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Optics & Laser Technology 39 (2007) 968–972

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Experimental investigation of the collapse of laser-generatedcavitation bubbles near a solid boundary

Rui Zhaoa, Rong-qing Xub, Zhong-hua Shena, Jian Lua, Xiao-wu Nia,�

aDepartment of Applied Physics, Nanjing University of Science & Technology, Nanjing 210094, ChinabSchool of Electronics & Information, Jiangsu University of Science & Technology, Zhenjiang 212003, China

Received 8 April 2005; received in revised form 6 June 2006; accepted 8 June 2006

Available online 25 July 2006

Abstract

The oscillation of a laser-generated single cavitation bubble near a solid boundary is investigated by a fiber-optic diagnostic technique

based on optical beam deflection (OBD). The maximum bubble radii and collapse time for each oscillation cycle are determined from a

sequence of bubble oscillations. Furthermore, by combining the revised Rayleigh theory, the prolongation factor k at different

dimensionless parameter g (g ¼ L=Rmax, where Rmax is the maximum bubble radius and L is the distance of a cavity inception point from

a boundary) is obtained. In addition, the prolongation factor of the collapse time versus laser energy is also derived, which are valuable in

the fields of hydraulic cavitation, laser lithotripsy and laser ophthalmology.

r 2006 Elsevier Ltd. All rights reserved.

PACS: 47.55.Bx

Keywords: Cavitation bubble; Prolongation factor; Optical beam deflection

1. Introduction

Cavitation is a dynamic phenomenon occurred inflowing liquids, where the local pressure is lower than thesaturated vapor pressure at ambient temperature. Theinterest in the dynamics of cavitation bubbles in liquidsmainly arises from their destructive consequences. In thefield of hydraulic machinery or materials science, thegrowth and collapse of cavitation bubble leads to corrosionand pitting of metal surface. Cavitation noise deprivesunderwater weapons of shelter and interferes with sonop-robes’ performance. Moreover, cavitation phenomenonalso leads to the loss of mechanical efficiency. In medicalapplication, such as intraocular laser surgery, pulsed laseris used to produce an optical breakdown with subsequentbubble formation. More often, however, they are thesource of unwanted collateral effects, e.g., in intraoculartissue cutting near sensitive structures of eyes, or in pulsed

e front matter r 2006 Elsevier Ltd. All rights reserved.

tlastec.2006.06.005

ing author.

ess: nxw@mail.njust.edu.cn (X.-w. Ni).

laser angioplasty, where cavitation bubble leads to a strongdilatation of the vessel walls. Therefore, a great deal ofresearch has been focused in this field [1–6].For investigating the physics of cavitation bubble

phenomena, scholars adopt kinetic impulse [7] or sparkdischarge [8] to generate the cavity. Since the creation timeand inception point of the cavity induced by kineticimpulse or spark discharge are difficult to control, in modelexperiments the cavitation bubbles are mostly produced bylaser pulses now [9]. When high-intensity laser pulses arefocused into a transparent liquid, an optical breakdownleads to plasma formation, acoustic emission and cavita-tion bubble generation [2,10,11]. A cavitation bubble canbe produced by high-pressure plasma and its radial motionis driven by the pressure gradient between the outside andinside of the bubble [12]. The bubble generally oscillatesseveral times with acoustic transience until its whole energyand gas content are completely dissipated into thesurrounding fluid [13].In a theoretical analysis, Rayleigh [14] developed a

relationship between the collapsed time Tc and themaximum radius Rmax for the spherical cavitation bubble

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(a) (b)

16

7

6Cavitation

bubble

Cavitation

bubble

1

2

3

4

5

8

9

7

10

11

12

14

15

13

17

6

Fig. 1. Diagram of experimental setup. (1) Q-switched Nd: YAG laser

(1.06mm wavelength, pulse duration 10 ns), (2) beam splitter, (3)

attenuator group, (4) concave lens (f 1 ¼ 50mm), (5) convex lens

(f 2 ¼ 150mm), (6) aluminum target, (7) glass cuvette

(100� 100� 150mm3), (8) He–Ne laser (Power 5mW, 0.63mm wave-

length), (9) convex lens (f 3 ¼ 50mm), (10) microscope objective (20� ,

f 4 ¼ 4mm), (11) interference filter (0.63mm wavelength), (12) 5-axis fiber

chuck positioner (0.1mm spatial resolution), (13) single-mode optical fiber,

(14) photomultiplier (Hamamatsu H5773 with 2 ns rise time), (15) digital

oscilloscope (Tektronix THS730A), (16) PIN photodiode (with 0.1 ns rise

edge), (17) two-dimensional platform (10mm spatial resolution).

R. Zhao et al. / Optics & Laser Technology 39 (2007) 968–972 969

in an infinite liquid

Rmax ¼T c

0:915ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffir=ðP1 � P0Þ

p , (1)

where Rmax is the maximum radius of the spherical bubble,Tc is the collapsing time of the spherical bubble, r is thedensity of fluid, PN is the static pressure, P0 is the vaporpressure inside the bubble (2330 Pa at 20 1C). However,when cavitation bubble collapse occurs near a solidboundary, it does not maintain a spherical shape butelongates along the normal direction of the solid boundary.In addition, the solid boundary causes a prolongation ofthe collapse time. Therefore, Rayleigh’s theory does notsuit the cavitation bubble collapse near a solid boundaryany more [15–18].

On the experiment front, Qi et al. [17] have measured thecollapse time of cavitation bubble and its prolongationfactor detected by a hydrophone. However, the activeelement of the hydrophone is usually flat, which makes itdifficult to detect collapse time and prolongation factoraccurately. In the present work, a new detection techniquebased on fiber-coupling optical beam deflection (OBD) isproposed. This detection method has many advantages,such as low cost, a simple structure, high-frequencyresponse (more than 10MHz). Using this optical diagnos-tic system, the variations of sequential waveforms inducedby the motion of a laser-generated bubble near a solidboundary are investigated in detail. The maximum bubbleradii and collapse time for each oscillation cycle can bedetermined from the characteristic signals. In addition, bytracking the maximum radius and the collapse time of thecollapsing bubble, the dependence of the prolongationfactor k on the dimensionless distance g between the bubbleand the boundary, and the laser energy was experimentallyinvestigated.

2. Experimental setup

The experimental arrangement is outlined in Fig. 1. Asingle bubble is generated near the target immersed in aglass cuvette (100mm� 50mm), filled with distilled water,by using a Q-switched Nd:YAG (wavelength1.06 mm, pulseduration 10 ns). An attenuator adjusts the incident laserenergy without changing its spatial distribution. Opticalcomponents 4 and 5 consist of an adjustable-focus extenderlens. In order to reduce the probability of generatingmultiple plasmas and to keep a bubble in spherical shape,the laser pulse is expanded and collimated by this extenderlens so that it has a relative large cone angle in water. It isworth mentioning that the laser beam is parallel to thetarget surface in the experiment, as shown in Fig. 1(a).

The probe beam emitted by a He–Ne laser is focused onthe area of optical breakdown. The deflected beam is thenfocused into a single-mode optical fiber by means of amicroscope objective. This fiber serves as a positionsensitive detector and is mounted on a five-dimensionalfiber-regulating stand with 0.1 mm spatial resolution. The

light from the optical fiber is then fed into a photomulti-plier (Hamamatsu H5773 with 2 ns rise time) and recordedwith a digital oscilloscope (Tektronix THS730A). In orderto increase the signal-to-noise ratio, a narrow-bandinterference filter (central wavelength 0.63 mm) is placedin front of the fiber. The scattered light from each laserpulse is monitored as a trigger signal with a photoelectricdiode 16 having a 0.1 ns rise time. Elements numbered 8–13shown in Fig. 1 build up an OBD diagnostic system. ThisOBD part is placed on a two-dimensional platform thatcan be moved in the direction of the arrow with a spatialresolution of 10 mm, as shown in Fig. 1(b).

3. Results and discussion

3.1. The maximum bubble radii

A laser-generated bubble generally undergoes severalperiodic oscillations until it finally dissolves in thesurrounding water. In order to investigate the bubblebehavior near a solid boundary, the position of theplatform is adjusted, to control the distance between theprobe beam and the solid boundary, with a minimum stepof 10 mm. The ‘‘zero’’ spatial position is marked when thecross-sectional area of the probe beam is reduced to half bythe target. This can be judged by the signal amplitudeshown on the oscilloscope. The experimental criteria forjudging the maximum bubble radius depend on whetherthe characteristic peak signals appear.

ARTICLE IN PRESSR. Zhao et al. / Optics & Laser Technology 39 (2007) 968–972970

Fig. 2 is a diagram of the probe beam passing through anoscillating cavity based on the simulated results of thevariation of the bubble radius [1], where a, b, c and d are aseries of lines that parallel the target surface and passthrough the position of beam focus shown in Fig. 1. Fig. 3shows the sequence of waveforms during the bubblegrowth and collapse. In this figure, the applied laser energyis 25mJ and the distance L from the laser focus to theboundary is 4.25mm. When the probe beam lies outsidethe maximum bubble radius, as denoted by position ‘a’marked in Fig. 2, only the laser-generated plasma shockwave and collapse shock wave will appear, whichcorresponds to the conditions shown in Fig. 3(a). If theprobe beam moves closer toward the target, where is justinside the first maximum bubble radius, as in the positionmarked ‘b’ in Fig. 2, the corresponding deflection signal ofthe first pulsation appears, shown as a peak signal inFig. 3(b). When the detection distance is reduced further,the refractive index gradient inside the cavitation bubbleregion is large enough to make the probe beam deflectcompletely out of the fiber core, which leads to a flat-topped

Probe beam

t

R0

First bubble oscillation

Second

Third

Solid boundary

dc

b

a

Solid boundary

bubb

le r

adiu

s R

Time t

Fig. 2. Diagram of probe beam passing through an oscillating bubble.

0 200 400 600 800-0.04

0.00

0.04

0.08

Rel

ativ

e in

tens

ity/a

.u.

Time (μs)

0 200 400 600 800 1000Time (μs)

0.00

0.04

0.08

0.12

(a)

Rel

ativ

e in

tens

ity/a

.u.

(c) (d

(

Fig. 3. The typical waveforms produced by a laser-g

signal. Further decreasing the distance to the locations ‘c’ and‘d’ marked in Fig. 2, another two peak signals induced by thesecond and third bubble oscillations appear successively, asshown in Fig. 3(c) and (d). Hence these distancescorrespond to the second and third maximum radii.According to the experimental criteria mentioned above,the maximum bubble radii during the first three oscillationswere determined as follows: R1max ¼ 2:60mm, R2max ¼

1:09mm, R3max ¼ 0:85mm. From these experimentalresults, it can be seen that the maximum bubble radiireduces rapidly during successive bubble oscillations.By tracking the arrival times of the bubble walls during

its expanding and contracting stages at the correspondingdetection distance, the temporal oscillation characteristicsof a cavitation bubble oscillation near a solid boundary canbe obtained. Fig. 4 shows the variation of bubble radiuswith time. Here, each point is the average of five datavalues for laser pulse energy of 25mJ. The correspondingvalue for the non-dimensional distance g is 1.63.By varying the applied laser energy, the relationship

between the maximum radii and the applied laser energiescan be obtained shown in Fig. 5. The data indicates thatthe maximum bubble radii during each oscillation decreasesharply for successive oscillations and increase with theapplied laser energy. At the same time, the reduction in thegas content and dissipation in the energy of the bubble,during the cavitation bubble oscillations, causes somevibrations in the values of the second and third maximumradii.

3.2. The collapse time and the prolongation factor

As mentioned previously, when a cavitation bubblecollapses near a rigid boundary, it does not keep spherical

0 200 400 600 800 1000Time (μs)

Rel

ativ

e in

tens

ity/a

.u.

)

0 200 400 600 800-0.04

0.00

0.04

0.08

Rel

ativ

e in

tens

ity/a

.u.

Time (μs)b)

0.00

0.04

0.08

0.12

0.16

enerated bubble at different detection distances.

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0 200 400 600 800 1000

0.000

0.001

0.002

0.003

Bub

ble

radi

us (

mm

)

Time (μs)

Fig. 4. Radius–time relationship of a cavitation bubble as determined by

the optical beam deflection technique.

0 10 20 30 40

0

1

2

3

4 R1max

R2max

R3max

Max

imum

rad

ii (m

m)

Laser energy (mJ)

Fig. 5. Relationship between the maximum radii and the applied laser

energies.

R. Zhao et al. / Optics & Laser Technology 39 (2007) 968–972 971

shape any longer. Generally, the bubble is elongated alongthe normal direction of the boundary during the collapse.Moreover, the nearby boundary also causes a prolongationof the collapse period in comparison with that predicted byRayleigh’s model for a spherical cavitation bubble [14].Therefore, Rayleigh’s theory does not suit the case ofcavitation bubble collapse near a solid boundary any more.According to Rattray [18], correction to the Rayleighcollapse time is possible if the location of the bubble withrespect to the solid boundary is available. Rattray derivedan approximate relationship between the prolongationfactor k and the dimensionless parameter g

k ¼T 0CTC¼ 1þ 0:41

1

2g, (2)

where TC is the collapse time of the spherical bubble; T0C isthe prolonged collapse time of an equivalent maximumradius bubble; k is the prolongation factor of the collapsetime; g is the dimensionless distance parameter g ¼ L=Rmax

(Rmax being the maximum bubble radius and L the distance

of the cavity inception from a boundary). However, Eq. (2)is not suitable for very small g, because it predicts k-N

for g-0.Rearranging Eq. (1) leads to the following relationship:

TC ¼ 0:915Rmax

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffir

P1 � P0

r, (10)

where Rmax is the maximum radius of the bubble, Tc is thecollapse time of the spherical bubble, r is the density ofdistilled water (r ¼ 1:0� 103 kg=m3), PN is the staticpressure, P0 is the vapor pressure inside the bubble(2330 Pa at 20 1C) [19].Substituting (10) into (2) yields

k ¼T 0C

0:915Rmax

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffir=ðP1 � P0Þ

p , (3)

where Rmax is the maximum radius of the bubble; T0C is theprolonged collapse time of an equivalent maximum radiusbubble collapsing near the solid boundary; k is theprolongation factor with its definition k ¼ T 0C=TC (TC isthe collapse time of a spherical bubble collapse in infinitewater and T0C is the collapse time of an equivalentmaximum radius bubble collapse near a solid boundary).The prolongation factor can be determined from Eq. (3) ifthe bubble parameters T0C and Rmax are known.Lauterborn [20] has demonstrated that the expansion

and collapse of laser-generated bubbles are highly symme-trical, Provided that the laser pulse duration is muchshorter than the oscillation period of the bubble and theviscosity of the liquid is small. This is the case for bubblegeneration in water using laser pulses with duration in thenanosecond range. The time interval between the shockwaves originating from bubble generation and collapserespectively is considered to be twice the collapse time.Therefore, from Fig. 4 the prolonged collapse time T 0C1 ¼

270ms can be calculated. Substituting T 0C1 ¼ 270ms,R1max ¼ 2:60mm, r ¼ 1:0� 103 kg=m3, P1 ¼ 1:0�105 Pa and P0 ¼ 2330Pa into the modified Rayleighequation (3), the prolongation factor k ¼ 1:12 is calculatedat a laser pulse energy level of 25mJ and with a distanceparameter g ¼ 1:63.By varying the applied laser energy and the dimension-

less distance parameter g, respectively, the curves of theprolongation factor k versus the applied laser energy andthe dimensionless parameter g can be achieved. The resultsof this analysis are plotted in Figs. 6 and 7. It is obviousthat the prolongation factor increases with the applied laserpulse energy, from the data shown in Fig. 6. From Fig. 7, itis seen that the characteristic parameter k decreases whilethe dimensionless parameter g increases as the laser pulseenergy keeps constant. When the dimensionless parameterg is increased further, the prolongation factor k decreasesslowly and converges to one, which corresponds toRayleigh’s theory in an infinite liquid. This conclusiondoes agree well with the results obtained in other researchstudies [12,17,18].

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0.5 1.0 1.5 2.0 2.5 3.0 3.51.0

1.1

1.2

1.3

1.4

The

pro

long

atio

n fa

ctor

κκ

Dimensionless parameter γ

Fig. 7. The prolongation factor k vs. the dimensionless distance parameter g.

0 10 20 30 401.00

1.04

1.08

1.12

1.16

The

pro

long

atio

n fa

ctor

κκ

Laser energy (mJ)

Fig. 6. The prolongation factor of the collapse time vs. the applied laser

energy.

R. Zhao et al. / Optics & Laser Technology 39 (2007) 968–972972

4. Conclusion

Based on experimental results obtained with a highlysensitive fiber-optic sensor, the maximum bubble radii ateach oscillation of a laser-generated cavitation bubble inthe vicinity of a wall have been detected. Combining theseresults with the modified Rayleigh’s model, the collapsetime prolongation factor versus the applied laser energyand dimensionless parameter g were obtained. The experi-mental results show that the maximum radii increase withthe applied laser energy, while decreasing in turn duringsuccessive oscillations. The prolongation factor k increaseswith the applied laser energy, but decreases as thedimensionless parameter g is increased. When the dimen-sionless parameter is increased further, the prolongationfactor k continues to reduce and converges slowly to one,corresponding to Rayleigh’s theory for a cavitation bubblein an infinite liquid. These results may help to explain someof the interaction mechanisms in laser medical surgery andhydraulic cavitation.

Acknowledgments

The work is supported by the National Natural ScienceFoundation of China (Grant no. 60578015), the NaturalScience Foundation of the Jiangsu Higher EducationInstitutions of China (Grant no. 05KTB510028), theTeaching and Research Award Program for OutstandingYoung Professor in Higher Education Institute. MOE, PRChina and the Specialized Research Fund for the DoctoralProgram of Higher Education of China (Grant no.20050288025).

References

[1] Shima A. Studies on bubble dynamics. Shock Waves 1997;7:33–42.

[2] Philipp A, Lauterborn W. Cavitation erosion by single-laser

produced bubbles. J. Fluid Mech 1998;361:75–116.

[3] Niemz MH. Laser-tissue interactions: fundamentals and applications.

Germany: Springer; 1996.

[4] Kodama T, Tomita Y. Cavitation bubble behavior and bubble-shock

wave interaction near a gelatin surface as a study of in vivo bubble

dynamics. Appl Phys B: Lasers Opt 2000;70:139–49.

[5] Vogel A, Engelhard R, Behnle U, Parlitz U. Minimization of

cavitation effects in pulsed laser ablation-illustrated on laser

angioplasty. Appl Phys B 1996;62:173–82.

[6] Brennen CE. Cavitation and bubble dynamics. New York, Oxford:

Oxford University Press; 1995.

[7] Benjamin TB, Ellis AT. The collapse of cavitation bubbles and the

pressure thereby produced against solid boundaries. Phil Trans Roy

Soc London Ser A 1966;260:221–40.

[8] Blake JR, Gibson DC, Doheriy G. Transient cavities near

boundaries, part 1 rigid boundary. J Fluid Mech 1981;170:479–97.

[9] Schiffers WP, Shaw SJ, Emmony DC. Acoustical and optical tracking

of the collapse of a laser-generated cavitation bubble near a solid

boundary. Ultrasonics 1998;36:559–63.

[10] Vogel A, Lauterborn W. Acoustic transient generation by laser-

produced cavitation bubbles near solid boundaries. J Acoust Soc Am

1988;84:719–31.

[11] Shaw SJ, Schiffers WP, Emmony DC. Experimental observations of

the stress experienced by a solid surface when a laser-created bubble

oscillates in its vicinity. J Acoust Soc Am 2001;110:1822–6.

[12] Vogel A, Lauterborn W, Timm R. Optical and acoustic investigations

of the dynamics of laser-produced cavitation bubbles near a solid

boundary. J Fluid Mech 1989;206:299–338.

[13] Shaw SJ, Jin YH, Schiffers WP, Emmony DC. The interaction of a

single laser-generated cavity in water with a solid surface. J Acoust

Soc Am 1996;99(5):2811–24.

[14] Lord Rayleigh (John William Strutt). On the pressure developed in a

liquid during the collapse of a spherical cavity. Phil Mag

1917;34:94–8.

[15] Plesset MS, Chapman RB. Collapse of an initially spherical vapour

cavity in the neighborhood of a solid boundary. J Fluid Mech

1971;47:283–90.

[16] Kodama T, Tomita Y. Cavitation bubble behavior and bubble–shock

wave interaction near a gelation surface as a study of in vivo bubble

dynamics. Appl Phys B 2000;70:139–49.

[17] Qi DM, Lu CJ. Experimental investigations of cavitation collapse

noise. Acta Acustica 2000;25(6):532–6.

[18] Rattray M. PhD thesis, California Institute of Technology, 1951.

[19] Vogel A, Busch S, Parlitz U. Shock wave emission and cavitation

bubble generation by picosecond and nanosecond optical breakdown

in water. J Acoust Soc Am 1996;100:148–65.

[20] Lauterborn W. Kavitation durch laserlicht. Acustica 1974;31:51–78

[in German].