Study on the Relationship between the Behavior and Wave Radiation of Micro-capsule under the Ultrasound Field

(1)

Study on the Relationship between the Behavior and Wave Radiation of Micro-capsule under the Ultrasound Field

Minoru SUDO*㧘Kenji YOSHIDA* and Yoshiaki WATANABE*

(Received March 30, 2007)

A micro-capsule which is surrounded by the shells can hold gas or liquid such as drug solution. The role of the shell is to separate internal material from surrounding material and to prevent the diffusion of internal material. Making use of these advantages, the micro-capsule is applied in various fields. Particularly, in medical fields, the micro-capsule is expected as a tool of gene therapy and drug delivery system (DDS) under the ultrasonic control. In these medical applications, the micro-capsules work as a carrier, which collapse and release the internal material at the effective point of the body. Therefore, both the control and evaluation of micro-capsule collapse are important. In addition, it is required that the information of the collapse is obtained nondestructively from the acoustic wave caused by micro-capsule destruction. There are few reports on the relationship between collapsing behavior and the generated acoustic wave from micro-capsule. In order to investigate these mechanisms, the micro-capsule behavior is observed using a high speed video camera. The acoustic wave from the micro-capsule is observed using hydrophone, simultaneously.

The frequency spectrum of the received wave changed due to the micro-capsule behaviors. Moreover, generation of sub-harmonic component depends on the initial micro-capsule radius. In some specific cases of initial radius, sub-harmonic component of the radiated wave was observed before the collapse. This indicates the sub-harmonic observation becomes a strong tool to predict the collapse of the micro-capsule.

-G[YQTFUmicro-capsule㧘collapse㧘acoustic signal㧘high speed video camera㧘

ࠠ࡯ࡢ࡯࠼ࡑࠗࠢࡠࠞࡊ࠮࡞㧘፣უ㧘㖸㗀ାภ㧘㜞ㅦᐲࡆ࠺ࠝࠞࡔ࡜㧘

⿥㖸ᵄߢ㚟േߐࠇࠆࡑࠗࠢࡠࠞࡊ࠮࡞ߩᝄേ᜼േߣ㖸㗀᡼኿ାภߦ㑐ߔࠆᬌ⸛

㗇⮮ ታ㧘ศ↰ ᙗม㧘ᷰㄝ ᅢ┨

ߪߓ߼ߦ

ࡑࠗࠢࡠࠞࡊ࠮࡞ߪࠪࠚ࡞ࠍᜬߜߘߩౝㇱߦ

᳇૕߽ߒߊߪᶧ૕ࠍ଻ᜬߔࠆߎߣ߇ߢ߈ࠆ㧚ߎߩ ߚ߼ࡑࠗࠢࡠࠞࡊ࠮࡞ߪ᭽ޘߥಽ㊁ߢ೑↪ߐࠇߡ

޿ࠆ㧚․ߦක≮ಽ㊁ߦ߅޿ߡ㧘ㆮવሶᴦ≮߿࠼࡜

࠶ࠣ࠺࡝ࡃ࡝࡯ࠪࠬ࠹ࡓ ¹⁾ߦ߅ߌࠆㆮવሶ߿⮎‛

ߩ៝ㅍ૕ߣߒߡߩᓎഀࠍᦼᓙߐࠇߡ޿ࠆ㧚ߎߩ႐ ว㧘ౝኈ‛ࠍ᡼಴ߐߖࠆߚ߼ߦࠞࡊ࠮࡞ࠍ፣უߐ

ߖࠆᔅⷐ߇޽ࠅ㧘ߘߩ፣უࠍ೙ᓮߔࠆߎߣ߇㊀ⷐ ߥᛛⴚ⺖㗴ߣߥࠆ㧚ߘߩߚ߼㧘ࡑࠗࠢࡠࠞࡊ࠮࡞

ߩ᜼േࠍᛠីߔࠆ⋡⊛ߢ㧘⿥㖸ᵄᾖ኿ᤨߦ߅ߌࠆ ࡑࠗࠢࡠࠞࡊ࠮࡞᜼േࠍ᷹ⷰߒߚႎ๔ ^2-6)߇ߥߐ ࠇߡ޿ࠆ㧚߹ߚߎࠇࠄߩᛛⴚߩᔕ↪ߦ޽ߚߞߡ㧘 ࡑࠗࠢࡠࠞࡊ࠮࡞ߩ፣უᖱႎߪᦨ⚳⊛ߦߪ㖸㗀ା

ภࠍ⸃ᨆߔࠆߎߣߦࠃߞߡᓧࠆߎߣ߇ᦸ߹ߒ޿ߣ

⠨߃ࠄࠇࠆ㧚ߒ߆ߒߥ߇ࠄ㧘ࡑࠗࠢࡠࠞࡊ࠮࡞፣

უᤨߩ㖸㗀ାภ․ᕈߦߟ޿ߡ⹦ㅀߒߚႎ๔ߪዋߥ

*Department of Electronics Engineering, Doshisha University, Kyoto Telephone/Fax: +81-774-65-6300, E-mail: etf1103@mail4.doshisha.ac.jp

(2)

޿㧚ߘߎߢ㧘ࡑࠗࠢࡠࠞࡊ࠮࡞፣უᤨߩ㖸㗀․ᕈ ࠍࠃࠅ᣿⏕ߦᓧࠆ੐ࠍ⋡⊛ߣߒ㧘㜞ㅦᐲࡆ࠺ࠝࠞ

ࡔ࡜ࠍ↪޿ߡࡑࠗࠢࡠࠞࡊ࠮࡞ߩ፣უ᜼േࠍ᣿⏕

ߦ⏕⹺ߔࠆߣߣ߽ߦ㧘ࠞࡊ࠮࡞ߦࠃࠆੑᰴ⊛ߥ᡼

኿㖸ᵄߩ᷹ⷰࠍ⹜ߺߚ㧚ᧄႎ๔ߢߪ᷹ⷰ⚿ᨐ߆ࠄ

ࠞࡊ࠮࡞᜼േߣࠞࡊ࠮࡞߆ࠄ᡼኿ߐࠇࠆ㖸ᵄߩ๟

ᵄᢙࡍࠢ࠻࡞ߩ㑐ଥߦߟ޿ߡᬌ⸛ߔࠆ㧚

ታ㛎♽

ታ㛎♽ࠍFig.1ߦ␜ߔ㧚᳓ᮏࠍ⣕᳇᳓ߢḩߚߒ㧘

ㅘ᣿☼⌕࠹࡯ࡊߦන৻ߩࡑࠗࠢࡠࠞࡊ࠮࡞ࠍઃ⌕

ߐߖߚ㧚ࡑࠗࠢࡠࠞࡊ࠮࡞ࠍಳ㕙ဳᝄേሶ(ᦛ₸㧦 40mm㧘㐿ญᓘ㧦50mm)ߩὶὐઃㄭߦ⸳⟎ߒ㧘ᝄേ

ሶ߆ࠄ⿥㖸ᵄࠍᾖ኿ߒߚ႐วߩࠞࡊ࠮࡞ߩᝄേ᜼

േࠍ㜞ㅦᐲࡆ࠺ࠝࠞࡔ࡜ࠍ↪޿ߡశቇ⊛ߦ᷹ⷰߒ ߚ㧚߹ߚ㧘ᝄേሶߣㅘ᣿☼⌕࠹࡯ࡊࠍ⚿߱⋥✢਄ߦ

㈩⟎ߐࠇߚPVDFࡂࠗ࠼ࡠࡈࠜࡦ(⋥ᓘ㧦2mm)ߦࠃ ߞߡࡑࠗࠢࡠࠞࡊ࠮࡞߆ࠄߩੑᰴ⊛ߥ᡼኿㖸ᵄߩ หᤨ᷹ⷰࠍ⹜ߺߚ㧚ಳ㕙ဳᝄേሶߪ๟ᵄᢙ 270kHz ߩᱜᒏࡃ࡯ࠬ࠻25ᵄߢ㚟േߒߚ㧚Fig.2ߦㅘ᣿☼⌕

࠹࡯ࡊߦࡑࠗࠢࡠࠞࡊ࠮࡞ࠍઃ⌕ߐߖߥ߆ߞߚ႐ วߦ PVDF ࡂࠗ࠼ࡠࡈࠜࡦߦࠃࠅ᷹ⷰߒߚฃᵄ㖸

࿶ᵄᒻࠍ␜ߔ㧚ᧄታ㛎ߢߪห࿑ߦ␜ߒߚᾖ኿㖸ᵄࠍ ࡑࠗࠢࡠࠞࡊ࠮࡞ߦᾖ኿ߔࠆߎߣࠍ 1 ࿁ߩ⹜ⴕߣ

⠨߃㧘ࠞࡊ࠮࡞ߩౝㇱ᳇૕߇ቢోߦ᡼಴ߐࠇࠆ߹ߢ ⶄᢙ࿁➅ࠅ㄰ߒߚ㧚߹ߚ㧘᜼േ᷹ⷰᤨߩ㜞ㅦᐲࡆ࠺

ࠝࠞࡔ࡜ߩ᠟ᓇㅦᐲߪ10⁶frame/secߢ޽ࠆ㧚ࠞࡔ࡜

ߩ᠟ᓇᨎᢙ߇100ᨎߣ㒢ࠄࠇߡ޿ࠆߚ߼㧘ߎߩ᧦ઙ ߢ᠟ᓇࠍⴕ߁ߣ㧘ࠞࡊ࠮࡞ߩ᜼േࠍᾖ኿㖸ᵄߩ⚂

25๟ᦼಽ᠟ᓇߢ߈㧘1๟ᦼ޽ߚࠅߩ᠟ᓇᨎᢙߪ⚂4 ᨎߣߥࠆ㧚߹ߚ㧘ᧄታ㛎ߢ↪޿ߚࡑࠗࠢࡠࠞࡊ࠮࡞

ߪ᧻ᧄᴤ⢽⵾⮎(ᩣ)⵾ F-80E ߢ㧘ࠪࠚ࡞ߩ᧚⾰ߪ PVC ߢ㧘᧚⾰ߩࡗࡦࠣ₸㧘ࡐࠕ࠰ࡦᲧߪ౒ߦਇ᣿

ߢ޽ࠆ㧚ࠪࠚ࡞ߩෘߺߪ㧘ೋᦼඨᓘߦኻߒߡ2%⒟ ᐲߢ޽ࠆ㧚

Xenon Lamp High-speed Lens

video camera

Power Amp.

PC Oscilloscope Hydrophone PC

Adhered microcapsule Transducer

trigger FG

Xenon Lamp High-speed Lens

video camera

Power Amp.

PC Oscilloscope Hydrophone PC

Adhered microcapsule Transducer

trigger FG

Fig.1 Measurement system.

200 100 0 -100 -200

Sound pressure [kPa]

300x10^-6 250

200 150 100 50

Time [s]

Fig.2. Irradiated sound wave.

⚿ᨐ

ࠞࡊ࠮࡞᜼േߣฃᵄࠬࡍࠢ࠻࡞ߩ㑐ଥ ᧄ▵ߢߪ㧘ࠞࡊ࠮࡞᜼േߣࠞࡊ࠮࡞߆ࠄߩ᡼኿㖸 ᵄߣߩ㑐ଥߦߟ޿ߡᬌ⸛ߔࠆ㧚

ᧄታ㛎♽ߢߪᝄേሶߣࡂࠗ࠼ࡠࡈࠜࡦࠍኻะߐ ߖߡ⋥✢⁁ߦ㈩⟎ߒߚߚ߼㧘ฃᵄ㖸ᵄߦߪᝄേሶߦ ࠃࠆ᡼኿㖸ᵄߣࠞࡊ࠮࡞ߦࠃࠆੑᰴ⊛ߥ᡼኿㖸ᵄ ߇฽߹ࠇࠆ㧚ߒߚ߇ߞߡ㧘ࠞࡊ࠮࡞߆ࠄߩੑᰴ⊛ߥ

᡼኿㖸ᵄࠍᬌ⸛ߔࠆߚ߼ߦߪࠞࡊ࠮࡞ሽ࿷ߩ᦭ή

෺ᣇߩฃᵄ㖸ᵄࠍᲧセᬌ⸛ߔࠆᔅⷐ߇޽ࠆ㧚ࠞࡊ࠮

࡞߇ሽ࿷ߒߥ޿႐วߩฃᵄ㖸࿶ᵄᒻߢ޽ࠆFig.2ࠍ FFT ಣℂߒߡ᳞߼ߚࠬࡍࠢ࠻࡞⚿ᨐࠍၮᧄᵄ๟ᵄ ᢙᚑಽߢⷙᩰൻߒߡFig.3ߦ␜ߔ㧚

harmonic components fundamental component

-80 -60 -40 -20 0

Relative level [dB]

800x10³ 600

400 200

0

Frequency [Hz]

harmonic components fundamental component

-80 -60 -40 -20 0

Relative level [dB]

800x10³ 600

400 200

0

Frequency [Hz]

Fig.3. Frequency spectrum of received sound wave without micro-capsule.

(3)

ห࿑ࠃࠅၮᧄ๟ᵄᢙᚑಽ f(270kHz)ߩ߶߆ߦ㜞⺞

ᵄᚑಽ2f(540kHz)㧘3f(810kHz)ࠍ⏕⹺ߢ߈ࠆ㧚ၮᧄ

๟ᵄᢙᚑಽߪಳ㕙ဳᝄേሶߩ᡼኿㖸ᵄࠍ⋥ធฃᵄ ߒߚ߽ߩߢ޽ࠅ㧘㜞⺞ᵄᚑಽߪ⿥㖸ᵄߩᇦ⾰વ៝ᤨ

ߩ㖸㗀⊛㕖✢ᒻലᨐߦ⿠࿃ߔࠆ߽ߩߣ⠨߃ࠄࠇࠆ㧚

ᰴߦ㧘න৻ࠞࡊ࠮࡞㧔ೋᦼඨᓘR0㧦60Pm㧕ࠍㅘ

᣿☼⌕࠹࡯ࡊߦઃ⌕ߐߖߚ႐วߩ⚿ᨐࠍ␜ߔ㧚੹࿁

ߩ᷹ቯߢߪࠞࡊ࠮࡞ߩౝㇱ᳇૕߇ቢోߦ᡼಴ߐࠇ ࠆ߹ߢ35࿁ߩ⹜ⴕࠍⷐߒߚ㧚᷹ⷰߐࠇߚࠞࡊ࠮࡞

ߪౝㇱ᳇૕ࠍቢోߦ᡼಴ߔࠆ߹ߢ㧘ਥߦ3Ბ㓏ߩ᜼

േߦಽ߆ࠇߚ㧚ߘߩࠞࡊ࠮࡞᜼േߩ᷹ⷰ↹௝ࠍߘࠇ ߙࠇFig.4~6(a)ߦ␜ߔ㧚Fig.4~6ߪ⹜ⴕ10㧘15㧘32࿁

⋡ࠍ⴫ߒߡ޿ࠆ㧚ߥ߅㧘↹௝Ԙ㧔initial㧕ߪߘࠇߙࠇ ߩ⹜ⴕߦ߅޿ߡ⿥㖸ᵄ߇ᾖ኿ߐࠇࠆ೨ߩೋᦼ⁁ᘒ ߦ߅ߌࠆ᷹ⷰ↹௝ߢ޽ࠅ㧘↹௝ԙ㨪ԟߩᤨ㑆ߪFig.2 ߩᤨ㑆ゲߦኻᔕߒߡ޿ࠆ㧚ߐࠄߦᾖ኿㖸ᵄߦኻߔࠆ

ࠞࡊ࠮࡞ߩ⤘ᒛ࡮෼❗ㆇേࠍ⹏ଔߔࠆߚ߼ߦ᷹ⷰ↹

௝਄ߩᓇߩ㕙ⓍSࠍ⸘᷹ߒߚ㧚ߘߩ⚿ᨐࠍߘࠇߙࠇ

Fig.4~6(b)ߦ␜ߔ㧚߹ߚߎࠇࠄߩࠞࡊ࠮࡞᜼േࠍ๒

ߒߚ႐วߦฃᵄߐࠇߚ㖸㗀ାภࠍFFTಣℂߒ㧘๟

ᵄ ᢙ ࠬ ࡍ ࠢ ࠻ ࡞ ࠍ ᳞ ߼ 㧘 ߘ ߩ ⚿ ᨐ ࠍ ߘ ࠇ ߙ ࠇ

Fig.4~6(c)ߦ␜ߔ㧚ߥ߅ฦ๟ᵄᢙᚑಽࠍࠞࡊ࠮࡞߇

ሽ࿷ߒߥ޿႐ว(Fig.3)ߩၮᧄ๟ᵄᢙᚑಽߩ୯ߢⷙ

ᩰൻߒߚ㧚

Fig.4(a)㧘(b)ࠃࠅ㧘ࠞࡊ࠮࡞ߪ⤘ᒛᣇะߦ߶ߣࠎ

ߤᄌ૏ߖߕ෼❗ᣇะߦߩߺᄌ૏ߒߡ޿ࠆߎߣࠍ⏕

⹺ߢ߈ࠆ㧚ߎࠇߪࡂ࡯࠼ࠪࠚ࡞ࠍ᦭ߔࠆࠞࡊ࠮࡞ࠍ

↪޿ߡ޿ࠆߚ߼ࠪࠚ࡞ߩᝄേᛥ೙ലᨐ߇ߪߚࠄ޿

ߡ޿ࠆߚ߼ߛߣ⠨߃ࠄࠇࠆ㧚߹ߚ㧘Fig.4(b)ࠃࠅࠞ

ࡊ࠮࡞ߪ㚟േ㖸ᵄߦኻߒߡੑ୚๟ᦼߢᝄേߒߡ޿

ࠆߎߣࠍ⏕⹺ߢ߈㧘 Fig.4(c)ࠃࠅࠞࡊ࠮࡞߇ሽ࿷ߒ ߥ޿႐วߦ⏕⹺ߢ߈ߥ޿ಽ⺞ᵄᚑಽ㧔f/2㧘3f/2㧕߇

↢ᚑߐࠇߡ޿ࠆߎߣࠍ⏕⹺ߢ߈ࠆ㧚

Fig.5(a)㧘(b)ࠃࠅ㧘⿥㖸ᵄᾖ኿ᤨ㑆߇50Ps߹ߢߪ

Fig.4 ߩ⹜ⴕߣห᭽ߩᝄേࠍ߅ߎߥߞߡ޿ࠆߎߣࠍ

⏕⹺ߢ߈ࠆ㧚ߘߩᓟ᜼േ᷹ⷰ↹௝ߦ߅޿ߡߪᓇߩ㕙

ⓍߩჇട߇⹺߼ࠄࠇࠆ㧚ߒߚ߇ߞߡߎߩ႐วߦߪ㧘 50Ps ߢౝㇱ᳇૕߇৻᳇ߦ᡼಴ߒߚߣ⠨߃ࠄࠇࠆ㧚 ߘߩᓟ᡼಴ߐࠇߚౝㇱ᳇૕߇㚟േ㖸ᵄߦหᦼߒߡ

⤘ᒛ෼❗ㆇേࠍⴕߞߡ޿ࠆߎߣࠍ⏕⹺ߢ߈ࠆ㧚৻ᣇ

ߢ๟ᵄᢙࠬࡍࠢ࠻࡞㧔Fig.5(c)㧕ࠍ⷗ࠆߣ㧘Fig.4 ߩ

⹜ⴕߢ↢ᚑߐࠇߡ޿ߚಽ⺞ᵄߩሽ࿷ࠍ᣿⏕ߦ⏕⹺

ߔࠆߎߣ߇ߢ߈ߥ޿㧚

Fig.6(a)Ԙߦ␜ߔࠃ߁ߥࠞࡊ࠮࡞ౝㇱߦᓸዊ᳇૕

߇ሽ࿷ߔࠆೋᦼ⁁ᘒ߆ࠄᓸዊ᳇૕߇ᝄേࠍⴕ߁㧚߹

ߚ㧘ߎߩ⁁ᘒߢߪౝㇱ᳇૕߇ೋᦼඨᓘߦኻߒߡỗߒ ߊ⤘ᒛ෼❗ᝄേࠍⴕߞߡ޿ࠆߩߢ㧘ࠪࠚ࡞ߦࠃࠆᝄ

േᛥ೙ലᨐ߇㕖Ᏹߦᒙߊߥࠅ⥄↱᳇ᵃߦㄭ޿ᝄേ

ࠍⴕߥߞߡ޿ࠆߣ⠨߃ࠄࠇࠆ㧚߹ߚห࿑ࠃࠅౝㇱ᳇

૕߇㚟േ㖸ᵄߦኻߒߡੑ୚๟ᦼߢᝄേߒߡ޿ࠆߎ ߣࠍ⏕⹺ߢ߈㧘 Fig.6(c)ࠃࠅࠞࡊ࠮࡞߇ሽ࿷ߒߥ޿

႐วߦ⏕⹺ߢ߈ߥ޿ಽ⺞ᵄᚑಽ߇↢ᚑߐࠇߡ޿ࠆ ߎߣࠍ⏕⹺ߢ߈ࠆ㧚

એ਄ࠃࠅ㧘ౝㇱ᳇૕ࠍ৻᳇ߦ᡼಴ߔࠆ⹜ⴕߩ೨ᓟ ߢࠞࡊ࠮࡞ߩ⁁ᘒ߇ᄌൻߒ㧘ᝄേᒻᘒߦᄌൻ߇޽ࠄ ࠊࠇߚ㧚߹ߚࠞࡊ࠮࡞ߩ᜼േߩᄌൻߦ઻޿ฃᵄ㖸ᵄ ߩ๟ᵄᢙࠬࡍࠢ࠻࡞ߦ߽ᄌൻ߇޽ࠄࠊࠇߚ㧚

㽲Initial 㽳56Ps 㽴58Ps 㽵60Ps

200Pm

㽶62Ps 㽷64Ps 㽸66Ps 㽹68Ps

200Pm

㽶62Ps 㽷64Ps 㽸66Ps 㽹68Ps

(a) Image of the micro-capsule behaviors.

200 100 0 -100 -200

120x10^-6 100

80 60 40

Time [s]

16x10³ 12 8 4 S [Pm2 ]

S Irradiated sound wave

(b) Temporary variant of shadow area S.

sub-harmonic components

-80 -60 -40 -20 0

Relative level [dB]

800x10³ 600

400 200

0

Frequency [Hz]

-80 -60 -40 -20 0

Relative level [dB]

800x10³ 600

400 200

0

Frequency [Hz]

(c) Frequency spectrum of received sound wave with micro-capsule.

Fig.4. Tenth trial.

(4)

㽲Initial 㽳50Ps 㽴52Ps 㽵54Ps

200Pm

㽶56Ps 㽷58Ps 㽸60Ps 㽹62Ps 㽲Initial 㽳50Ps 㽴52Ps 㽵54Ps

200Pm

㽶56Ps 㽷58Ps 㽸60Ps 㽹62Ps

200 100 0 -100 -200

120x10^-6 100

80 60 40

Time [s]

30x10³ 20

2 S [Pm] 10

(emission)50Ps

200 100 0 -100 -200

120x10^-6 100

80 60 40

Time [s]

30x10³ 20

2 S [Pm] 10

(emission)50Ps

-80 -60 -40 -20 0

Relative level [dB]

800x10³ 600

400 200

0

Frequency [Hz]

Fig.5. Fifteenth trial.

200Pm

㽶112Ps 㽷114Ps 㽸116Ps 㽹118Ps 㽲Initial 㽳106Ps 㽴108Ps 㽵110Ps

200Pm

㽶112Ps 㽷114Ps 㽸116Ps 㽹118Ps

200 100 0 -100 -200

120x10^-6 100

80 60 40

Time [s]

12x10³ 108 64 S [Pm2 ]

-80 -60 -40 -20 0

Relative level [dB]

800x10³ 600

400 200

0

Frequency [Hz]

-80 -60 -40 -20 0

Relative level [dB]

800x10³ 600

400 200

0

Frequency [Hz]

Fig.6. Thirty-second trial.

ࠞࡊ࠮࡞᜼േߣฃᵄࠬࡍࠢ࠻࡞ߩ㑐ଥ ೨▵ߩ⚿ᨐࠃࠅ(Fig.4㨪Fig.6)㧘ࠞࡊ࠮࡞᜼േ߇ᄌ ൻߔࠆߦߟࠇ㧘ฃᵄ㖸ᵄߩ๟ᵄᢙࠬࡍࠢ࠻࡞߽ᄌൻ ߔࠆߎߣ߇⏕⹺ߐࠇߚ㧚ߎߩ⚿ᨐߪࠞࡊ࠮࡞߆ࠄߩ

᡼኿㖸ᵄ߇ࠞࡊ࠮࡞᜼േߦଐሽߔࠆߎߣࠍ␜ໂߔ ࠆ㧚ߘߎߢ㧘᜼േᄌൻߦ઻߁ࠞࡊ࠮࡞߆ࠄߩ᡼኿㖸 ᵄߩᄌൻࠍ⹦⚦ߦᬌ⸛ߔࠆߚ߼ߦ⹜ⴕ࿁ᢙߦኻߔ ࠆฃᵄ㖸ᵄߩࠬࡍࠢ࠻࡞ᄌൻࠍ᳞߼ߚ㧚ߘߩ⚿ᨐࠍ

Fig.7(a)ߦ␜ߔ㧚ߐࠄߦၮᧄ๟ᵄᢙᚑ㧘㜞⺞ᵄᚑಽ㧘

ಽ⺞ᵄᚑಽߩߺࠍ᜛ᄢߒߚ߽ߩࠍߘࠇߙࠇ Fig.7(b)㧘 Fig.7(c)㧘Fig.7(d)ߦ␜ߔ㧚Fig.7ߪ❑ゲ߇๟ᵄᢙ㧘ᮮ ゲ߇⹜ⴕ࿁ᢙࠍ⴫ߒߡ߅ࠅ㧘ฦ๟ᵄᢙᚑಽߩᒝᐲࠍ

ࠞ࡜࡯ࠬࠤ࡯࡞ߢ⴫ߒߚ㧚ߥ߅㧘ࠞࡊ࠮࡞߇ሽ࿷ߒ ߥ޿႐วࠍၮḰߣߒߡᲧセࠍⴕ߁ߚ߼㧘ߎߩ႐วߩ

⚿ᨐࠍ0࿁⋡ߩ૏⟎ߦ␜ߔ㧚߹ߚ㧘Fig.3 ߆ࠄ⏕⹺

ߐࠇࠆࠃ߁ߦ㧙45dB એਅߪ㧘ࡁࠗ࠭࡟ࡌ࡞ߣߺߥ ߔߎߣ߇ߢ߈ࠆߚ߼ήⷞߔࠆ㧚

Fig.7(b)㨪(d)ࠃࠅࠞࡊ࠮࡞߆ࠄౝㇱ᳇૕ࠍ᡼಴ߔ

ࠆ㧔⹜ⴕ15࿁⋡㧕೨ᓟߢၮᧄ๟ᵄᢙᚑಽ㧘㜞⺞ᵄ ᚑಽ㧘ಽ⺞ᵄᚑಽߩᄌൻࠍ⏕⹺ߢ߈ࠆ㧚ၮᧄ๟ᵄᢙ ᚑಽߪ⹜ⴕ15࿁⋡ߦ߅޿ߡዊߐߊߥࠆߎߣࠍ⏕⹺

ߢ߈ࠆ㧚߹ߚ㜞⺞ᵄᚑಽߪ⹜ⴕ16࿁⋡એ㒠ߦዊߐ ߊߥࠆߎߣࠍ⏕⹺ߢ߈ࠆ㧚৻ᣇߢಽ⺞ᵄᚑಽߪ⹜ⴕ 1㨪14 ࿁⋡ߢ↢ᚑߐࠇ㧘⹜ⴕ15 ࿁⋡ࠍႺߦ↢ᚑߐ ࠇߥߊߥߞߚ㧚ߘߩᓟ㧘⹜ⴕ32㧘33࿁⋡ߦ߅޿ߡ

ౣᐲ↢ᚑߐࠇߡ޿ࠆߎߣࠍ⏕⹺ߢ߈ࠆ㧚

(5)

Number of trial

Frequency [Hz] Relative level [dB]

15 (emission)

Number of trial

15 (emission)

Number of trial

15 (emission)

Number of trial

15 (emission)

(a) whole (b) fundamental component.

Number of trial

15 (emission)

Number of trial

15 (emission)

Number of trial

15 (emission)

Number of trial

15 (emission)

(c) harmonic component. (d) sub-harmonic component.

Fig.7. Trial variant of frequency spectra.(R0:60Pm)

Number of trial

9 (emission)

Number of trial

9 (emission)

Number of trial

9 (emission)

Number of trial

9 (emission)

Number of trial

9 (emission)

Number of trial

9 (emission)

Number of trial

9 (emission)

Number of trial

9 (emission)

Fig.8. Trial variant of frequency spectra. (R0:40Pm)

(6)

Number of trial

30 (emission)

Number of trial

30 (emission)

Number of trial

30 (emission)

Number of trial

30 (emission)

Number of trial

30 (emission)

Number of trial

30 (emission)

Number of trial

30 (emission)

Number of trial

30 (emission)

Fig.9. Trial variant of frequency spectra. (R0:104Pm)

ೋᦼඨᓘࠍᄌൻߐߖߚ႐วߩࠬࡍࠢ࠻࡞ᄌൻ 3.1㧘3.2▵ߢߪೋᦼඨᓘ㧦R0߇60Pmߢ޽ࠆࠞࡊ

࠮࡞ߩ᜼േߣ๟ᵄᢙࠬࡍࠢ࠻࡞ߩᄌൻࠍ␜ߒߚ㧚ߒ ߆ߒߥ߇ࠄታ↪ࠍᗐቯߒߚ႐ว㧘৻⥸⊛ߦࠞࡊ࠮࡞

ߪ࿕᦭ߩ☸ᐲಽᏓࠍᜬߟߚ߼㧘᭽ޘߥࠨࠗ࠭ߩࠞࡊ

࠮࡞߇ᔅߕหᤨߦሽ࿷ߔࠆ㧚ߒߚ߇ߞߡ㧘᭽ޘߥࠞ

ࡊ࠮࡞ඨᓘߦ߅޿ߡ㧘ࠞࡊ࠮࡞᜼േߣ๟ᵄᢙࠬࡍࠢ

࠻࡞ߩ㑐ଥࠍᛠីߒߡ߅ߊᔅⷐ߇޽ࠆ㧚ߘߎߢᧄ▵

ߢߪࠞࡊ࠮࡞ߩೋᦼඨᓘ㧦R0ࠍ40Pm㧘104Pmߣᄌ ൻߐߖߚߣ߈ߩ๟ᵄᢙࠬࡍࠢ࠻࡞ߩᄌൻࠍ␜ߔ㧚

ታ㛎♽ߪFig.1ߣห᭽ߩ߽ߣ㧘ታ㛎᧦ઙࠍ๟ᵄᢙ

270kHz㧘ᱜᒏࡃ࡯ࠬ࠻25ᵄ㧘㖸࿶450kPap-pߣߒ㧘

ೋᦼࠞࡊ࠮࡞ඨᓘ㧦R0ࠍ40Pm㧘104Pmߣᄌൻߐߖ ߚ㧚ೋᦼࠞࡊ࠮࡞ඨᓘ40Pm㧘104Pmߩ႐วߦᓧࠄ ࠇߚ⹜ⴕ࿁ᢙߦࠃࠆࠬࡍࠢ࠻࡞ᄌൻࠍߘࠇߙࠇ Fig.8㧘Fig.9ߦ␜ߔ㧚

Fig.8(b)㧘9(b)ࠃࠅၮᧄ๟ᵄᢙᚑಽߪౝㇱ᳇૕ࠍ৻

᳇ߦ᡼಴ߔࠆ⹜ⴕߦ߅޿ߡዊߐߊߥߞߡ޿ࠆߎߣ ࠍ⏕⹺ߢ߈ࠆ㧚߹ߚFig.8(c)㧘9(c)ࠃࠅ㜞⺞ᵄᚑಽߪ

ౝㇱ᳇૕ࠍ৻᳇ߦ᡼಴ߒߚ⹜ⴕߩᓟߦዊߐߊߥߞ ߡ޿ࠆߎߣࠍ⏕⹺ߢ߈ࠆ㧚৻ᣇߢಽ⺞ᵄᚑಽߩᄌൻ

ࠍߺࠆߣFig.8(d)ࠃࠅೋᦼඨᓘ40Pmߩ႐วߦߪౝ

ㇱ᳇૕ࠍ৻᳇ߦ᡼಴ߔࠆ⹜ⴕએ೨ߦߪ↢ᚑߐࠇߡ ߅ࠄߕ㧘ౝㇱ᳇૕᡼಴ᓟߪ⹜ⴕ12࿁⋡ߦ߅޿ߡ↢

ᚑߐࠇߡ޿ࠆߎߣࠍ⏕⹺ߢ߈ࠆ㧚߹ߚ㧘ೋᦼඨᓘ

104Pmߩ႐วߦߪFig.9(d)ࠃࠅౝㇱ᳇૕᡼಴એ೨ߦ

ߪ㧘↢ᚑߐࠇࠆ႐วߣ↢ᚑߐࠇߥ޿႐ว߇޽ࠆ㧚ౝ

ㇱ᳇૕᡼಴ᓟߪ⹜ⴕ71㨪74࿁⋡ߦ߅޿ߡ↢ᚑߐࠇ ߡ޿ࠆߩࠍ⏕⹺ߢ߈ࠆ㧚

⠨ኤ

3.2㧘3.3▵ࠃࠅೋᦼඨᓘߩᄌൻߦࠃࠄߕၮᧄ๟ᵄ ᢙᚑಽߣ㜞ầ⺞ᵄᚑಽߪห᭽ߩ௑ะࠍ␜ߒߚ㧚৻ᣇ ߢಽ⺞ᵄᚑಽߪೋᦼඨᓘߦࠃࠅౝㇱ᳇૕ࠍ৻᳇ߦ

᡼಴ߔࠆએ೨ߦ↢ᚑߐࠇࠆ႐วߣ↢ᚑߐࠇߥ޿႐ วࠍ⏕⹺ߒߚ㧚ᧄ▵ߢߪߎࠇࠄߩⷐ࿃ߦߟ޿ߡ⠨ኤ ߔࠆ㧚

(7)

ೋ߼ߦ㧘ၮᧄ๟ᵄᢙᚑಽ㧘㜞⺞ᵄᚑಽߩᄌൻߦߟ

޿ߡ⠨ኤߔࠆ㧚Fig.3㧘Fig.4~6(c)ࠃࠅࠞࡊ࠮࡞ઃ⌕

ߩ᦭ήߦࠃࠄߕ๟ᵄᢙࠬࡍࠢ࠻࡞ߦߪၮᧄ๟ᵄᢙ ᚑಽߣ㜞⺞ᵄᚑಽ߇฽߹ࠇࠆ㧚ߒߚ߇ߞߡၮᧄ๟ᵄ ᢙᚑಽߣ㜞⺞ᵄᚑಽߩᄌൻߪ㚟േ㖸ᵄߣࠞࡊ࠮࡞

߆ࠄߩ᡼኿㖸ᵄߣߩ૏⋧Ꮕߥߤࠍ⠨ᘦߒߥߌࠇ߫

ߥࠄߥ޿㧚ߒ߆ߒߥ߇ࠄ੹࿁ߩታ㛎ߢߪㅘㆊᵄࠍ᷹

ቯߒߡ޿ࠆߚ߼ߦ⹦⚦ߥᬌ⸛ࠍ߅ߎߥ߁ߎߣ㔍ߒ

޿㧚ߒߚ߇ߞߡታ㛎♽ࠍᡷༀߒ㧘ࠃࠅ⹦⚦ߥᬌ⸛ࠍ ߅ߎߥ߁ᔅⷐ߇޽ࠆ㧚

৻ᣇߢಽ⺞ᵄᚑಽߪࠞࡊ࠮࡞ᝄേߦࠃࠅߩߺ↢

ᚑߐࠇࠆᚑಽߢ޽ࠆߚ߼㧘ߎߩಽ⺞ᵄᚑಽߩ⹜ⴕ࿁

ᢙߦࠃࠆᄌൻߦߟ޿ߡᬌ⸛ߔࠆ㧚ಽ⺞ᵄᚑಽߪ

Fig.7(d)㧘Fig.9(d)ࠃࠅౝㇱ᳇૕᡼಴એ೨ߦ↢ᚑߐࠇ㧘

ౝㇱ᳇૕ࠍ᡼಴ߔࠆ⹜ⴕࠍႺߦ↢ᚑߐࠇߥߊߥߞ ߚ㧚ߘߩᓟ㧘ౣᐲ↢ᚑߐࠇߡ޿ࠆߎߣࠍ⏕⹺ߢ߈ࠆ㧚 3.1 ▵ߢ␜ߒߚࠃ߁ߦౝㇱ᳇૕ࠍ৻᳇ߦ᡼಴ߔࠆ⹜

ⴕߩ೨ᓟߢࠞࡊ࠮࡞ߩ⁁ᘒ߇ᄌൻߒ㧘ᝄേᒻᘒ߇ᄌ ൻߒߡ޿ࠆ㧚ߒߚ߇ߞߡౝㇱ᳇૕᡼಴એ೨ߣએᓟߦ ߅޿ߡߪಽ⺞ᵄ߇↢ᚑߐࠇߚࡔࠞ࠾࠭ࡓ߇⇣ߥࠆ ߣ⠨߃ࠄࠇࠆ㧚

ౝㇱ᳇૕᡼಴એ೨ߩ⹜ⴕߦ߅޿ߡߪ㧘ࠪࠚ࡞ߩᝄ

േᛥ೙ലᨐ߇௛޿ߡ޿ࠆ⁁ᘒߢ޽ࠆ㧚ߘߩߚ߼㧘ࠪ

ࠚ࡞߇ࡑࠗࠢࡠࠞࡊ࠮࡞ᝄേߦਈ߃ࠆᓇ㗀ࠍ⠨ᘦ ߒ㧘ࠞࡊ࠮࡞߇㚟േ㖸ᵄߦኻߒߡੑ୚ߩ๟ᦼߢᝄേ

ߒߚⷐ࿃ߦߟ޿ߡᬌ⸛ߒߥߌࠇ߫ߥࠄߥ޿㧚ߒ߆ߒ ߥ߇ࠄ㧘ᧄታ㛎ߢ૶↪ߒߚࡑࠗࠢࡠࠞࡊ࠮࡞ߩࠪࠚ

࡞㧔PVC ᕈ㧕ߩ․ᕈߦ㑐ߒߡߪਇ᣿ߥὐ߇ᄙߊ㧘

ࠪࠚ࡞߇ࡑࠗࠢࡠࠞࡊ࠮࡞ᝄേߦਈ߃ࠆᓇ㗀ߩᬌ

⸛ߪ㔍ߒ޿㧚ߘߩߚ߼㧘ಽ⺞ᵄ߇↢ᚑߐࠇߚⷐ࿃ߪ

⃻Ბ㓏ߢߪਇ᣿ߢ޽ࠅ㧘੹ᓟߩᬌ⸛⺖㗴ߢ޽ࠆ㧚

ౝㇱ᳇૕᡼಴ᓟߦ߅޿ߡಽ⺞ᵄ߇↢ᚑߐࠇߚⷐ

࿃ߟ޿ߡ⠨ኤߔࠆ㧚਄ㅀߒߚࠃ߁ߦౝㇱ᳇૕᡼಴ᓟ ߩಽ⺞ᵄ߇᷹ⷰߐࠇߚ⹜ⴕߢߪ㧘ࠞࡊ࠮࡞ߩࠪࠚ࡞

ߩᝄേᛥ೙ലᨐ߇߶ߣࠎߤߪߚࠄ޿ߡ߅ࠄߕౝㇱ

᳇૕߇⥄↱᳇ᵃߩࠃ߁ߦᝄ⥰ߞߡ޿ࠆߣ⠨߃ࠄࠇ ࠆ㧚⥄↱᳇ᵃߦ߅ߌࠆಽ⺞ᵄ↢ᚑ᧦ઙߪߎࠇ߹ߢℂ

⺰⊛ߦᬌ⸛ߐࠇߡ߅ࠅ㧘᳇ᵃߩ౒ᝄ๟ᵄᢙߩੑ୚ߢ 㚟േߐߖߚ႐วߦᦨ߽ૐ޿㚟േ㖸࿶ߢಽ⺞ᵄᚑಽ ߇↢ᚑߐࠇࠆߣ⸒ࠊࠇߡ޿ࠆ⁷⁾㧚એᓟ㧘ߎߩಽ⺞ᵄ

ᚑಽ߇↢ᚑߐࠇ߿ߔ޿᧦ઙࠍଢቱ਄㧘ಽ⺞ᵄ↢ᚑ᧦

ઙߣ⴫⃻ߔࠆ㧚ߎߩ⚿ᨐࠍ੹࿁ߩታ㛎᧦ઙߦᒰߡߪ

߼ࠆߣ㧘㚟േ๟ᵄᢙ߇270kHzߢ޽ࠆߎߣࠃࠅ᳇ᵃ ߩ౒ᝄ๟ᵄᢙ߇135kHzߩ႐วߦಽ⺞ᵄ↢ᚑ᧦ઙࠍ ḩߚߔߎߣࠍℂ⸃ߢ߈ࠆ㧚ߎߎߢ⥄↱᳇ᵃߩ౒ᝄ๟

ᵄᢙߩℂ⺰ᑼ⁸⁾ࠍ↪޿ࠆߣ๟ᵄᢙ135kHzߦ߅ߌࠆ

᳇ᵃߩ౒ᝄඨᓘߪ20Pmߣߥࠆ㧚ߒߚ߇ߞߡ੹࿁ߩ ታ㛎᧦ઙߢߪ㧘᳇ᵃඨᓘ߇20Pmߣߥࠆߣ߈ߦᦨ߽

ಽ⺞ᵄᚑಽ߇↢ᚑߐࠇ߿ߔ޿ߎߣ߇ℂ⸃ߢ߈ࠆ㧚એ

਄ߩᬌ⸛⚿ᨐࠍ⠨ᘦߒ㧘⹜ⴕ࿁ᢙߦኻߔࠆࠞࡊ࠮࡞

ࠨࠗ࠭ߩᄌൻࠍᬌ⸛ߔࠆ㧚3.1 ▵ߦ߅޿ߡ㧘ౝㇱ᳇

૕᡼಴ᓟߩ⹜ⴕߦߟ޿ߡߪ㧘ࠞࡊ࠮࡞ౝㇱߦ᳇ᵃ߇ ᱷሽߒߚ⁁ᘒߣߥࠅ㧘ߎߩౝㇱ᳇ᵃߩೋᦼࠨࠗ࠭ߪ㧘

ౝㇱ᳇૕᡼಴೨ߩ⹜ⴕߦ߅ߌࠆࠞࡊ࠮࡞ೋᦼࠨࠗ

࠭ࠃࠅ᣿ࠄ߆ߦዊߐ޿ߎߣ߇⏕⹺ߐࠇࠆ㧚 ߘߎߢ㧘

Fig.10ߦ⹜ⴕ࿁ᢙߦኻߔࠆࠞࡊ࠮࡞ߩೋᦼඨᓘ㧔ౝ

ㇱ᳇૕᡼಴ᓟߩ⹜ⴕߦߟ޿ߡߪౝㇱ᳇ᵃߩೋᦼඨ ᓘ㧕ߩᄌൻࠍ␜ߔ㧚

100 80 60 40 20

Initial radius [Pm]

70 60 50 40 30 20 10

Number of trial

R0104Pm R₀:60Pm R₀:40Pm

100 80 60 40 20

Initial radius [Pm]

70 60 50 40 30 20 10

Number of trial

R0104Pm R₀:60Pm R₀:40Pm

Fig.10. Trial variant of initial radius.

ห࿑ߦ␜ߔع㧘ً㧘٨ࡊࡠ࠶࠻ߪౝㇱ᳇૕ࠍ৻᳇

ߦ᡼಴ߒߚ⹜ⴕࠍ޽ࠄࠊߒߡ޿ࠆ㧚ห࿑ࠃࠅ㧘޿ߕ ࠇߩ᷹ⷰ⚿ᨐߦ߅޿ߡ߽㧘ౝㇱ᳇૕ࠍ৻᳇ߦ᡼಴ߒ ߚ⹜ⴕߩᓟߦౝㇱ᳇ᵃߩೋᦼඨᓘ߇ᷫዋߒߡ޿ࠆ ߎߣࠍ⏕⹺ߢ߈ࠆ㧚ߎࠇߪ㧘ࠞࡊ࠮࡞߆ࠄ᡼಴ߐࠇ ߚౝㇱ᳇૕߇๟࿐ᶧ૕ߦṁ಴ߒߚߚ߼ߛߣ⠨߃ࠄ ࠇࠆ㧚߹ߚ㧘Fig.7㨪9(d)ߣFig.10ࠃࠅ㧘ಽ⺞ᵄ߇↢

ᚑߐࠇߡ޿ࠆ⹜ⴕߦ߅޿ߡౝㇱ᳇ᵃߩೋᦼඨᓘߪ

⚂ 20Pmߣߥߞߡ޿ࠆߎߣࠍ⏕⹺ߢ߈ࠆ㧚ߎࠇߪ㧘

ࠪࠚ࡞ߩᝄേലᨐ߇ᒙߊߥࠅ⥄↱᳇ᵃߩಽ⺞ᵄ↢

ᚑ᧦ઙ߇ḩߚߐࠇߚ⚿ᨐ㧘ࠞࡊ࠮࡞ౝߦᱷሽߒߚౝ

ㇱ᳇૕߇㚟േ๟ᦼߦኻߒߡੑ୚ߩ๟ᦼߢᝄേߒ㧘ಽ

⺞ᵄ߇↢ᚑߐࠇߚߎߣࠍ␜ໂߒߡ޿ࠆ㧚

(8)

߹ߣ߼

ࡑࠗࠢࡠࠞࡊ࠮࡞ߩ፣უᖱႎߩ᛽಴ࠍ⋡⊛ߣߒ ߡࠞࡊ࠮࡞᜼േߣࠞࡊ࠮࡞߆ࠄ᡼኿ߐࠇࠆ㖸ᵄߩ

๟ᵄᢙࠬࡍࠢ࠻࡞ߩᬌ⸛ࠍ߅ߎߥߞߚ㧚ߘߩ⚿ᨐ㧘

ࠞࡊ࠮࡞ߩ᜼േ߇ᄌൻߔࠆߦߟࠇฃᵄ㖸ᵄߩ๟ᵄ ᢙࠬࡍࠢ࠻࡞ߦ߽ᄌൻ߇޽ࠄࠊࠇߚ㧚߹ߚታ㓙ߩᔕ

↪ࠍᗐቯߒ᭽ޘߥࠞࡊ࠮࡞ඨᓘߦ߅޿ߡ⹜ⴕ࿁ᢙ ߦࠃࠆࠬࡍࠢ࠻࡞ᄌൻࠍ⺞ߴߚ႐ว㧘ၮᧄ๟ᵄᢙᚑ ಽߣ㜞⺞ᵄᚑಽߩᄌൻߪߤߩඨᓘߦኻߒߡ߽ห᭽

ߩ௑ะࠍᓧߚ㧚৻ᣇߢ㧘ࠞࡊ࠮࡞ඨᓘࠍᄌൻߐߖࠆ ߣಽ⺞ᵄᚑಽߩ↢ᚑ௑ะߦᄌൻ߇޽ࠄࠊࠇߚ㧚ߒߚ ߇ߞߡታ㓙ߩᔕ↪ߢߪ☸ᐲಽᏓߦ㍈޿ࡇ࡯ࠢࠍᜬ ߚߖࠆߎߣߢၮᧄ๟ᵄᢙᚑಽ㧘㜞⺞ᵄᚑಽ㧘ಽ⺞ᵄ ᚑಽߩᄌൻࠍ᷹ⷰߔࠆߎߣߦࠃࠅࠞࡊ࠮࡞ߩ⁁ᘒ ࠍᛠីߔࠆߎߣ߇น⢻ߢ޽ࠆߣ⠨߃ࠄࠇࠆ㧚

ෳ⠨ᢥ₂

1) K.Tachibana and S.Tachibana, “Application of ultrasound energy as a new drug delivery system,” Jpn. J. Appl. Phys. 38, No.5, pp.3014-3019 (1999).

2) D. Koyama, W. Kiyan and Y. Watanabe, “Optical Observation of Microcapsule Destruction in an Acoustic Standing Wave,” Jpn. J. Appl. Phys. Vol.43 pp.3215-3219 Part 1 No.5B (2004).

3) D.Koyama, A.Osaki, W.Kiyan and Y.Watanabe, “Acoustic Destruction of Microcapsule Having a Hard Plastic Shell,”

IEEE Trans. Ultrasonics, Ferroelectrics, and Frequency control, Vol.53, No.7, pp.1314-1321 (2006).

4) ᄢ๺ື㇢㧘ศ↰ᙗม㧘༑ደᱞᒎ㧘ᷰㄝᅢ┨̌㜞ㅦᐲࡆ

࠺ࠝࠞࡔ࡜ߦࠃࠆࡑࠗࠢࡠࠞࡊ࠮࡞ߩ᜼േ᷹ⷰ㧘̍ାቇᛛ ႎ㧘US2006-82, (2006).

5) 㗇⮮ታ㧘ศ↰ᙗม㧘ᷰㄝᅢ┨̌⿥㖸ᵄ㚟േᤨߩࡑࠗࠢ

ࡠࠞࡊ࠮࡞᜼േߩశቇ⊛࡮㖸㗀⊛หᤨ᷹ⷰ㧘̍ାቇᛛႎ㧘 US2006-96, (2007).

6) ᄢ๺ື㇢㧘ศ↰ᙗม㧘ᷰㄝᅢ┨ “⿥㖸ᵄ㚟േᤨߦ߅ߌ ࠆࡑࠗࠢࡠࠞࡊ࠮࡞ߩ፣უ᜼േߩశቇ⊛᷹ⷰ㧙᳇ᵃߣࡑ

ࠗࠢࡠࠞࡊ࠮࡞ߩ⋧੕૞↪㧙,” ାቇᛛႎ㧘US2006-120, (2007).

7) Anthony Eller and H.G. Flynn, “Generation of Subhramonics of Order One-Half Bubbles in a Sound Field,”J.

Acoust. Soc. Am. Vol.46, No.3, pp.722-727 (1969).

8) T.G.Leighton, The ACOUSTIC BUBBLE, (ACADEMIC

PRESS, 1997), pp. 136-139.