,6

while Yule and Al-Suleimani7 have studied the formation of fine droplets due to the collapse of

capillary waves produced by surface vibration of shallow water.

Various types of jet formation exist, such as jets in the form of free-surface spike during the

collapse of cavitation bubbles near a free surface,811 and Worthington jets induced by drop impact

against a water surface.12, 13 These are also regarded, in a broader sense, as jet ejection involving drop

separation. Tan et al.14 used accelerated Rayleigh waves to produce jets that ejected up to 12 cm

from the free surface of a sessile drop, and classified several types of drop atomization. Motivatedmainly by a potential use in medical applications, recent studies have investigated laser focusing15, 16

as a means of elucidating the mechanisms of liquid jet breakup and spray formation. Focused US

is also recognized as an effective device for the study of jet behavior,17 and is likely suitable for

a)Contributed paper, published as part of the Proceedings of the 19th International Symposium on Nonlinear Acoustics,2124 May 2012, Tokyo, Japan.

b)Electronic mail: [email protected]

1070-6631/2014/26(9)/097105/11/$30.00 C2014 AIP Publishing LLC26, 097105-1


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097105-2 Y. Tomita Phys. Fluids26, 097105 (2014)

therapeutic studies because of its ability to target energy into a small area of tissues or cells.18 Similar

to a pressure impulse generated by a focused US, an axisymmetric impulse in pressure has been

numerically applied to solve the deformation of a free surface and generation of drops.19 Although a

number of investigations have examined atomization by either vibration or US,20 there is a paucity of

knowledge concerning the features of atomization induced by high-frequency US; this is because of

the complex physics associated with the phenomena that accompany jet ejection, when this involvesinteractions at a boundary consisting of two media with different acoustic impedances.

Therefore, in the present paper, we conductedan experiment on the interaction of 1 MHz focused

US with a water surface, in order to explore various aspects of jet behavior such as water surface

elevation and liquid breakup, including drop separation and spray formation (although vigorous

spraying was not considered in this study). High-speed photography, with a maximum rate of 50 000

frames/s, together with still photographs using light with a short exposure time, revealed a variety of

jet behaviors, and for a set of specified conditions, captured cavitation phenomena produced inside

a drop-shaped water mass positioned at the tip of a jet.

II. EXPERIMENTAL FACILITIES AND METHODS

US waves with a frequency,f, of 1 MHz were generated using a multi-purpose synthesizer and

bipolar amplifier (NF Corporation, WF 1946 A & HAS 4101), and focused continuously at a water

surface by a concave transducer, made of lead zirconate titanate (PZT) ceramic, with a geometric

focal length,R, of 80 mm. The transducer was fixed at the bottom of a plastic rectangular container

(200 100 300 mm) filled with distilled water at 20 C, with its center-axis vertical to the water

surface, and the distance between the bottom of the vibrating surface and water surface maintained

at 80 mm. The D factor of this transducer, an indicator expressing the convergence performance

of the US, was defined as D = a2/(R); its value was calculated to be 3.4, where a (=20 mm)

represents the radius of the chord length of the transducer and (=1.48 mm) the wavelength of

1 MHz US in distilled water at 20 C. Pressures were detected with a hydrophone (Onda HNC-

0400). The maximum pressure, pmax, defined as half the value of the full amplitude of the maximal

pressure signal among the leading 20 waves, ranged from 1.42 to 2.55 MPa. The characteristic length

of the region where the acoustic energy was focused, i.e., the full width half maximum (FWHM) of

pmax

is theoretically given by 2R/(a), and wascalculated to be 3.8 mm. The corresponding acoustic

intensities,I, expressed aspmax2/(2c) where is the density of water and cthe US velocity in water,

were calculated as ranging from 68 to 220 W/cm2. The acoustic energy density,Ein J/cm2, may be

calculated as the product ofIand the US exposure time,Tex. To observe the dynamics of a jet and the

subsequent phenomena, especially to determine the liquid breakup position and spray onset position,

high-speed photography was conducted utilizing a high-speed digital camera (Photron FASTCAM

SA5) at a frame rate of up to 50 000 frames/s. A xenon lamp, with a pulse duration of 2 s, was

flashed 54 s after the US irradiation in order to precisely determine the time at which the US began

to interact with the water surface. Due to capturing high quality of images, still photographs were

taken as necessary, using two types of light source with a short-pulse duration, in a dark room. One

was a xenon lamp with a pulse duration of 2 s and the other a nano-pulse light with 180 ns; the

latter was also used when taking shadowgraphs of standing waves that developed in the water near its

surface.

III. RESULTS AND DISCUSSION

It is known that standing waves aregenerally formedafter irradiation with US. In ourstudy, under

the conditions thatI= 220 W/cm2 andTex = 1000 ms, no fringes occurred in the shadowgraphs up

to 55 s, but a black and white fringe pattern appeared after 60 s, as shown in Fig.1(a). An ejecting

jet can be seen in Fig.1(b),which was taken at 4.5 ms. Each black or white fringe location coincides

with a pressure anti-node where the density was locally higher or lower than that of undisturbed

water at 20 C. As a result, light was refracted while US passed through the region because the space

derivative of the refractive index is proportional to the density gradient with respect to space. We

obtained 1.46 mm as the average gap length between two black or white fringes, which is very close


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FIG. 1. Shadowgraphs taken at (a)60 s and(b) 4.5ms after theinteraction.Standing waves maybe seen inthe water layer in

both (a) and (b), and an ejecting jet may be seen in (b). The acoustic intensity was 220 W/cm2 and the exposure time 1000 ms.

WS denotes the water surface. The scale bars represent 5 mm. (c) The onset time, Tex,e, of the water surface elevation plotted

as a function of the acoustic intensity, I.

to the wavelength, , of 1.48 mm calculated using the relation, f = c, where f is the frequency

of an US wave and c the US velocity. Once the pressure at the focus exceeded a threshold value,

the water surface became elevated, producing a conical-shaped swelling. However, this is not the

state that represents the production of a jet; further acoustic energy is necessary to break the state

of swelling, and finally to generate a jet. For example, under the conditions that I= 220 W/cm2,

an ejecting jet without drop separation can be produced for Tex = 22.5 ms, whose accumulated

acoustic energies per unit area corresponded to 0.440.55 J/cm2. Because the FWHM ofpmax was

calculated as 3.8 mm, the lowest accumulated acoustic energy was determined to be 5.0 J. In the

case whereTex = 2 ms, corresponding to Fig.2(a),the kinetic energy of a jet,Ek, was calculated to

be 4.7 J, since the initial jet velocity was 0.7 m/s and the mass of the jet 19.1 g. This suggests

that almost all the acoustic energy was converted into the energy required for the motion of a jet

without drop separation. Of course, surface tension will affect the jet motion, contributing to move

the liquid column downwards during its falling process. If a larger acoustic energy is used, a jet

can grow further followed by surface fluctuation, which may occur in the radial direction of the jet

surface due to capillary perturbations. In the range 2.5 ms Tex < 5 ms, drop separation without

spray occurred.

The jet tip may be seen above the water surface in Fig. 1(b). This might be an ejecting jet

in a stage of growth, because it was taken at 4.5 ms, being longer than the necessary time for jet

formation, i.e., 2.5 ms. The jet configuration was a domed, swollen shape connected to a drop-shaped

water mass, obviously differing from the shape of a conically round edge at the top of the swollen

water column that is the most typical shape of a swelling. The onset times of the surface elevations,

Tex,e, are shown in Fig.1(c)for five acoustic intensities,I. For a smaller intensity, a longer onset time

was needed. In contrast, for largerI, and specifically for I 150 W/cm2, Tex,e tended to approach

1.5 ms. The corresponding acoustic energy,Ee, was calculated as 0.23 J/cm2 whenI= 150 W/cm2.

Knowing the limiting onset time, Tex,e, to be 1.5 ms, we selected an acoustic intensity ofI=

220 W/cm2, and then varied the exposure times to observe what happened. When the exposure time

exceeded 1.5 ms, the water surface was deformed to form a swelling, with a conically round edgeat the top, and a height that varied with Tex. A conical swelling appeared and grew, with a similar

shape, in the range 1.5 ms Tex


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(a)

(b)

(c)

(d)

(e)

FIG. 2. Jet behaviors for various exposure times,Tex(I= 220 W/cm2). (a)t= 3, 5, 10, 15, and 20 ms, for Tex = 2 ms. (b)

t= 3, 15, 22, 25, and 30 ms, for Tex = 3 ms. (c) t= 3, 5, 5.8, 10, and 30 ms, for Tex = 5 ms (Multimedia View) [URL:

http://dx.doi.org/10.1063/1.4895902.1] . (d)t= 3, 6, 7, 10, and 12 ms, for Tex = 20 ms. (e) t= 3, 6, 7, 10, and 15 ms, for Tex=

1000 ms (Multimedia View) [URL: http://dx.doi.org/10.1063/1.4895902.2].The scale bars represent 10 mm.

Five series of still photographs are shown side-by-side in Figs. 2(a)2(e). The firstframeof each

row in the photographs presented in Figs. 2(a)2(e)was taken at 3 ms after the interaction, showing

that the top of an elevated liquid column seems to be a state slightly over a swelling. Comparing the

first two photographs in Figs. 2(d)and 2(e),it is clear that the base diameter of a conical swelling

in the case of (d) is larger than that of (e). This suggests that the convergence rate of the focused

US in (e) was superior to that in (d), resulting in a rapid growth of the jet. Some of the modes of

surface waves generated on the curved surface of an oscillator may influence the convergence of

acoustic energy by a focused US. In case (a), where Tex = 2 ms, a jet was produced that reached

its maximal height without separation. In case (b), where Tex = 3 ms, a jet moved upwards with

slight fluctuations in the radial direction, mainly due to capillary perturbations, as shown in the

second picture (t= 15 ms). Following this, drop separation occurred at around 20 ms. The detacheddrop continuously moved upwards at a velocity of 0.13 m/s, inducing surface oscillation in the

second mode. In contrast, a locally high pressure was produced at the separated jet tip due to its

large curvature, causing it to move downward quickly. During this process, capillary waves were

induced, traveling downwards over the jet surface with a phase speed of 2.1 m/s; this was calculated

using Eq.(1),21 whereis the surface tension of water, and the wavelength, , was measured to be

0.22 mm:

Vc =

2

. (1)


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FIG. 3. Effects of exposure times on liquid jet breakup and spray formation (I= 220 W/cm2). Lb is the first jet breakup

position, Ls the position of the first spray formation, andTs,th the spray threshold exposure time at which the liquid breakup

pattern changes from drop separation to jet breakup with spraying.

On the other hand, the pattern of jet ejection that developed in Fig. 2(c)at Tex = 5 ms was

clearly different from that in (a) and (b). Multiple beaded water masses were formed at the leading

part of the jet column during its development. As evident in the fourth frame from the left, taken at

10 ms, the second drop-shaped water mass was elongated along the vertical axis. Subsequently, the

primary drop separated, followed by a satellite. Although the US power supply was terminated at 5

ms in case (c), the water surface fluctuation continued for a long period, until about 60 ms, because

the surface wave motion was strongly affected by the vessel configurations as well as the mechanical

inertia of the transducer. In case (d), Tex = 20 ms, and case (e), Tex = 1000 ms, vigorous sprays

were generated at a lower location of each jet column before its breakup, while a very weak spray

was generated at 5.84 ms in (c) (a more detailed discussion of this will be given later). After jet

breakup, numerous drops or water masses of various sizes were dispersed into the surrounding air.

In addition, many fine sprays were scattered irregularly from the surface near the separated jet tip,

owing to continuous irradiation with US waves. In all cases (a)(e), the water surface fluctuated for a

long time even after termination of the US irradiation because of the inertial effect of the transducer

and the liquid motion generated near the concave surface of the transducer, which would influence

the duration required for stopping the oscillation of the transducer.

From these observations, it seems that the jet radius, Rj, depends slightly onTex. Values for the

jet radius,Rj, and the initial jet velocity, Vj, determined from Fig.2are as follows: (a)Rj = 1.0 mm,

Vj = 0.7 m/s for Tex = 2 ms; (b) Rj = 0.9 mm, Vj = 1.2 m/s for Tex = 3 ms; (c) Rj = 0.8 mm,

Vj = 2.2 m/s for Tex = 5 ms; (d) Rj = 0.8 mm, Vj = 1.6 m/s for Tex = 20 ms; (e) Rj = 0.7 mm,

Vj = 1.6 m/s forTex = 1000 ms.

Figure3 shows the jet breakup positions measured from an undisturbed water surface (open

circles,), and the onset position of spraying (solid circles, ), for a wide range of US exposure

times, Tex, where the acoustic intensity, I, was fixed at 220 W/cm2 (i.e., the same value as that used

in Fig.2). Drop separation without spray discharge, such as that seen in Fig. 2(b),occurred in the

range 2.5 ms Tex


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FIG. 4. The temporal evolutions of the tip of a jet () and the isolated drop () are shown in (a), forI= 220 W/cm2 andTex= 5 ms; B1 and B2 correspond to the first and second breakups, respectively. (b) Jet velocities, Vj, are plotted as a function

of the exposure time,Tex, for two acoustic intensities, I= 220 W/cm2 () andI= 80 W/cm2 ().

drop-shaped mass at the jet tip (this will be discussed later). A very weak spray was also generatednear the neck of the drop-shaped mass. In Fig. 4(a), B1 and B2 are the first and second breakup times,

corresponding to 12.5 ms and 15.83 ms, respectively. To explore the effect of jet Weber number, Wej(defined as Vj

2Rj/, with Rj being the jet radius), on the position of the drop separation without

spraying,Lb, we examined the jet velocities, Vj, for various exposure times,Tex. Figure4(b)shows

the results for two acoustic intensities, namely, 220 W/cm 2 () and 80 W/cm2 (). In the case ofI

= 220 W/cm2, a single drop separation occurred in the range 2.5 ms Tex < 5.0 ms, and the jet

velocity increased with increasing Tex, reaching 2.2 m/s at Tex = 5 ms; at this point, the breakup

pattern changed from drop atomization to water mass separation. In contrast, in the range Tex> 5 ms,

the jet velocity decreased due to the pressure plateau at the focus resulting from the interactions of

US waves, presumably induced by various modes of surface vibration of the oscillator. Since the jet

Froude number, Frj, defined asVj2/(Rjg) withg being the gravitational acceleration, was 746 forTex

= 5 ms and 292 for Tex = 20 ms, jet motion in the latter case seems to be influenced by a gravitational

effect, as compared with the former case. This may cause multiple beaded water masses. On theother hand, in the case ofI= 80 W/cm2, drop atomization occurred in the range Tex 12 ms; no

drops separated in the rangeTex< 12 ms, even though a jet was ejected, breaking through the state

of swelling.

Next, the dimensionless position of drop separation,Lb/Rj, was examined for various jet Weber

numbers, Wej, as well as the jet Reynolds number, Rej, defined asVjRj/, whereRj is the jet radius

and the kinematic viscosity of water. Figure 5 shows the variation ofLb/Rjas a logarithmic function

of Wej, which ranged from 0.95 to 333.2; the Reynolds number varied from 202 to 4252. The solid

line in Fig.5denotes the power-law fitting expressed by

L b/Rj = 11.6 We0.128j . (2)


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FIG. 5. Drop separation position without spraying, Lb/Rj, versus the jet Weber number, Wej, with Rj being the radius

of a jet.

This gives that the jet breakup length,Lb/Rj, is 11.6 when Wej = 1; this is slightly larger than

the Lj/Rj value of about 9 predicted by Tan et al.14 for the same Weber number. This is because

the jet breakup length, Lb, consists of the sum of the swelling height, Hs, and the jet length, Lj.

Supposing that the liquid breakup length, Lb, is proportional to both the jet velocity, Vj, and the

characteristic time, tc, defined as the time necessary for drop separation, Tan et al. deduced the

following relation: Lb/Rj Vj tc/Rj. The value tc is connected with the phase speed, Vc, given by

Eq.(1 ),so thatLb/Rj must be correlated with Wej1/2. A similar consideration has been made in the

capillary breakup of a Worthington jet.13 However, Eq.(2) indicates that the power value is 0.128,

about one-fourth of the value of 0.5 obtained by Tan et al.14 This may result from the different

processes of jet formation. Tan et al.14 produced a jet using accelerated Rayleigh waves generated

by electro-elastic acoustic waves with a frequency of 20 MHz, which traveled over the curved drop

surface from four directions before finally being focused. On the other hand, our jet was produced

by focusing 1 MHz US, and was vertically ejected into the air after breaking through the swelling

state of a flat water surface. During jet development, pressure waves continuously influence the jet

surface. Some of these pressure waves may contribute to the suppression of jet surface fluctuation

in the radial direction due to capillary perturbations. Although the jet tip in Fig. 4(a)seems to move

at a constant velocity, the actual displacement of the jet tip varied slightly from that predicted by

a constant velocity, evident as several stages of growth followed by relative stasis; this occurred

because the US waves continuously affected the surface of the ejecting jet. Consequently, the jet

tip along the center axis of symmetry moved at a velocity of about 2 m/s with a fluctuation of

1 m/s. Takahira22 numerically explained the growth process of a jet produced by the interaction of

focused 1 MHz US with a water surface. Before a rapid increase in jet velocity, the jet tip location

changes with time through several stages of growth and stasis; this may be related to the increase

in wave number in the acoustic field between the vibrating surface of the transducer and the water

surface. When the water surface moves upwards, pressure anti-nodes first increase in the region of

the off-center axis area, and then develop near the center, to produce a higher pressure just below the

water surface. Gordillo and Gekle13

pointed out the import contributions of the velocity gradient inthe axial direction, i.e.,Vj /z, to the breakup of Worthington jets. In particular, they numerically

elucidated that capillary disturbances resulting from deceleration of the jet tip was one of the most

important factors for drop separation. This may result in a delay in the disruption of the jet into

drops.

A more detailed observation of the motion of a jet, generated under the conditions that I= 220

W/cm2 andTex = 5 ms, was carried out using high-speed photography at a rate of 50 000 frames/s.

Figure6 shows four sequential frames taken every 20 s; the first frame was captured at 5.80 ms,

when two drop-shaped water masses were linked together at the tip of an ejecting jet. The primary

water mass formed an ellipsoid with major and minor axes of 1.44 mm and 1.40 mm, respectively.

In case (a), nothing was evident inside the primary water mass. However, in case (b), 5.82 ms, and


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(a) (b) (c) (d)

FIG. 6. Cavitation produced inside a drop-shaped water mass at the jet head (I= 220 W/cm2,Tex = 5 ms). The photographs

were taken at times t= 5.80, 5.82, 5.84, and 5.86 ms after the interaction. The scale bar represents 1.0 mm.

case (c), 5.84 ms, some dark-colored region may be seen near its center. Subsequently, this region

lightened in color, as shown in Fig. 6(d) taken at 5.86 ms, before finally disappearing from view.

The dark-colored region was visible for 4050 s at most, i.e., it disturbed light for this duration.

The jet tip moved upwards by 0.13 mm along the symmetric axis during the 60 s over which

these images were taken, yielding a jet velocity of 2.1 m/s. To observe these phenomena with at

shorter exposure times, several still photographs were taken under the same conditions at a fixed

time oft= 5.835 ms, using light with a pulse duration of 2 s, emitted from a xenon flash-lamp.

Figure7(a)shows a representative photograph of the whole jet standing above the water surface,

denoted by WS; the maximum jet height was 5.14 mm. The configuration of the jet base was adeformed, swollen shape connected to a domed water mass, above which two beaded water masses 1

were positioned. The beaded jet shape at the tip was presumably created from the mixed effects of

capillary perturbations on the jet surface and US wave interactions. Again, a dark-colored region

appeared inside the primary drop-shaped water mass, although its shape differed slightly from that

observed in Fig. 6. A magnified image of (a) is shown in (b). The main part of the dark-colored

region, C, was located near the center of the water mass, accompanied by another small shadow

on the right side. This phenomenon disturbed light for 4050 s. The primary drop-shaped water

mass had the form of an ellipsoid with major and minor axes of 1.44 mm and 1.40 mm, respectively,

identical to those shown in Fig. 6, although the curvatures of the tips were slightly different. The

radius of a spheroid having the same volume as that of the primary drop-shaped water mass would

be 0.71 mm. Immediately after the arrival of ultrasonic waves at the curved surface of the jet tip, the

pressure changed its phase by 180, reversing the pressure amplitude (e.g., from negative to positive).

Finally, the US waves were focused at the center of the primary water mass as expansion waves to

produce an extremely low pressure, because the distance from the curved surface to the center of the

primary water mass equals almost half the wavelength of the US. If the pressure was to fall below the

saturated vapor pressure of water at 20 C, i.e., 2.34 kPa, some of the water would instantaneously be

vaporized to create vapor bubbles. Using the same conditions, we obtained similar phenomena with

good repeatability. Therefore, it is likely that the dark-colored region represents cavitation caused by

local tension waves, resulting from the superimposition of focused expansion waves that originated

(a) (b)

FIG. 7. A snapshot taken under the same conditions as Fig.6 (I= 220 W/cm2, Tex =5 ms). (a) The entire jet is shown,

taken at 5.835 ms; WS denotes the water surface. The scale bar represents 1.0 mm. (b) Magnified image of (a), where C and

S correspond to cavitation and spray, respectively. The scale bar represents 0.5 mm.


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at the air-water boundary surface of the jet tip. Of relevance to this, the resonant radius of a vapor

bubble corresponding to 1 MHz US is 3.2 m. We conjecture that the dark-colored region is a cluster

of cavitation bubbles of various sizes, with a mean bubble radius of 3.2 m. Recently, Obreschkow

et al.23 proposed a new path of erosion caused by a particular drop impact, due to the collapse of

far-side cavitation generated at the focus of a confined expansion wave inside an isolated liquid

volume. Cavitation bubble dynamics have also been studied inside liquid drops in microgravity24, 25

and within a liquid jet.26 In all cases, shock waves emitted from an individual cavitation bubble were

reflected at the curved boundary, propagating back to each focal point as expansion waves, eventually

producing secondary cavitation.9 We observed cavitation phenomena even for Tex = 1000 ms,

where an ejecting jet would proceed in a similar way to that developed in Tex = 5 ms, while acoustic

energy was feeding into the inside of the drop. An interaction between a curved boundary of the

leading part of the jet and US waves seems to be an important factor to generate cavitation.

Viewing Fig.7(b)more carefully, a small amount of spray may be seen discharging from the

neck between the primary and secondary drop-shaped water masses. It is known that capillary waves

are induced vigorously by the repeated interaction of US with a free surface.1, 2 This is particularly

the case when capillary waves are produced near the waist between two beaded water masses, and

the two waves propagating just above and below the waist are superposed in phase, as the amplitude

of these waves can be enlarged owing to the high curvature at the neck. Subsequently, numerous

fine drops would become isolated from the crests of the individual liquid ligaments developed from

the capillary waves, and be discharged into the air. By introducing the surface wavelength, c, of a

capillary wave, the fine drop diameter, d, may be predicted from the following expression:2, 7

d= K c = K

8

f2

13

, (3)

whereKis a coefficient determined empirically. For example, Lang2 determined Kto be 0.34 for

surface waves covering a wide range of frequencies, from low to moderate, while Chiba27 obtained a

value ofK= 0.63 that is suitable for surface waves with high-frequencies. Since c = 12.2 m when

f= 1 MHz and K= 0.63, we derived a value of 8 m using Eq.(3) as the mean droplet diameter,

which is in good agreement with the mean droplet diameter measured from the data obtained in

the present experiment, i.e., 79 m. Scattering of light by spherical particles such as droplets with

diameters ranging from severalm to several tens ofm is likely caused by Mie scattering, becausethe spectral characteristics in visible light region of a xenon lamp are very similar to those of sunlight.

It is well known that the border of a particle image becomes blurred due to Mie scattering. As a

result, spray was captured as a fuzzy image.

Figure 8 shows the maximum separation position of a drop without spraying (), and the

threshold position of spraying (), for five acoustic intensities. Both positions slightly increase with

increasing acoustic intensity. It can be easily estimated that more than 80 W/cm2 was necessary for

FIG. 8. Effects of acoustic intensity,I, on the maximum separation position of a drop without spraying, Lb (), and the

threshold position for spraying,Ls,th (). The dashed line implies the swelling limit for I= 220 W/cm2, of height 3.2 mm.


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spraying. However, it must be noted that spraying required a definite energy even when a higher

acoustic intensity was applied. This suggests that the threshold exposure times depend on acoustic

intensity. For instance, whenI= 220 W/cm2 and the exposure time,Tex, was 1.5 ms, a swelling was

maintained during US irradiation even after surface elevation. For slightly longer exposure times,

such as 2.0 ms Tex < 2.5 ms, a jet was ejected, but no atomization occurred. Drop separation

without spraying was produced in the range 2.5 ms Tex< 5 ms, while spraying inevitably occurredforTex 5 ms.

IV. CONCLUSION

Jet breakup and atomization produced by the interaction of 1 MHz US with a water surface

have been investigated for various combinations of acoustic intensity,I, and exposure times, Tex. The

onset time for surface elevation depended on the acoustic intensity; however, a threshold acoustic

intensity, Ith, existed, below which a water surface was deformed to produce a swelling but no

jet was formed. When the acoustic intensity was fixed at 220 W/cm2, jets were ejected without

drop separation in the range 2.0 ms Tex < 2.5 ms, whereas drop separation without spraying

occurred in the range 2.5 ms Tex < 5 ms. The dimensionless drop separation position, Lb/Rj,

can be expressed by Lb/Rj = 11.6 Wej0.128, where Wej is the jet Weber number defined as Wej =

Vj2Rj/. The jet breakup pattern changed from drop separation to jet breakup at an exposure time

of about 5 ms, and was sometimes accompanied by the spraying of numerous fine droplets with an

average diameter of 8m. Cavitation phenomena occurred at the center of the primary drop-shaped

water mass, presumably due to the production of a local pressure that was lower than the saturated

vapor pressure, generated by the superimposition of focused expansion waves reflected at the curved

air-water boundary surface of the primary water mass.

ACKNOWLEDGMENTS

The author would like to express his hearty thanks to Dr. O. A. Sapozhnikov for his valuable

contribution about papers on atomization and ultrasonic fountains. The author is also grateful to

Mr. Y. Hamada, SANPICO Ltd., and Mr. A. Sakamaki, Photron Ltd., for their help in conducting the

high-speed photography experiments. Assistance in performing some of the present experiments was

received from Messrs S. Tanaka and A. Okada. This study was supported by a JSPS Grant-in-Aid

for Challenging Exploratory Research (23656124).

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