Optics and Lasers in Engineering 49 (2011) 428–433

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Optics and Lasers in Engineering

0143-81

doi:10.1

n Corr

E-m

nxw@m

journal homepage: www.elsevier.com/locate/optlaseng

Mechanical effects of laser-induced cavitation bubble on different geometricalconfinements for laser propulsion in water

Bing Han, Yun-Xiang Pan, Ya-Li Xue, Jun Chen, Zhong-Hua Shen, Jian Lu, Xiao-Wu Ni n

School of Science, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, People’s Republic of China

a r t i c l e i n f o

Article history:

Received 6 August 2010

Received in revised form

8 October 2010

Accepted 12 November 2010Available online 7 December 2010

Keywords:

Laser propulsion

Confinement

Cavitation

Bubble collapse

66/$ - see front matter & 2010 Elsevier Ltd. A

016/j.optlaseng.2010.11.012

esponding author. Tel.: +86 025 84315075; f

ail addresses: hanbingnjust@gmail.com (B. Ha

ail.njust.edu.cn (X.-W. Ni).

a b s t r a c t

Laser propulsions of six kinds of propelled objects in water and air are studied in this paper. The kinetic

energy and momentum coupling coefficients gained by the objects after implementation of single laser

pulses are investigated experimentally. It is shown that the propulsion effects are better in water than in air.

Both in water and in air, the propulsion effects are better if there is a cavity on the laser irradiated surface of

the object, and a hemispherical cavity works better than a 901-conical cavity. A concept of equivalent

reference pressure is proposed in this paper. It means that the asymmetry in the liquid induced by a rigid

boundary near a spherical or nonspherical oscillating bubble can be approximated as the perturbation

induced by a compressive stress wave passing through a bubble in the infinite static liquid. Thus, the

collapse time and the pressure surrounding the nonspherical collapsing bubble can be estimated based on

the maximum velocity of the liquid jet tip. Experiments also show that cavitation with oscillations and

collapse can be induced at the object–water interface on the outside surface of the object head by the

penetrating intensive stress wave and the elastic deformation of the object head. The bulging velocity of the

object surface is calculated based on the propagation theory of stress waves at medium interfaces.

& 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Investigations of laser propulsion in atmosphere and vacuumshow that the propelling effect is influenced greatly by thegeometry of the propelled objects [1–5]. Different kinds of geome-trical confinements have been designed, among which the Myrabo-type [2] and the bell-type[4] are the most famous ones. For laserpropulsion in water [6], the sources of the propelling force includethe laser ablation shock wave, the bubble oscillating shock wavesand the final bubble collapse impact. According to our investiga-tions, the major part of propelling power is from the laser ablationshock wave and the final collapse impact. Only less than 1% ofpropelling power is from the latter bubble oscillating shock waves[6]. Variation in geometrical confinement of the propelled objectinfluences all three sources of propelling force [7]. Therefore, sixkinds of geometrical confinements are designed in this paper basedon numerical investigation results [7].

Investigations on the laser-induced bubble are concentrated onoscillating properties of the spherical bubble in the infinite liquidenvironment [8,9] and collapsing properties of the quasi-sphericalbubble near different interfaces [10–14]. In this paper, the bubblesinduced on the six kinds of propelled objects are quasi-half (whenthe laser irradiated surface is flat or there is a hemispherical cavity

ll rights reserved.

ax: +86 025 84318430.

n),

on the laser irradiated surface) and quasi-quarter (when there is a901-conical cavity on the laser irradiated surface) spherical cavita-tion bubbles elongated in the opposite direction of the laser beam.In addition, there are two other kinds of investigations on bubbledynamics that are connected with the compressive stress wavepassing through the liquid are of great interest to researchers. Oneof them is the collapse of the bubble exposed to a compressivestress wave passing through the infinite static liquid [15]. The otheris the shock wave-induced cavitation in a liquid, which is widelystudied in clinical medicine [16], for example, minimization or cureof the tissue damages induced by exposure to shock wave and therecently developed cell detachment and membrane permeabiliza-tion assisted by shock wave-induced cavitation.

In this paper, laser propulsions of six kinds of propelled objectsin water and in air are studied experimentally. The kinetic energyand momentum coupling coefficients gained by the objects afterimplementation of single laser pulses are investigated with differ-ent pulse energies. The experimental results are compared with thenumerical ones. It is very difficult to measure the parameters(pressure, temperature, velocity, etc.) of the fluid field surroundingthe collapsing bubble experimentally, especially for bubblesinduced in sunken areas, e.g. the cavities on the laser irradiatedsurface of the objects discussed in this paper, because the spatialand temporal scales of a collapsing bubble are micrometers andmicroseconds, respectively, and the bubble cannot be disturbedby measuring equipments. It is proposed in this paper that theasymmetry in the liquid induced by a rigid boundary near aspherical or nonspherical oscillating bubble can be approximated

B. Han et al. / Optics and Lasers in Engineering 49 (2011) 428–433 429

as the perturbation induced by a compressive stress wave passingthrough a bubble in the infinite static liquid. Thus, the collapse timeand the pressure surrounding the nonspherical collapsing bubblecan be estimated based on the numerically calculated maximumvelocity of the liquid jet tip. Experiments also show that cavitationwith oscillations and collapse can be induced at the object–waterinterface on the outside surface of the object head. The velocity ofelastic deformation of the object head surface is calculated basedon the propagation theory of stress waves at medium interfaces.The calculations are compared with numerical results of thevelocity field of the liquid near the object head.

2. Experimental setup

The experimental layout is illustrated in Fig. 1. Bubbles weregenerated on the propelled objects placed in the glass cuvette by a Q-switched Nd:YAG laser (TEM00, 1.06 mm, 10 ns). The propelled objectswere suspended as a pendulum, as shown in the inset of Fig. 1(b). Allthe surfaces of the objects were polished. The internal side-length ofthe bottom side of the cuvette is 21 cm. Its internal height is 15 cm.The oscilloscope was triggered by the signal from PIN photodiode (risetime 5 ns). The objects could be moved by a translational platformwith a resolution of 10 mm along the positive and negative directionsof x as shown in Fig. 1. A continuous detecting He–Ne laser beam(0.6328 mm) was focused onto the photoelectric detector. The timedurations that the objects need to pass through a distance s afterimplementation of every single Nd:YAG laser pulse were measured.

Nd:YAG laser 7

He-Ne laser

velocity direction

s

Inset (c)

Top view

9

8

7

10

12

1314

6 5 4 3 2 1x

11

Frontview

He-Ne laser7

solid bar,

with two ends

fixed on 8

suspension

wire

Inset (b) Front view

Inset (a) Six objects

Fig. 1. Experimental setup: 1—Nd:YAG laser, 2 and3—beam splitter, 4—attenua-

tion group, 5—concave–convex lens group, 6—focusing lens, 7—propelled object,

8—glass cuvette, 9—He–Ne laser, 10—focusing lens, 11—photoelectric detector,

12—oscilloscope, 13—PIN photodiode and 14—energy meter. Inset (a) shows the

photograph of the propelled objects, inset (b) shows the pendulum and inset

(c) shows the initial movement distance s.

Table 1Geometrical parameters of the six kinds of aluminum axisymmetric objects used in the

Serial number 1 2 3

Configuration

and dimension (mm)

3 6

6

3 6

64

3 6Mass (g) 0.57 0.37 0.69

s (mm) 0.880 0.880 0.805

In order to approximate the initial velocities, s should be assmall as possible. As a compromise between the accurate initialvelocities and the stable measurements, s was determined asfollows. Before the experiment, make sure that the detecting beamin its entirety is captured by the photoelectric detector. Then movethe object using the translational platform along the negativedirection of x, till 3/4 of the detecting beam energy is blocked fromreaching the photoelectric detector, which can be read out throughthe oscilloscope. Record the reading of the translational platform asthe initial position of the propelled object, which is also the startingpoint of s. Continue moving the object along the negative directionof x, till all of the detecting beam energy is blocked from reachingthe photoelectric detector, which means that the object is at theterminal of s. A schematic diagram of distance s is shown in theinset of Fig. 1(c). Move the object back to the initial positionthrough the translational platform. Adjust the position of thebiconvex lens to focus the Nd:YAG laser onto the propelled surface.In order to prevent linear breakdown in water, the Nd:YAG laserbeam was first expanded by a concave–convex lens group. In theexperiment, the oscilloscope will record the energy variation in thedetecting He–Ne laser beam when it is continuously blocked by theaccelerated object. Thus, the time duration that the object needs topass through s after implementation of every single Nd:YAG laserpulse can be read out by means of the oscilloscope wave. In thispaper, s is less than 1 mm; hence the resistance to the object isneglected. The geometrical parameters of the six kinds of alumi-num axisymmetric objects are given in Table 1. The serial numbersin Table 1 are consistent with the matter in inset of Fig. 1(a).

3. Experimental results and discussion

3.1. Effects of geometrical confinements

Fig. 2 shows the kinetic energy, including (a1)–(c1), andmomentum coupling coefficients, including (a2)–(c2), gained bythe six kinds of objects after implementation of single laser pulseswith different pulse energies in water and in air. Fig. 2(a1) and (a2)shows that the propulsion effects are better in water than in air, nomatter whether or not there is a cavity on the tail (the laserirradiated surface) of the object. For laser propulsion in water, thenumerical simulations predict that the objects with cavities on thetail gain more energy during the first expansion of the bubble, butthe object with no cavity (plane tail) gain far more energy duringthe final bubble collapse. So the total energy gained by the plane tailobject is higher [7]. This deviation can be attributed to the neglectof the recoil pressure, which is induced by the explosive expansionof the inception of the bubble in the numerical simulation. Theamplitude of the recoil pressure can be more than 108 Pa, whichleads to underestimation of energy that the objects gain from thefirst expansion of the bubble in the numerical simulations,especially for objects with cavities on the tail.

Fig. 2(b1) and (b2) shows that the propulsion effects are better ifthere is a cavity on the laser irradiated surface of the object in air,

experiment.

4 5 6

6

3 6

64

3 3

64

3 3

64

0.46 0.18 0.26

0.805 0.880 0.805

0 50 100 150 200

0

15

30

45

60

Kin

etic

Ene

rgy(

J)

Laser Pulse Energy (mJ)

1 in air 1 in water 5 in air 5 in water

0 50 100 150 2000.0

0.4

0.8

1.2

1.6

2.0

Cm

(10

-3 N

s/J

)

Laser Pulse Energy (mJ)

1 in air1 in water5 in air5 in water

0 50 100 150 200

0.0

0.8

1.6

2.4

3.2

Laser Pulse Energy (mJ)

Kin

etic

Ene

rgy(

J)

1 in air2 in air3 in air4 in air

0 50 100 150 200 2500.00

0.08

0.16

0.24

0.32

0.40

Cm

(10

-3 N

s/J

)Laser Pulse Energy (mJ)

1 in air2 in air3 in air4 in air

0 50 100 150 2000

153045607590

Kin

etic

Ene

rgy(

J)

Laser Pulse Energy (mJ)

1 in water3 in water5 in water6 in water

0 50 100 150 2000.0

0.7

1.4

2.1

2.8

3.5

Cm

(10

-3 N

s/J

)

Laser Pulse Energy (mJ)

1 in water3 in water5 in water6 in water

Fig. 2. Kinetic energy, including (a1)–(c1), and momentum coupling coefficients, including (a2)–(c2), gained by the six kinds of objects after implementation of single laser

pulses with different pulse energies in water and in air.

B. Han et al. / Optics and Lasers in Engineering 49 (2011) 428–433430

and a hemispherical cavity works better than a 901-conical cavity.Fig. 2(b1) shows that the kinetic energy increases faster as the pulseenergy increases for objects with a cavity on the tail. Fig. 2(b2)shows that momentum coupling coefficients decrease as the pulseenergy increases in air. It decreases to 50% of the maximum valuefor objects without a cavity on the tail, and only to 70% of themaximum value for objects with a cavity.

Fig. 2(c1) and (c2) shows that the cavities on the object tails arealso the main factor to improve propulsion effects in water, and ahemispherical cavity works better than a 901-conical cavity,consistent with the numerical results [7]. Fig. 2(c2) shows thatmomentum coupling coefficients increase as the pulse energyincreases in water. The maximum coupling coefficients are similarfor objects with no tail cavities (nos. 1 and 3), which is about 70% ofthe maximum value of objects with a 901-conical cavity, and 40% ofthe maximum value of objects with a hemispherical cavity.

3.2. Estimation of collapse time and collapse pressure

Ref. [15] pointed out the relation between reference collapse jetvelocity (vjet,ref) and pressure amplitude of the passing throughcompressive stress wave (Pref) for bubbles in the infinite staticliquid, as

vjet,ref ¼

ffiffiffiffiffiffiffiffiPref

r

sð1Þ

where r is the density of the liquid. For bubbles incepted near arigid boundary, the collapse jet velocity can reach 50–160 m/s,which is 5–10 times of vjet,ref at 25 1C and standard atmospherepressure (Pref¼1.01�105 Pa, r¼1.0�103 kg/m3) [17]. We pro-pose that the asymmetry in the liquid induced by the rigidboundary near the spherical oscillating bubble can be approxi-mated as the perturbation induced by a compressive stress wavewith an amplitude that is 25–100 times that of the standardatmosphere pressure passing through the bubble in the infinitestatic liquid. Here we call this 25–100 times the standard atmo-sphere pressure the equivalent reference pressure (Peq). Ref. [15]also pointed out the relation between the maximum collapse jet tipvelocity (vjet,max) and vjet,ref, and the relation between the referencecollapse time (tc,ref) and Pref for bubbles in the infinite static liquid:

vjet,max

vjet,ref� 2� 3 ð2Þ

tc,ref ¼ Rm

ffiffiffiffiffiffiffiffir

Pref

sð3Þ

where Rm is the maximum bubble radius. From Eqs. (1)–(3) and thenumerical results [7] of vjet,max from quasi-half (when the laserirradiated surface is flat or there is a hemispherical cavity on thelaser irradiated surface) and quasi-quarter (when there is a901-conical cavity on the laser irradiated surface) sphericalcavitation bubbles, Peq induced by the 3 kinds of geometrical

Table 2Effects of geometrical confinements on bubbles incepted on them.

Configurations vjet,max (m/s) Peq (Pa) tc,eq (ms) Pnum (Pa) tc,num (ms)

Flat 993 1.1�108–2.5�108 1.2–1.8 1.0�108–3.0�108 1.6

Hemispherical cavity 859 8.3�107–1.9�108 1.2–1.8 9.0�107–2.5�108 1.2

901-conical cavity 866 8.4�107–1.9�108 1.4–2.1 7.0�107–1.5�108 1.4

0 200 400 600 800 1000

0.0

0.1

0.2

0.3

0.4

Osc

illog

raph

Sig

nal/m

v

Time/ s

0 200 400 600 800 10000.0

0.2

0.4

Oscillation Shock Wave

Shock Wave

Osc

illog

raph

Sig

nal/m

v

Time/ s

0 200 400 600 800 10000.3

0.6

0.9

OscillationShock Wave

Shock Wave

Osc

illog

raph

Sig

nal/m

v

Time/ s

Nd:YAG laser 7

He-Ne laser

velocity direction

head tail

cavitation bubble shock wave

shock wave

Fig. 3. (a) Schematic diagram of the shock waves and bubbles on the object tail and head. (b)–(d) Oscilloscope wave corresponding to the oscillating bubble at the tail of no. 3

object, the oscillating bubble and the shock waves at the head of no. 3 object and the shock waves detected off the outside surface of no. 3 object head, respectively.

B. Han et al. / Optics and Lasers in Engineering 49 (2011) 428–433 431

confinements, including the flat, the hemispherical cavity and the901-conical cavity, can be calculated. The corresponding tc,eq alsocan be calculated. The calculated results are listed in Table 2. Thenumerical simulation results [7] for the collapse time (tc,num) andthe fluctuation ranges of pressure amplitude of the fluid fieldsurrounding the collapsing bubbles (Pnum) incepted in the samegeometrical confinements, are listed in Table 2 too.

The overlapping ratio of the fluctuation ranges of Pnum and theestimation ranges of Peq can be calculated according to

ULðPnum \ PeqÞ�LLðPnum \ PeqÞ

ULðPnum [ PeqÞ�LLðPnum [ PeqÞð4Þ

where \ and [ refers to the set intersection and the set union,respectively. UL(A) and LL(A) means to take the upper limit and thelower limit of set A, respectively. The overlapping ratios of Pnum andPeq of the flat, the hemispherical cavity and the 901-conical cavityare 70%, 60% and 55%, respectively. All the tc,num are within theestimation ranges of tc,eq. When the bubble begins to collapse, theliquid around will concentrate inward with the bubble as thecenter. Because of the compressibility and the inertia in the liquid,it will result in a high pressure area surrounding the collapsingbubble. For bubbles in the infinite static liquid, it is a sphericallysymmetric high pressure area surrounding the collapsing bubble.For bubbles near a rigid boundary, a hemispherical shell shapedhigh pressure area will be induced in the liquid surrounding andcontracting the collapsing bubble, which is results from theasymmetry induced by the rigid boundary. For the nonsphericalbubbles discussed in this paper, cambered shell shaped highpressure areas will be induced in the liquid surrounding andcontracting the collapsing bubbles. Thus, the contracting cambered

shell shaped high pressure area induced by the geometricalconfinements is similar to a compressive stress wave passingthrough a bubble in the infinite static liquid. Furthermore, thecollapse time and the pressure surrounding the nonsphericalcollapsing bubble can be estimated through vjet,max and theconception of Peq. However, the accuracy of the estimation willdecrease as the deviation from the spherical symmetry in thebubble increases.

3.3. Cavitation on the outside surface of the object head

It was observed in the experiment that cavitation with oscilla-tions and collapse can be induced not only at the laser focus on theobject tail but also on the outside surface of the object head, whenlaser pulse energy was a bit higher, e.g. 61 mJ for no. 3 object. Fig. 3(a)shows a schematic diagram of the shock waves and bubbles on theobject tail and head, respectively. Fig. 3(b) and (c) shows theoscilloscope wave corresponding to the oscillating bubble at thetail and the head of no. 3 object when laser pulse energy was 61 mJ,respectively. Fig. 3(d) shows the oscilloscope wave corresponding tothe shock waves detected when the He–Ne laser was 5 mm off theoutside surface of the no. 3 object head. The measurements ofFig. 3(b)–(d) were based on the optical beam deflection method[13,18]. Experiments also show that the pulse energy needed toinduce cavitations on the outside surface of the object head wassmaller if there was a cavity on the object tail, e.g. no. 2, 4–6 objects.

As mentioned above, a high intensity recoil pressure is inducedby explosive expansion of inception of the bubble on the laserirradiated surface. This intensive stress wave will propagate towardthe outside surface of the object head. After leaving the object, it

r/mm D

B. Han et al. / Optics and Lasers in Engineering 49 (2011) 428–433432

will continue propagating in the liquid as a compressive stresswave with a negative pressure tail [16]. When it comes to the solid–liquid interface on the outside object surface, the liquid layer willbe pushed to detach from the object surface first and thenexperience the tensile force induced by the negative pressure ofthe stress wave tail. These double splitting effects give chance forthe initial cavitation nucleus to develop and finally detectablecavitations appear on the outside surface of the object head, asshown in Fig. 3(c) and (d).

Besides the cavitation mechanisms described above, we thinkthere is another factor that helps the growth of head cavitations,which are elastic deformation of the outside surface of the objecthead [12] induced by the recoil pressure. Hereinafter, the bulgingvelocity of the object surface is calculated. Fig. 4 shows thegeometry of the interested area, where d is the thickness of thewall of the object head. Suppose that a high density content bubbleis incepted by the Nd:YAG laser on the inside surface of the objecthead with a radius of h/2 and an expansion velocity of vb withintime duration t. The cylindrical bar in the object contacted with thehemispherical bubble, as shown in Fig. 4 by a gray bar, will sustain ahigh intensity recoil pressure P and therefore gain elastic deforma-tion and bulging with a velocity of vs in the direction pointed out inFig. 4 by the gray thick arrow.

3.3.1. Calculation of P based on the jet model

Momentum conservation for the system gives

Pp h

2

� �2

t¼ vbrb

2

3p h

2

� �3

ð5Þ

where rb is the density of the high density content bubble.Experiments show that the formation time t of the high densitycontent bubble related to the recoil pressure is so short that theliquid involved in the bubble formation, in other words thevaporized liquid, has no time to expand. Thus, rb can be set tothe density of water, which is 1.0�103 kg/m3. Based on theexperiment, we can take h¼0.2 mm, d¼1 mm, vb¼250 m/s andt¼1.0�10�7 s. Thus, we get P¼1.7�108 Pa, consistent withexperimental results of Ref. [12].

3.3.2. Calculation of vs based on the propagation theory of stress

waves at medium interfaces

The intensive stress wave induced by the recoil pressure P canbe treated as the one-dimensional traveling wave propagating inthe cylindrical bar in the object (the gray bar in Fig. 4). Thedifferential equation of longitudinal vibration in the medium of theone dimensional traveling wave can be written as

@2u

@x2¼

1

C2

@2u

@t2ð6Þ

C ¼

ffiffiffiffiE

r

sð7Þ

where C is the wave velocity, E is the elastic modulus, r is themedium density, u is the longitudinal displacement of the medium,

laser -induced

bubble

surface

bulging

direction

h

d

Nd:YAG

laser

part of 7

Fig. 4. Geometry of the model used in calculating the elastic deformation of the

object head induced by the recoil pressure.

x is the coordinate along the wave path (�NoxoN) and t is thetime (t40). According to the D’Alembert formula, the generalsolution for Eq. (6) is

uðx,tÞ ¼ f ðxþCtÞþgðx�CtÞ ð8Þ

where f and g are up-going and down-going waves propagating inthe bar, respectively. Consider the gray bar in Fig. 4 as part of a longbar; the stress sustained by the volume element at the insidesurface of the object head can be described as

P¼�E@g

@xð9Þ

When the stress wave propagates to the solid–liquid interface onthe outside object surface, it will be partially reflected. Thereflectivity R can be written as

R¼Z1�Z2

Z2þZ1ð10Þ

where Z1 and Z2 are acoustic impedances of the solid and the liquid,respectively. The motion equation of the volume element at theoutside surface of the object head becomes

usðx,tÞ ¼ gðx�CtÞþRgðxþCtÞ ð11Þ

Thus, vs can be calculated from

vs ¼@us

@t¼�C

@g

@xþRC

@g

@x¼�ð1�RÞC

@g

@xð12Þ

Finally, from (9), (10) and (12), vs is obtained as follows:

vs ¼2Z2

Z1þZ2

CP

Eð13Þ

Taking Z1¼13.5 MPa s/m, Z2¼1.5 MPa s/m, E¼71.7 GPa, C¼5000m/s and P as the recoil pressure calculated in Section 3.3.1 we getvs¼2.4 m/s.

3.3.3. Numerical simulation for the velocity field of the liquid near the

object head

Numerical simulation is implemented of a hemispherical shellthat is identical to the head part of no. 4 or 6 object. The geometry ofthe interested area is shown in Fig. 5. Region D represents water.Please refer to Ref. [7] for detailed introductions of the numericalmethod. The simulation is initiated as follows. A circular area withpoint z2 as the center and a radius of 1 mm on the inside surface ofthe hemispherical shell, which is the laser irradiated surface, isimpacted by an intensive pressure of 1.5�108 Pa. The numericalresults of the x-component of the velocity field of the liquid near theoutside surface of the object head with point z1 as the center, whichis marked by a gray bar AB in Fig. 5, are shown in Fig. 6. The abscissain Fig. 6 is the distance to point B along vector BA

�!. Fig. 6 shows that

the highest x-component velocity of the circular area in the liquidwith a radius of 0.1 mm and 46 mm away from the object head isabout �2.9 m/s, which is approximately equal to the estimationmade in Sections 3 and 3.2.

z3z1

x/mm

25-25

25

r1r2

z2

z1 =-1z2 =0

r2 =2

z3 =2

r1 =3

A

B

A(-0.6,3.5)

B(-1.046,0)

Fig. 5. Geometry for the numerical simulation of the velocity field of the liquid near

the outside surface of the object head induced by the recoil pressure.

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

Vel

ocity

(m

/s)

BA vector length(mm)

Fig. 6. Numerical results of the x-component of the velocity field in the liquid

marked by the gray bar AB in Fig. 5.

B. Han et al. / Optics and Lasers in Engineering 49 (2011) 428–433 433

4. Conclusions

For the six kinds of objects discussed in this paper, thepropulsion effects are better in water than in air. The momentumcoupling coefficient increases as the pulse energy increases inwater, while it slightly decreases in air. Both in water and in air, thepropulsion effects are better if there is a cavity on the laserirradiated surface of the object, and a hemispherical cavity worksbetter than a 901-conical cavity. Experiments also show that theenergy that the objects gain from the first expansion of the bubblewill be underestimated if the propulsion effect induced by theexplosive expansion of the inception of the bubble is neglected.

The asymmetry in the liquid induced by a rigid boundary near aspherical or nonspherical oscillating bubble can be approximatedas the perturbation induced by a compressive stress wave passingthrough a bubble in the infinite static liquid. Thus, the collapse timeand pressure surrounding the nonspherical collapsing bubble canbe estimated based on the concept of equivalent reference pressureand the maximum velocity of the liquid jet tip. However, theaccuracy of the estimation decreases as the deviation from thespherical symmetry in the bubble increases.

Cavitation with oscillations and collapse can be induced at theobject–water interface on the outside surface of the object head bypenetrated intensive stress wave and the elastic deformation of theobject head. To estimate the bulging velocity of the elasticdeformation, the method based on the propagation theory of stresswaves at medium interfaces provides realistic results.

Acknowledgment

This project was supported by the NUST Research Fundingunder Grant no. 2010ZDJH09.

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