ながれ34（2015）355−362355〔原著論文〕

࣐࢖ࢡࣟࣂࣈࣝ◊✲ࡢ㐍ᒎ*ᒸᒣ኱Ꮫ኱Ꮫ㝔⮬↛⛉Ꮫ◊✲⛉   ᰗ ℩ ┾୍㑻†ᒸᒣ኱Ꮫ኱Ꮫ㝔་ṑ⸆Ꮫ⥲ྜ◊✲⛉   ᯇᾆ ᏹ ἞ ࣐࢖ࢡࣟࣂࣈࣝࢆྵࡴὶࢀ㸪ᾮయࡢ◊✲࡟ࡘ࠸࡚㸪᭱㏆ࡢⓎᒎࢆⴭ⪅ࡽࡢ◊✲ࢆᇶ࡟ࡋ࡚ゎㄝࡍࡿ㸬᭱ึ࡟㸪࣐࢖ࢡࣟࣂࣈࣝࡢ୍⯡ⓗ࡞≀⌮ⓗ࣭໬Ꮫⓗᛶ㉁ࢆㄝ᫂ࡍࡿ㸬ḟ࡟㸪࣐࢖ࢡࣟࣂࣈࣝࢆྵࡴὶࢀ࡟ࡼࡿ᢬ᢠపῶ㸪⇕ఏ㐩ᢚไຠᯝ࡟㛵ࡍࡿᐇ㦂⤖ᯝࢆ㏙࡭㸪᭱ᚋ࡟࣐࢖ࢡࣟࣂࣈࣝࢆྵࡴỈ࡟ࡼࡿ␯ỈᛶởࢀࡢὙίຠᯝࢆ⤂௓ࡋ㸪௒ᚋࡢ◊✲Ⓨᒎࡢཧ⪃࡜ࡋࡓ࠸㸬

Recent Development of the Micro-bubble Science

Shinichiro YANASE, Graduate School of Natural Science and Technology, Okayama University
Koji MATSUURA, Graduate School of Medicine, Dentistry and Pharmaceutical Sciences, Okayama University(Received 29 May, 2015; in revised form 20 August 2015)
Recent development on the research of fluid containing micro-bubbles is addressed. First, basic physical andchemical properties of micro-bubbles are explained. Then the experimental results of flows containing micro-bubbles
are shown from the viewpoint of drag reduction and suppress of heat transfer. Finally, cleaning effect using
micro-bubble fluid on a hydrophobic stain is addressed, and a future study plan is given.
(KEY WORDS): micro-bubble, drag reduction, heat transfer, cleaning effect

1 ᗎㄽ⌧ᅾ࡛ࡶከࡃࡢ࣓࣮࣮࢝ࡀ࣐࢖ࢡࣟࣂࣈࣝⓎ⏕⿦⨨ࢆ௜ࡅࡓᾎᵴࢆ㈍኎ࡋ࡚࠸ࡿ㸬࠺ࡓ࠸ᩥྃࡣ㸪⾑⾜ࡀࡼࡃ࡞ ࣐࢖ࢡࣟࣂࣈࣝ࡜ࡣᾮయ㸦୺࡟Ỉ㸧ࡢ୰ࡢ㸪ᚤᑠẼἻࡾయࡀ ࡲࡿ࡜࠸࠺Ⅼ࡛࠶ࡿࡀ㸪ࡇࢀࡀ࡝ࡢ⛬ᗘࡢ་Ꮫࡢ⥲⛠࡛࠶ࡿ㸬ࡶࡕࢁࢇ㸪⮬↛⏺࡟ࡶᏑᅾࡍࡿྍ⬟ᛶࡣⓗ᰿ᣐࢆᣢࡘࡢ࠿ࡣ࠸ࡉࡉ࠿୙࡛᫂࠶ࡿ㸬ࡉࡽ࡟㸪⯪⯧࠶ࡿࡀ㸪㏻ᖖࡣ㸪ேᕤⓗ࡟⏕ᡂࡉࢀࡿ㸬Ẽయ࡜ࡋ࡚ࡣ✵ࡢ⇞ᩱᾘ㈝ࢆᢚ࠼ࡿࡓࡵ㸪࣐࢖ࢡࣟࣂࣈࣝࢆ⏝࠸ࡓ᢬ᢠẼࡀከ࠸ࡀ㸪㓟⣲㸪Ỉ⣲㸪࢜ࢰࣥࡶࡼࡃ⏝࠸ࡽࢀࡿ㸬࣐పῶࡢヨࡳࡀ㸪࠸ࡃࡘ࠿ࡢ㐀⯪఍♫࡟ࡼࡗ࡚ᐇ⾜ࡉࢀ࡚࢖ࢡࣟࣂࣈࣝࡢ┤ᚄࡣ㸪㏻ᖖ㸪ᩘ 10 Pm ࡛㸪100 Pm ௨࠸ࡿ 2)㸬ࡇࢀࡣ㸪⯪ᗏࡢቃ⏺ᒙ࡟ẼἻࢆὀධࡍࡿࡶࡢ࡛

ୗࡢࡶࡢࢆᣦࡍሙྜࡀከ࠸㸬୍᪉㸪ࢼࣀࣂࣈࣝࡣ㸪┤ᚄ࠶ࡿࡀ㸪࣐࢖ࢡࣟࣂࣈࣝ࡜⛠ࡋ࡚࠸ࡿࡀᐇ㝿ࡢ኱ࡁࡉࡣ㸪ࡀ1 Pm௨ୗ࡛࠶ࡾ㸪ከࡃࡣᩘⓒnm࡜᥎ᐃࡉࢀ࡚࠸ࡿ㸬ࡣࡿ࠿࡟኱ࡁ࠸┤ᚄ㸦୰ᚰ್ࡀ 0.5 mm㸧ࢆᣢࡘࡶࡢ࡛࠶

ࡇࢀࡽ࡟ࡘ࠸࡚㸪㏆ᖺάⓎ࡟◊✲ࡉࢀ࡚࠸ࡿࡇ࡜ࡣࡼࡃࡾ㸪࡝ࡢࡼ࠺࡞ᶵᵓ࡛᢬ᢠపῶࡀᐇ⌧ࡉࢀ࡚࠸ࡿ࠿࡟ࡘ

▱ࡽࢀ࡚࠸ࡿࡀ㸪ࡑࡢືᶵ࡟ࡘ࠸࡚ࡣ௨ୗࡢࡼ࠺࡞ࡶࡢ

࠸࡚ࡶࡑࢀ࡯࡝᫂ࡽ࠿࡛ࡣ࡞࠸㸬࡛࠶ࡿ㸬᭱ึ࡟࣐࢖ࢡࣟࣂࣈࣝࡀ᭷ྡ࡜࡞ࡗࡓࡢࡣ㸪࢝

௨ୖ㏙࡭ࡓࡼ࠺࡟㸪࣐࢖ࢡࣟࣂࣈࣝࡣ㸪ከࡃࡢศ㔝࢟ࡢ㣴Ṫ࡛࠶ࡗ࡚㸪༑ศ࡞㓟⣲ࢆ౪⤥ࡍࡿࡓࡵ㸪࣐࢖ࢡ

࡛ᵝࠎ࡞ຠᯝ࣭ຠ⬟ࡀ࠶ࡿ࡜ᮇᚅࡉࢀ㸪◊✲ࡉࢀ࡚࠸ࡿࣟࣂࣈࣝⓎ⏕⿦⨨ࡀ฼⏝ࡉࢀࡓ 1)㸬ࡓࡔࡋ㸪ࡇࡢᡂຌࡢ

ࡀ㸪ࡑࡢᮏᙜࡢ≀⌮ⓗ࣭໬Ꮫⓗ࣓࢝ࢽࢬ࣒ࡣࡑࢀ࡯࡝ࡼཎᅉࡀ㸪࣐࢖ࢡࣟࣂࣈࣝࡢ≉ᛶࢆ฼⏝ࡋࡓࡶࡢ࡛࠶ࡿ࠿㸪 ࡃ⌮ゎࡉࢀ࡚࠸ࡿ࡜ࡣゝ࠼࡞࠸㸬ࡇࡢࡼ࠺࡞≧ἣ࡟࠾࠸࠶ࡿ࠸ࡣ༢࡟Ỉ୰࡟㓟⣲ࢆ౪⤥ࡋࡓࡓࡵ࡛࠶ࡿ࠿ࡣⱝᖸ࡚㸪ࡉࡽ࡟ࢼࣀࣂࣈࣝࡢ◊✲ࡀ㐍ࢇ࡛࠸ࡿ㸬ࡇࢀࡣඛ࡯␲ࢃࡋ࠸ࡀ㸪࡜ࡶ࠿ࡃࡇࢀ୍࡛Ẽ࡟࣐࢖ࢡࣟࣂࣈࣝࡢᏑ

࡝㏙࡭ࡓࡼ࠺࡟┤ᚄࡀ 1 Pm ௨ୗࡢẼἻ࡛࠶ࡿࡀ㸪⌧ᅾ㸪ᅾࡀ▱ࡽࢀࡿࡼ࠺࡟࡞ࡗࡓ㸬ḟ࡟㸪ᾎᵴෆ࡛ࡢ฼⏝࡛㸪ගᏛⓗ࡟ほ ࡛ࡁࡿẼἻࡢ኱ࡁࡉࡣ㸪ᩘPm ࡀ㝈⏺࡛࠶*ࠛ700-8530 ᒸᒣᕷ໭༊ὠᓥ୰㸱㸫㸯㸫㸯͊E-mail: yanase@okayama-u.ac.jpࡾ㸪Ỉ୰࡟ศᩓࡋ࡚࠸ࡿࢼࣀࣂࣈࣝࡢᏑᅾࡣ㸪ගᩓ஘ἲࡲࡓࡣࢮ࣮ࢱ㟁఩ィࢆ⏝࠸࡚㸪㛫᥋ⓗ࡟᥎ᐃࡉࢀࡿࡢࡳ

マイクロバブル研究の進展356࡛࠶ࡿ 3)㸬

࡛࠶ࡿ࠿ࡽ㸪⤊➃㏿ᗘࢆồࡵࡿࡓࡵ㸪F = Fg ࡜௬ᐃࡍࡿ㏆ᖺ㸪ⴭ⪅ࡽࡣ㸪࣐࢖ࢡࣟࣂࣈࣝࡢຠᯝ࡜ࡋ࡚㸪෇࡜⟶ෆὶࡢ᢬ᢠపῶ㸪␯ỈᛶởࢀࡢὙί࡟㛵ࡋ࡚㸪ᐃ㔞ⓗ࡞⤖ᯝࢆᚓࡿࡇ࡜ࡀ࡛ࡁࡓ㸬≉࡟㸪ᚋ⪅࡟㛵ࡋ࡚ࡣ㸪ࡑ

U=ࡢ࣓࢝ࢽࢬ࣒࡟ࡘ࠸࡚ࡶ࠶ࡿ⛬ᗘࡢ▱ぢࡀᚓࡽࢀࡓ㸬ᮏ

R 2 ȡJ
3ȝ

(4)

ㄽᩥ࡛ࡣ㸪ࡇࢀࡽࡢෆᐜࢆ୰ᚰ࡟ࡋ࡚㸪࣐࢖ࢡࣟࣂࣈࣝࡀᚓࡽࢀࡿ㸬༙ᚄ 15 Pm ࡢ࣐࢖ࢡࣟࣂࣈ࡛ࣝࡣ㸪20rC

ࡢ୍⯡ⓗ࡞ゎㄝࢆ⾜࠺㸬࡛ࡢ್ P = 1.8u10-5 Pa s ࢆ⏝࠸ࡿ࡜㸪U = 4.08u10-2 m/s =2.45 m/min ࡜࡞ࡾ㸪2 ⛊ࡶ⤒㐣ࡍࢀࡤ㸪10 cmୖ᪼ࡋ㸪㏻2 ࣐࢖ࢡ࣭ࣟࢼࣀࣂࣈࣝࡢ≀⌮ⓗ࣭໬Ꮫⓗᛶ㉁

ᖖࡢᐜჾ࡛ࡣእ㒊࡬ฟ࡚࠸ࡃࡇ࡜ࡀࢃ࠿ࡿ㸬ࡋࡓࡀࡗ࡚㸪࣐࢖ࢡࣟࣂࣈࣝࡢຠᯝࢆ༑ศ࡟ㄪ࡭ࡿࡓࡵ࡟ࡣ㸪ᖖ᫬᪂ Ỉ୰ࡢẼἻࡢᙧ≧ࡣ㸪㔜ຊຠᯝࢆ↓どࡍࢀࡤ㸪⌫㠃≧ࡋ࠸࣐࢖ࢡࣟࣂࣈࣝࢆ〇㐀ࡍࡿࡼ࠺࡞⿦⨨ࡀᚲせ࡛࠶ࡿ࡜࡞ࡿ㸬ࡑࡢ⌮⏤ࡣ㸪Ẽᾮ⏺㠃࡟ാࡃ⾲㠃ᙇຊࡀ᭤㠃ࡢࡇ࡜ࡀࢃ࠿ࡿ㸬୍᪉㸪༙ᚄ 150 nm ࡢࢼࣀࣂࣈ࡛ࣝࡣ㸪᭤⋡࡟ࡼࡗ࡚Ỵࡲࡿࡓࡵ㸪⌫㠃࡛࡞ࡅࢀࡤ⾲㠃ᙇຊࡢࣂU = 4.08u10-6 m/s = 1.47 cm/h ࡜࡞ࡾ㸪࠿࡞ࡾࡺࡗࡃࡾ࡜ࣛࣥࢫࡀ◚ࢀ㸪ᖹ⾮ᙧ≧ࢆ⥔ᣢ࡛ࡁ࡞ࡃ࡞ࡿࡓࡵ࡛࠶ࡿ㸬 ୖ᪼ࡍࡿࡇ࡜ࡀࢃ࠿ࡿ㸬Ỉ㐨Ỉࢆ⏝࠸㸪ᚋ㏙ࡍࡿࡏࢇ᩿ᮏㄽᩥ࡛ၥ㢟࡜ࡋ࡚࠸ࡿ࣐࢖ࢡ࣭ࣟࢼࣀࣂࣈࣝࡣ┤ᚄࡀ᪉ᘧ࡟ࡼࡗ࡚ࢃࢀࢃࢀࡢ◊✲ᐊ࡛సᡂࡋࡓ࣐࢖ࢡࣟࣂࣈ㠀ᖖ࡟ᑠࡉ࠸ࡓࡵ㸪㔜ຊຠᯝࡣ↓ど࡛ࡁࡿ࡜⪃࠼ࡽࢀࡿ㸬 ࣝࡢほ ࡟ࡼࢀࡤ㸪ୖ᪼㏿ᗘࡣࡍࡄ࡟⤊➃㏿ᗘ࡟㐩ࡍࡿࡉࡽ࡟㸪࿘ᅖࡢὶయࡢࡏࢇ᩿ࡢᙳ㡪࡟ࡼࡾ㸪⌫㠃࠿ࡽኚࡀ㸪ࡑࡢ್ࡣ㸪ẼἻ࡛ࡣ࡞ࡃ㸪࡝ࡕࡽ࠿࡜ゝ࠼ࡤ㸪ᅛయᙧࡍࡿྍ⬟ᛶࡀ࠶ࡿࡀ㸪ࡇࢀࡶ⪃ᐹ࠿ࡽ㝖ࡃࡇ࡜࡟ࡍࡿ㸬 ⌫ࡢ᢬ᢠ್ F = 6SPUR ࡟ᑐᛂࡍࡿ್ࡲࡎ㸪࡝ࢀࡃࡽ࠸ࡢ⾲㠃ᙇຊࡀാࡁ㸪ẼἻࡢෆእᅽຊᕪࡀ࡝ࢀࡃࡽ࠸࡟࡞ࡿ࠿ࢆ⪃࠼࡚ࡳࡼ࠺㸬⌫ࡢ༙ᚄࢆ R ࡜

U=4 R 2 ȡJ9ȝ  (5)ࡋ㸪✵Ẽ࡜Ỉࡢ⏺㠃ࡢ⾲㠃ᙇຊࢆV࡜ࡍࡿ࡜㸪⌫ࡢෆእ࡛ࡼࡃ⾲ࡉࢀ࡚࠸ࡿࡇ࡜ࡀ♧ࡉࢀࡓ 4)㸬ࡇࡢཎᅉࡣ㸪୙ᅽຊᕪ p ࡣ2Vp=R⣧≀ࡢᏑᅾࡢࡓࡵ㸪ẼἻࡢ⏺㠃ࡀᅛయⓗ࡞ᛶ㉁ࢆᣢࡗ࡚
 (1)࠸ࡿࡓࡵ࡛࠶ࡿ࡜⪃࠼ࡽࢀ࡚࠸ࡿ㸬ࡇࢀࡽࡢ⌧㇟࡟ᑐࡋ࡚ࡣ㸪ࢧࣈ࣑ࣜࢫࢣ࣮ࣝ┤ᚄࡢẼἻ࡟ᑐࡍࡿᐩᒣ➼ࡢヲ࡜࡞ࡿ㸬࣐࢖ࢡࣟࣂࣈࣝࡢ௦⾲್࡜ࡋ࡚ R = 15 Pm㸪ࡋ࠸◊✲ 5) ࡀ࠶ࡾ㸪ᢠຊಀᩘ CD ࡢᵓᡂ᪉⛬ᘧࡀᥦ♧ࡉ20Υ࡛ࡢ್ V = 72.75u10-3 N/m ࢆ௦ධࡍࡿ࡜㸪p =ࢀ࡚࠸ࡿ㸬ࡲࡓ㸪ᮏゎㄝࡢෆᐜ࡜㛵㐃ࡋ࡚㸪⏺㠃άᛶ๣

39.70u10 Pa = 0.0958 atm ࡜࡞ࡿ㸬ࡲࡓ㸪ࢼࣀࣂࣈࣝࡢ௦ࡀẼἻࡢ㐠ື࡟୚࠼ࡿᙳ㡪࡟㛵ࡍࡿヲ⣽࡞ゎㄝࡀ Takagi⾲್࡜ࡋ࡚ R = 150 nm ࢆ௦ධࡍࡿ࡜㸪p = 9.58 atm ࡜࡞and Matsumoto 6) ࡟ࡼࡗ࡚୚࠼ࡽࢀ࡚࠸ࡿ㸬ࡑࡇ࡛ࡣ㸪ࡿ㸬࣐࢖ࢡࣟࣂࣈ࡛ࣝࡢෆእᅽຊᕪࡣ㸪኱Ẽᅽ࡜ẚ࡭࡚㸪 ẼἻ㏆ഐࡀ⏺㠃άᛶ๣➼࡜┦஫స⏝ࡍࡿࡇ࡜࡟ࡼࡗ࡚ࡶ㸪ࡑࢀ࡯࡝኱ࡁ࡞್࡛ࡣ࡞࠸ࡀ㸪ࢼࣀࣂࣈ࡛ࣝࡣ㠀ᖖ࡟኱ẼἻ⏺㠃ࡀࡼࡾᅛయⓗ࡞ᛶ㉁ࢆᣢࡘࡇ࡜ࡀྍ⬟࡛࠶ࡿ⌧ࡁࡃ㸪ࢼࣀࣂࣈࣝࡢ≉␗ᛶࡀ᫂ࡽ࠿࡛࠶ࡿ㸬

㇟ࡀ㏙࡭ࡽࢀ࡚࠸ࡿ㸬ḟ࡟㸪ẼἻ࡟ᾋຊࡀാࡁୖ᪼ࡍࡿ࡜ࡁࡢ⤊➃㏿ᗘࢆ 㔜ຊ௨እࡢຊࡢᙳ㡪ࢆㄪ࡭࡚ࡳࡼ࠺㸬ẼἻ㏿ᗘࢆ୍ᐃồࡵ࡚ࡳࡼ࠺㸬᭱ึ࡟⌮᝿ⓗ࡞ሙྜ࡜ࡋ࡚㸪Ỉ୰࡟ศᩓ࡜௬ᐃࡍࡿ࡜㸪ࣂࢭࢵࢺ㸦Basset㸧㡯ࡀṧࡿࡀ 7, 8)㸪ࡇࡢࡋ㸪࿘ࡾ࡟୙⣧≀ࡀ↓࠸⎔ቃࡢẼἻࢆ⪃࠼ࡿ㸬㠀ᖖ࡟ࣞ㡯ࡣ᫬㛫࡜࡜ࡶ࡟㸪t -1/2 ࡟ẚ౛ࡋ࡚ῶᑡࡍࡿࡓࡵ㸪ᙳ㡪࢖ࣀࣝࢬᩘࡀᑠࡉ࠸ሙྜࢆ⪃࠼㸪ࢫࢺ࣮ࢡࢫ㏆ఝࡀᡂ❧ࢆ୚࠼࡞࠸࡜⪃࠼ࡽࢀࡿ㸬୍᪉㸪ࣈࣛ࢘ࣥ㐠ື࡟㉳ᅉࡍࡍࡿ࡜௬ᐃࡍࡿ࡜㸪ẼἻ࡟ാࡃ᢬ᢠຊࡣ㸪ẼἻࡢୖ᪼㏿ࡿຊࢆㄪ࡭࡚ࡳࡿ࡜㸪20ɮC㸦293 K㸧࡛ࡣ㸪࣐࢖ࢡࣟࣂᗘࢆ U㸪Ỉࡢ⢓ᛶಀᩘࢆP࡜ࡍࡿ࡜ࣈ࡛ࣝࡣ↓ど࡛ࡁࡿࡀ㸪ࢼࣀࣂࣈ࡛ࣝࡣ㸪㠀ᖖ࡟኱ࡁ࡞ᙳ㡪ࢆཷࡅࡿࡇ࡜ࡀࢃ࠿ࡿ㸬ࡑࡢࡓࡵ㸪ࢼࣀࣂࣈࣝࡢ㌶

F=4 Ⱥǋ85

(2)㊧ࡣ㸪ຊᏛⓗ࡞㐠ື᪉⛬ᘧࡔࡅ࡛ࡣண᝿ࡍࡿࡇ࡜ࡀ࡛ࡁ࡞࠸ࡇ࡜ࡣ᫂ࡽ࠿࡛࠶ࡿ㸬࡛㸪ࡑࡢ኱ࡁࡉࡣ㸪ᅛయࡢሙྜࡢ 2/3 ಸ࡛࠶ࡿ㸬ࡉࡽ࡟ ࡞࠾㸪࣐࢖ࢡࣟࣂࣈࣝࡣࡋࡤࡋࡤ༢୍≧ែ࡛ࡣ࡞ࡃ㸪㔜ຊ࡜ᾋຊࡢᕪࡣ㸪Ẽయࡢᐦᗘࢆ↓どࡍࢀࡤ㸪UࢆỈࡢࢡࣛ࢘ࢻ≧࡟✵㛫ศᕸࢆࡋ࡚࠸ࡿሙྜࡀ࠶ࡾᚓࡿ㸬ࡑࡢᐦᗘ㸪g ࢆ㔜ຊຍ㏿ᗘ࡜ࡋ࡚ሙྜ㸪ࡇࡇ࡛㏙࡭ࡓỈ୰ࡢ༢୍ẼἻࢆ᝿ᐃࡋࡓ㆟ㄽࡣ㸪ᖖ࡟ᡂ❧ࡍࡿ࡜ࡣ㝈ࡽ࡞࠸ࡀ㸪࣐࢖ࢡࣟࣂࣈࣝ㸦ࢼࣀࣂ4Ⱥ 3
Fg=R ǏJ
3(3)ࣈࣝࡶྵࡵ࡚㸧ࡢ◊✲ࡢᇶ♏▱㆑࡜ࡋ࡚㸪ࡇࡇ࡛ゐࢀࡿࡇ࡜࡟ࡋࡓ㸬ࡲࡓ㸪ᩘ್ゎᯒ࡜ࡢᑐᛂࢆ⪃࠼ࡿሙྜ࡟ࡣ㸪柳瀬眞一郎・松浦宏治

357࡞ࡿ࡭ࡃᑡᩘࡢ࣐࢖ࢡࣟࣂࣈࣝࢆⓎ⏕ࡉࡏ㸪ィ⟬࡜ࡢẚ11)㍑ࢆࡍࡿࡢࡀ౽฼࡛࠶ࡾ㸪ࡑࡢࡓࡵࡢᇶ♏࡜ࡶ࡞ࡿ㸬nm ௨ୗࡢࢼࣀࣂࣈࣝ࡜ཎᏊ㛫ຊ㢧ᚤ㙾(AFM)ࣉ࣮ࣟࣈ

㸬ࡑࡢ௦⾲ⓗ࡞౛࡜ࡋ࡚ࡣ㸪ᇶᯈୖ࡟⏕ᡂࡋࡓ┤ᚄ 500࣐࢖ࢡࣟࣂࣈࣝࡣ㸪⾲㠃㟁Ⲵ࡟㉳ᅉࡍࡿ㟼㟁┦஫స⏝㛫࡟ാࡃຊࢆィ ࡋࡓሗ࿌ࡀ࠶ࡿ 11)㸬ࡇࡢຊࡣᙎᛶⓗ࡛ࢆ᭷ࡍࡿ㸬࣐࢖ࢡࣟ⢏Ꮚ⾲㠃࡟࠾ࡅࡿ࢖࢜ࣥศᕸࡢࣔࢹ࠶ࡾ㸪ࢼࣀࣂࣈࣝࡢ┤ᚄࡀᑠࡉࡃ࡞ࡿ࡟ࡘࢀ࡚㸪ࣉ࣮࡛ࣟࣝ࠶ࡿ㟁Ẽ஧㔜ᒙ࡟ࡘ࠸࡚㸪ᅗ 1 ࡟♧ࡍ㸬⾲㠃㟁఩ࡣࣈ㸫ࢼࣀࣂࣈࣝ㛫࡟ാࡃຊ࡜ࢼࣀࣂࣈࣝ࡟⏤᮶ࡍࡿᙎᛶ↓㝈㐲ࢆᇶ‽࡜ࡋࡓ⢏Ꮚ⾲㠃ࡢ㟁఩ࢆ♧ࡍ㸬࣐࢖ࢡࣟࣂ⋡ࡀୖ᪼ࡍࡿ㸬⌧ᅾࡢ࡜ࡇࢁࠊࡇࡢᙎᛶ⋡ࡀୖ᪼ࡍࡿ⌮ࣈࣝࡢ⾲㠃㟁఩ࡣ⌧ᅾࡢ࡜ࡇࢁィ ࡀᴟࡵ࡚ᅔ㞴࡛࠶ࡿ㸬 ⏤࡟ࡘ࠸࡚ࡣࡼࡃࢃ࠿ࡗ࡚࠸࡞࠸㸬Walczyk et al.ࡣ㸪AFM✀ࠎࡢศᯒ⿦⨨ࢆ⏝࠸࡚ィ ࡀྍ⬟࡞ࠕࢮ࣮ࢱ㟁఩ࠖࡣࢆ⏝࠸࡚ᇶᯈୖ࡟Ⓨ⏕ࡋࡓࢼࣀࣂࣈࣝࡢ≀ᛶࢆṇ☜࡟ぢ↓㝈㐲ࢆᇶ‽࡜ࡋࡓ⢏Ꮚࡢࠕࡍ࡭ࡾ㠃ࠖ࡟࠾ࡅࡿ㟁఩࡛✚ࡶࡿࡇ࡜ࡢ㞴ࡋࡉ࡟ࡘ࠸࡚ゝཬࡋ㸪ぶỈⓗ࠿ࡘඛ➃ࡀ࠶ࡿ㸬⣽࠸ࣉ࣮ࣟࣈࢆ⏝࠸ࡿࡇ࡜ࢆᥦ᱌ࡋ࡚࠸ࡿ 12)㸬ࢼࣀࣂࣈ࣐࢖ࢡࣟࣂࣈࣝࡢࢮ࣮ࢱ㟁఩ࡣࡑࡢ┤ᚄࡀ 20㹼30 Pmࣝࡢ⾲㠃ᙇຊ Vࡣ㸪࣐ࢡࣟࢫࢣ࣮ࣝࡢẼἻ࡜࡯ࡰྠࡌ࡛

ࡢሙྜࡣ30 㹼40 mV ⛬ᗘ࡛࠶ࡿࡀ㸪࣐࢖ࢡࣟࣂࣈࣝ࠶ࡿࡓࡵ㸪ᙼࡽࡣ㸪ࢼࣀࣂࣈࣝࡣẼయศᏊࡀจ㞟ࡋࡓࣔࡢ┤ᚄࡀᑠࡉࡃ࡞ࡿ࡟ࡘࢀ࡚పୗࡍࡿ࡜ሗ࿌ࡉࢀ࡚࠸ࡿࢹ࡛ࣝࡣ࡞࠸࡜⪃࠼࡚࠸ࡿ 12)㸬ࡲࡓ㸪┤᥋ほᐹࡀᅔ㞴࡛3, 9)࠶ࡿ⁐፹ෆ࡟ศᩓࡋࡓࢼࣀࣂࣈࣝࡀ᭷ࡍࡿᛶ㉁ࡢ⌮ゎ࡟࢜ࣥࡢ✀㢮࡜ᵓᡂࡀศ࠿ࢀࡤ㸪࣐࢖ࢡࣟࣂࣈࣝ┤ᚄ࡜ࢮࡘ࠸࡚ࡶ௒ᚋ◊✲ࡀ㐍ࢇ࡛࠸ࡃ࡜ᛮࢃࢀࡿ㸬࣮ࢱ㟁఩࡜ࡢ㛵㐃࡟ࡘ࠸࡚⌮ゎࡀ㐍ࡴ࡜ᛮࢃࢀࡿ㸬࣐࢖ࢡࣟࣂࣈࣝ࡟࠾࠸࡚ࢮ࣮ࢱ㟁఩ࡀ࣐࢖ࢼࢫ࡟࡞ࡗ࡚࠸ࡿ

3 ࣐࢖ࢡࣟࣂࣈࣝỈࡢ⏕ᡂ᪉ἲࡇ࡜ࡣ㸪ୖグࡍ࡭ࡾ㠃࡟࠾࠸࡚㝜࢖࢜ࣥࡀከᩘᏑᅾࡍࡿ㸬࣐࢖ࢡࣟࣂࣈࣝ⾲㠃࠿ࡽ࢖࢜ࣥᣑᩓᒙ࡟Ꮡᅾࡍࡿ࢖ࡇ࡜࡟ᑐᛂࡍࡿ࡜⪃࠼ࡽࢀࡿ㸬ࡑࡢሙྜ࡟ࡣ࣐࢖ࢡࣟࣂᮏゎㄝ࡛ࡣ㸪࣐࢖ࢡࣟࣂࣈࣝỈ࡜ࡣ࣐࢖ࢡࣟࣂࣈࣝࢆࣈࣝྠኈࡀ┤ࡕ࡟⼥ྜࡏࡎ㸪⁐፹ෆ࡛ศᩓࡉࢀࡓ≧ែ࡛ྵࡴỈࢆព࿡ࡍࡿࡇ࡜࡟ࡍࡿ㸬௒᪥⏝࠸ࡽࢀࡿ࣐࢖ࢡࣟᏑᅾࡍࡿࡇ࡜ࢆ♧၀ࡋ࡚࠸ࡿ㸬ࣂࣈࣝỈࡢ⏕ᡂ᪉ἲࡣᩘከ࠸ࡀ㸪ࡇࡇ࡛ࡣᮏ◊✲ᐊ࡛⏝࠸࡚࠸ࡿ㸪࣐࢖ࢡࣟࣂࣈࣝỈࡢ⏕ᡂࡢࡓࡵࡢ㸪2 ࡘࡢ᪉ἲ࡟ࡘ࠸࡚⡆༢࡟ㄝ᫂ࡍࡿ㸬
3.1 ࡏࢇ᩿ἲ
ࡇࡢ᪉ἲࡣࠊ⟶ෆὶࡢ᢬ᢠపῶ◊✲࡟⏝࠸㸪኱㔞࡟࣐࢖ࢡࣟࣂࣈࣝࢆ⏕ᡂࡍࡿࡢ࡟㐺ࡋ࡚࠸ࡿ㸬⏕ᡂཎ⌮ࡣ㸪ࢧ࢖ࢡࣟࣥࡢ୰࡟㸪࣏ࣥࣉ࠿ࡽ᥋⥺᪉ྥ࡟Ỉࢆὀධࡍࡿ࡜㸪ෆ㒊࡟᪕ᅇὶࡀⓎ⏕ࡍࡿ㸬ࢧ࢖ࢡࣟࣥ୰ᚰ㒊ศ࡬㸪እ㒊࠿ࡽ⟶ࢆ㏻ࡗ࡚㏦ධࡉࢀࡓ✵Ẽࡀ㸪పᅽࡢᅇ㌿୰ᚰ㒊ศ࡛✵Ẽᰕ࡜࡞ࡾ㸪ࢧ࢖ࢡࣟࣥฟཱྀ࡛ຍ㏿ࡉࢀࡓ᪕ᅇ
ὶࡢࡓࡵ࡟ษ᩿࣭⢊○ࡉࢀ㸪ᚤᑠẼἻࡀ⏕ᡂࡉࢀࡿ㸬ᅗ
2 ࡟㸪ᮏ◊✲࡛⏝࠸ࡓ⿦⨨ࢆ♧ࡍ㸬ᑐ㠃ᘧࡢࡏࢇ᩿Ⓨ⏕⿦⨨ࡣ㸪ᒣᮏᜤ஧ᒸᒣ኱Ꮫྡ㄃ᩍᤵࡀ㸪ᒸᒣ኱Ꮫ⌧ᙺᙜ

ᅗ 1 㟁Ẽ஧㔜ᒙ࡟ࡼࡿ⾲㠃㟁఩࡜ࢮ࣮ࢱ㟁఩ࡢᶍᘧᅗ㸬⢏Ꮚ⾲㠃࠿ࡽࡍ࡭ࡾ㠃ࡲ࡛ࡢ࢖࢜ࣥࡣ⢏Ꮚ࡟྾╔ࡋ࡚࠾ࡾ㸪ࡍ࡭ࡾ㠃࠿ࡽእഃࡢ࢖࢜ࣥࡣ⢏Ꮚ࡜ඹ࡟ືࡃࡶࡢ࡜࿘ࡾࡢ⁐ᾮෆ࡟␃ࡲࡿࡶࡢ࡜࡟ศࡅࡽࢀࡿ㸬᭱㏆ࡢᾏእ࠿ࡽࡢࢼࣀࣂࣈࣝ࡟㛵ࡍࡿᐇ㦂ⓗ◊✲ሗ࿌࡟㛵ࡋ࡚ࡣ㸪ᖹᆠ࡞ᇶᯈୖ࡟Ⓨ⏕ࡋࡓ┤᥋ほᐹࡀྍ⬟࡞ࢼࣀࣂࣈࣝࡢᛶ㉁࡟ࡘ࠸࡚ࡢ◊✲ࡀ࡯࡜ࢇ࡝࡛࠶ࡿ 10,ᅗ 2 ࡏࢇ᩿ἲ

マイクロバブル研究の進展

358

ᅗ 3 㟁Ẽศゎἲ࡟ࡼࡿ࣐࢖ࢡࣟࣂࣈࣝⓎ⏕⿦⨨᫬࡟㛤Ⓨࡋࡓࡶࡢ࡛㸪ᑐ㠃ᘧ࡛࡞࠸ࡶࡢࡼࡾࡶ㸪ᗄศ࠿㸪࣐࢖ࢡࣟࣂࣈࣝⓎ⏕ຠ⋡ࡀ㧗࠸ࡇ࡜ࡀࢃ࠿ࡗ࡚࠸ࡿ 13)㸬3.2 㟁Ẽศゎἲ

ᅗ 4 ࣐࢖ࢡࣟࣂࣈࣝ࡟ࡼࡿ⟶᢬ᢠపῶຠᯝ᳨ドࡢᐇ㦂⿦⨨ᅗ㸬⟶ෆᚄࡣ 22 mm ࡛࠶ࡿ㸬ࣝࢬᩘ Re = dpU/Q < 2.3u103 ࡛ࡣ㸪㏻ᖖࡢ⟶᢬ᢠಀᩘOࡢ ࡇࡢ᪉ἲࡣ㸪Ὑίࡢ◊✲࡟⏝࠸ࡓ㸬ᅗ 3 ࡟♧ࡍࡼ࠺࡟㸪 1/4 ࡛ᐃ⩏ࡉࢀࡓ⟶᢬ᢠಀᩘ f ࡣỈ୰࡟ࢱࣥࢢࢫࢸࣥ⥺ࢆᙇࡾ㟁ὶࢆὶࡍࡇ࡜࡟ࡼࡗ࡚Ỉࢆ㟁Ẽศゎࡋ㸪㝜ᴟ࠿ࡽⓎ⏕ࡋࡓỈ⣲ẼἻࢆ࣐࢖ࢡࣟࣂ

f =ࣈࣝ࡜ࡋ࡚฼⏝ࡍࡿ㸬ࡇࡢ᪉ἲ࡛ࡣ㸪኱㔞ࡢ࣐࢖ࢡࣟࣂ
ࣈࣝࢆ⏕ᡂࡍࡿࡇ࡜ࡣ࡛ࡁ࡞࠸ࡀ㸪⿦⨨ࡀࢥࣥࣃࢡࢺ࡜࡞ࡾ㸪ྲྀࡾᢅ࠸ࡀᐜ࡛᫆࠶ࡿ㸬ࡇࢀ௨እ࡟ࡶ㸪࣋ࣥࢳࣗࣜ⟶ᘧ㸪ຍᅽ⁐ゎἲ㸪⌫≧⾪

(7)࡜࡞ࡿࡇ࡜ࡀࡼࡃ▱ࡽࢀ࡚࠸ࡿ㸬ࡇࡇ࡛ dp ࡣ⟶┤ᚄ㸪Uࡣ⟶㍈᪉ྥᖹᆒ㏿ᗘ㸪Qࡣື⢓ᛶಀᩘ࡛࠶ࡿ㸬ࡲࡓ㸪ẚ
㍑ⓗ㧗࠸ࣞ࢖ࣀࣝࢬᩘ࡛ࡣࣈࣛࢪ࢘ࢫࡢබᘧ

ᧁἼ㸪᣺ືከᏍᯈࢆ⏝࠸ࡓ᪉ἲ࡞࡝ከࡃࡢ࣐࢖ࢡࣟࣂࣈ
ࣝ⏕ᡂἲࡀᐇ⏝໬ࡉࢀ࡚࠸ࡿࡀ㸪ࡑࢀ࡟㛵ࡋ࡚ࡣ㏆ᖺ࠸

16
Ref =0.0791
Re1 / 4(8)ࡃࡘ࠿ࡢࣁࣥࢻࣈࢵࢡࡀฟ∧ࡉࢀ࡚࠸ࡿࡢ࡛㸪ࡑࢀࡽࢆཧ↷ࡋ࡚࠸ࡓࡔࡁࡓ࠸ 3, 14)㸬4 ࣐࢖ࢡࣟࣂࣈࣝ࡟ࡼࡿ⟶᢬ᢠపῶຠᯝ

࡟ᚑ࠺㸬ᅗ 5 ࡟㸪Ỉᖹ┤⟶࡛ࡢ ᐃ⤖ᯝ࡜㸪ᘧ(7)㸪(8)㸪
ࡉࡽ࡟㖄┤⟶࡟࠾ࡅࡿ Serizawa ➼ 16) ࡢ⤖ᯝࢆ♧ࡍ㸬
ᅗ 6 ࡟ࡣ㸪⟶᢬ᢠಀᩘ f ࡢ࣐࢖ࢡࣟࣂࣈࣝࢆྵࡲ࡞࠸
ὶయࡢ᢬ᢠಀᩘ fw ࡟ᑐࡍࡿẚ࣐࢖ࢡࣟࣂࣈࣝࢆྵࡴỈ࡟ࡼࡿ᢬ᢠపῶຠᯝࡣẚ㍑ⓗ௨๓࠿ࡽὀ┠ࡉࢀ࡚࠸ࡿ㸬౛࠼ࡤᖹᯈ࡟࠾ࡅࡿ᢬ᢠపῶ࡟ࡘ࠸࡚ࡣ㸪ከࡃࡢ◊✲ᡂᯝࡀ࠶ࡿ 15)㸬ࡋ࠿ࡋ㸪᭱ࡶ

DR = 100 ufw  ffw

  
 (9)

඾ᆺⓗ࡞ᙧែ࡛࠶ࡿ෇⟶ෆὶ࡟࠾ࡅࡿ᢬ᢠపῶຠᯝࡢ◊✲ࡣ㸪ⴭ⪅ࡽࡢ▱ࡿ㝈ࡾ࡛ࡣ㸪Serizawa et al. 16) ࡟ࡼࡿࢆ♧ࡍ㸬᭱኱࡛㸪50%௨ୖࡢపῶ⋡ࡀᚓࡽࢀ࡚࠸ࡿࡇ࡜㖄┤෇⟶ෆὶࡔࡅ࡛࠶ࡗࡓࡓࡵ㸪Shatat et al. 17) ࡛ࡣ෇⟶ࡀࢃ࠿ࡿ㸬ࡇࡢ⤖ᯝ࠿ࡽࢃ࠿ࡿࡼ࠺࡟㸪Ỉᖹ⟶࡛ࡣ㍈ࢆỈᖹ࡟ࡋ࡚㸪 ᐃࢆ⾜ࡗࡓ㸬Serizawa ➼ࡢ⤖ᯝ 16) ࡯࡝㢧ⴭ࡛ࡣ࡞࠸ࡶࡢࡢ㸪஘ὶ㑄

ᅗ 4 ࡟㸪ᐇ㦂⿦⨨ᅗࢆ♧ࡍ㸬ࡏࢇ᩿ἲ࡟ࡼࡿ࣐࢖ࢡࣟ⛣ࡢ㐜ࢀࡀぢࡽࢀࡿ㸬࣎࢖ࢻ⋡ࢆ኱ࡁࡃࡍࡿ࡜㸪୍ᒙ஘ࣂࣈࣝ⏕ᡂ⿦⨨մ࡛⏕ᡂࡉࢀࡓ࣐࢖ࢡࣟࣂࣈࣝỈࡣ㸪࣏ὶ㑄⛣ࣞ࢖ࣀࣝࢬᩘࡀ኱ࡁࡃ࡞ࡿ㸬ࡓࡔࡋ㸪ࡇࢀ௨ୖ࣎

ࣥࣉո࡟ࡼࡾ㸪ᐇ㦂⏝ࢸࢫࢺࢭࢡࢩࣙࣥռ࡬ὀධࡉࢀ㸪࢖ࢻ⋡ࢆୖࡆࡓሙྜ㸪Ỉᖹ⟶࡛ࡣẼἻࡀ⟶ୖ㒊࡬㞟ࡲࡾ㸪ᐃᚋ㸪ᅇ཰ࡉࢀࡿᚠ⎔ᆺ࡜࡞ࡗ࡚࠸ࡿ㸬࣐࢖ࢡࣟࣂࣈ

ྜే࡟ࡼࡗ࡚኱ࡁ࡞ẼἻࢆᙧᡂࡋ㸪஘ὶ㑄⛣ࢆ㐜ࡽࡏࡿࣝࡢᖹᆒ༙ᚄࡣ⣙ 50 Pm ࡛㸪Ỉ୰࡟࠾ࡅࡿẼయࡢయ✚ẚຠᯝࡣⓎ⏕ࡋ࡞ࡃ࡞ࡗࡓ㸬࡞࠾㸪࣊ࣜ࢝ࣝ⟶࡛ࡶ㸪ࡑࡢ⋡࡛ᐃ⩏ࡉࢀࡿ࣎࢖ࢻ⋡ Df ࡣ 0.21 ࠿ࡽ 0.44 ࡲ࡛ኚ໬ࡉ኱ࡁࡉࡣῶᑡࡍࡿࡀ㸪⟶᢬ᢠࡢపῶຠᯝࡀᚓࡽࢀ࡚࠸ࡏࡓ㸬࡞࠾㸪┤෇⟶ࡢෆᚄࡣ 22 mm㸪࣊ࣜ࢝ࣝ⟶࡛ࡣෆ
ᚄ 20 mm ࡢ⟶ࢆ⏝࠸ࡓ㸬ࡲࡓ㸪5 ❶࡛㏙࡭ࡿ⇕ఏ㐩ᢚไຠᯝࡢᐇ㦂࡛ࡣ㸪⟶ෆᚄࡣ඲࡚ 14.4 mm ࡛࠶ࡿ㸬࣐࢖ࢡࣟࣂࣈࣝࢆྵࡲ࡞࠸㏻ᖖࡢỈ࡞ࡽ㸪పࣞ࢖ࣀࡿ㸬柳瀬眞一郎・松浦宏治

ᅗ 5 ⟶᢬ᢠಀᩘ

359

ᅗ 6 ⟶᢬ᢠపῶ⋡ ࡇࡢ⠇ࡢ᭱ᚋ࡟㸪࣐࢖ࢡࣟࣂࣈࣝࡢὀධ࡟ࡼࡾ᢬ᢠపῶࡀ⏕ࡌࡿ⌮⏤࡟ࡘ࠸࡚㸪ⴭ⪅ࡢぢゎࢆ㏙࡭ࡓ࠸㸬⏺㠃άᛶ๣ࢆὀධࡋࡓሙྜࡣ㸪ศᏊࡢ㙐≧ᵓ㐀ᙧᡂࡀ஘ὶ
ࡢⓎ⏕ࢆጉࡆࡿ࡜ゝࢃࢀ࡚࠸ࡿࡀ㸪࣐࢖ࢡࣟࣂࣈ࡛ࣝࡣ
ࡑࡢࡼ࠺࡞ࡇ࡜ࡣࡓ࡜࠼ࣂࣈࣝࡀࢡࣛ࢘ࢻࢆᙧᡂࡋ࡚ࡶ㸪㉳ࡇࡿྍ⬟ᛶࡀప࠸࡜ᛮࢃࢀࡿ㸬ᚋ࡛࣐࢖ࢡࣟࣂࣈࣝ࡟ࡼࡿὙί࡟㛵ࡋ࡚ㄝ᫂ࡍࡿࡼ࠺࡟㸪ࣂࣈࣝ⾲㠃ࡢ㟁Ẽⓗᛶ㉁ࡀ㸪஘ὶ ࡢᢚไ࡟ఱࡽ࠿ࡢᙺ๭ࢆᯝࡓࡋ࡚࠸ࡿࡢ࡛ࡣ࡞࠸࠿࡜⪃࠼࡚࠸ࡿ㸬ࡲࡓ㸪Serizawa ➼࡟ࡼࡿ㖄┤⟶ࡢ⤖ᯝࡀࡼࡾ኱ࡁ࡞᢬ᢠపῶࢆ♧ࡋ࡚࠸ࡿࡀ㸪ⴭ⪅ࡽ࡟ࡼࡿ㸪෇⟶㍈ࢆỈᖹ㠃࠿ࡽᩘ 10 ᗘഴࡅࡓᐇ㦂࡛ࡶ㸪Ỉᖹ⟶࡜ྠᵝࡢ⤖ᯝࡀᚓࡽࢀ࡚࠸ࡿࡇ࡜࠿ࡽ᥎ᐃࡍࡿ࡜㸪పῶ⋡ࡢᕪࡣ㸪⟶㍈ࡢ㔜ຊ᪉ྥ࡜ࡢゅᗘ࡛ࡣ࡞ࡃ㸪ࡴࡋࢁᐇ㦂᪉ἲࡢᵝࠎ࡞せᅉ࡟㉳ᅉࡍࡿࡢ࡛ࡣ࡞࠸࠿࡜ண᝿ࡋ࡚࠸ࡿ㸬
5 ࣐࢖ࢡࣟࣂࣈࣝ࡟ࡼࡿ⇕ఏ㐩ᢚไຠᯝ ୍⯡࡟㸪᢬ᢠపῶ࡜⇕ఏ㐩ᢚไຠᯝࡣඹ࡟Ⓨ⏕ࡍࡿ࡜⪃࠼ࡽࢀ࡚࠸ࡿ㸬ࡑࡢ⌮⏤ࡣ㸪᢬ᢠ࣭⇕ఏ㐩࡝ࡕࡽࡶ஘ὶ ࡟ࡼࡗ࡚ಁ㐍ࡉࢀࡿࡓࡵ㸪ఱࡽ࠿ࡢຠᯝ࡟ࡼࡗ࡚஘
ὶ ࡢⓎ⏕ࡀᢚไࡉࢀࡿ࡜㸪࡝ࡕࡽࡢຠᯝࡶῶᑡࡍࡿ࡜ண᝿ࡉࢀࡿ࠿ࡽ࡛࠶ࡿ㸬ࡑࢀ࡛ࡶ㸪ࡶࡋ࣐࢖ࢡࣟࣂࣈࣝ࡟⊂⮬ࡢ⇕ఏ㐩ಁ㐍ຠᯝࡀ࠶ࡿ࡞ࡽ㸪஘ὶ ࡢᢚไࢆ⿵࠺⇕ఏ㐩ຠᯝࡀほ ࡉࢀࡿྍ⬟ᛶࡀ࠶ࡿࡓࡵ㸪ࡑࢀࢆㄪᅗ 7 ⇕ఏ㐩ᐇ㦂⿦⨨ᅗマイクロバブル研究の進展360

ᅗ 8 ࢾࢵࢭࣝࢺᩘ

ᅗ 9 ⇕ఏ㐩ᢚไ⋡࡭࡚ࡳࡓ㸬ࡋ࠿ࡋ㸪┤⟶࡟࠾࠸࡚⇕ఏ㐩ຠᯝࢆㄪ࡭ࡓ⤖┤ὶయᒙࡢᐇ㦂࡛ࡣ㸪ᒁᡤ⇕ఏ㐩ಀᩘࡀᒙὶ㡿ᇦ࡛ࡣ 1.6ᯝ㸪ᙉ࠸⇕ఏ㐩ᢚไࡀⓎ⏕ࡍࡿࡇ࡜ࡀࢃ࠿ࡗࡓ㸬ࡋࡓࡀ

㹼2.0 ಸ㸪㑄⛣㡿ᇦ࡛ࡣ 1.5㹼2.0 ಸ࡟ቑຍࡋ࡚࠸ࡿࡇ࡜ࡀ

ࡗ࡚㸪࣐࢖ࢡࣟࣂࣈࣝࡢὀධ࡟ࡼࡿ㸪஘ὶ Ⓨ⏕ࢆᢚไ♧ࡉࢀࡓ㸬ㄽᩥ࡟ࡼࢀࡤ㸪ᒙὶ㡿ᇦࡢቑຍࡣΰྜຠᯝࡢࡍࡿ㸦࠶ࡿ࠸ࡣ஘ὶ࡬ࡢ㑄⛣ࢆ㐜ࡽࡏࡿ㸧ຠᯝࢆ⿵࠺࡯

ቑຍ࡟࠶ࡾ㸪㑄⛣㡿ᇦ࡛ࡢቑຍࡣ஘ὶ໬ࡢಁ㐍࡟࠶ࡿ࡜࡝ࡢ㸪࣐࢖ࢡࣟࣂࣈࣝ࡟ࡼࡿ⇕ఏ㐩ಁ㐍ຠᯝࡣᏑᅾࡋ࡞

㏙࡭ࡽࢀ࡚࠸ࡿ㸬ࡇࡢ⤖ᯝࡣ㸪࣐࢖ࢡࣟࣂࣈࣝࡢὶࢀࡢ

࠸ࡇ࡜ࡀ♧ࡉࢀࡓ㸬ࡇࡇ࡛ࡣShatatࡢ༤ኈㄽᩥ 18) ࡟ᚑ࠸㸪┤⟶ෆὶࡢ⇕ఏ㐩ᢚไຠᯝࢆ⤂௓ࡍࡿ㸬㑄⛣࡟୚࠼ࡿᙳ㡪ࡀᴟࡵ࡚」㞧࡛࠶ࡿࡇ࡜ࢆ♧ࡋ࡚࠸࡚㸪෇⟶ෆὶ࡛ࡢ஘ὶ㑄⛣࡟㛵ࡋ࡚ࡶ㸪ࡉࡽ࡞ࡿ◊✲ࡀᚲせᐇ㦂ࡣ㸪ᅗ 7 ࡟♧ࡍࡼ࠺࡟㸪┤⟶ࡢ࿘ࡾ࡟᩿⇕ᮦࢆᕳ࡛࠶ࡿࡇ࡜ࢆ♧၀ࡋ࡚࠸ࡿ㸬ࡁ㸪⇕㟁ᑐࢆྲྀࡾ௜ࡅ㸪 ᗘࡢ ᐃࢆ⾜ࡗࡓ㸬ᚓࡽࢀࡓ㹝ࢾࢵࢭࣝࢺᩘ Nuࡢ⤖ᯝࢆᅗ 8 ࡟♧ࡍ㸬ᐇ⥺ࡣ┤⟶ᒙὶ㹝ࡢ್ Nu = 4.36㸪◚⥺ࡣ㸪஘ὶ࡟ᑐࡋ࡚ Gnielinski 19) ࡟ࡼࡗ࡚ᥦ᱌ࡉࢀࡓ್

6 ࣐࢖ࢡࣟࣂࣈࣝ࡟ࡼࡿὙί
 ࣐࢖ࢡࣟࣂࣈࣝࢆ⏝࠸ࡓὙίࡢᛂ⏝ࡣᗄࡘ࠿ᥦ᱌ࡉࢀ
࡚࠸ࡿ࡜࡜ࡶ࡟୍㒊ࡣᐇ⏝໬ࡉࢀ࡚࠸ࡿ 1, 3, 21,22)㸬࣐࢖ࢡNu =( f/ 2)( Re - 1000)Pr
1+ 12.7( f/ 2)0.5 ( Pr 2 / 3 - 1)ࣟࣂࣈࣝࡣ␯Ỉⓗ⢏Ꮚࡸ⏺㠃࡟྾╔ࡍࡿࡓࡵ㸪Ὑί࡬ࡢ(10)ᛂ⏝ᒎ㛤ࡀྍ⬟࡛࠶ࡿࡀ㸬๓㏙ࡢ᢬ᢠపῶࡸ㸪⇕ఏ㐩ᢚไຠᯝ࡜ྠᵝ㸪ᐃ㔞ⓗ࡞◊✲ᡂᯝࡣஈࡋࡃ㸪Ὑίᶵᵓ㠃࡛࠶ࡿ㸬ࡇࡇ࡛ Pr ࡣࣉࣛࣥࢺࣝᩘ࡛࠶ࡿ㸬ࡇࢀ࠿ࡽࢃ࠿

ࡢ≀⌮ⓗ࣭໬Ꮫⓗ⌮ゎࡣ㐍ࢇ࡛࠸࡞࠸㸬ࢃࢀࢃࢀࡣ࣐࢖ࡿࡼ࠺࡟㸪࣐࢖ࢡࣟࣂࣈࣝࢆὀධࡍࡿࡇ࡜࡟ࡼࡗ࡚஘ὶࢡࣟࣂࣈࣝ࡟ࡼࡿὙίᶵᵓ࡟ࡘ࠸࡚⌮ゎࡍࡿࡓࡵ࡟㸪ᅗ㑄⛣ࡀ㐜ࢀ㸪ࡑࡢࡓࡵ࡟஘ὶ ࡀῶᑡࡋ㸪⇕ఏ㐩ࡀῶᑡ

3 ࡟♧ࡍ㟁Ẽศゎἲࡢ࣐࢖ࢡࣟࣂࣈࣝⓎ⏕⿦⨨ࢆ⏝࠸࡚㸪ࡋ࡚࠸ࡿࡇ࡜ࡀ♧ࡉࢀ࡚࠸ࡿ㸬␯Ỉᛶ࣏࣐࣮ࣜ࢖ࣥࢡࡢὙίᐇ㦂ࢆ⾜ࡗࡓ 23)㸬࣐࢖ࢡࣟࢫࢥ࣮ࣉࢆ⏝࠸࡚ほᐹࡉࢀࡓᮏᐇ㦂ࡢ࣐࢖HTR = 100 uNuw  NuNuw(11)ࢡࣟࣂࣈࣝࡢ┤ᚄࡣ㸪30㹼50 Pm ࡛࠶ࡗࡓ㸬࣏࣐࣮ࣜ࢖
ࣥࢡࡢ㔜㔞ࢆ ᐃࡍࡿࡇ࡜࡟ࡼࡾ㸪␯Ỉᛶ࢖ࣥࢡࡢὙί㔞ࡣ㸪Ⓨ⏕ࡋࡓ࣐࢖ࢡࣟࣂࣈࣝࡢᩘ࡜ṇࡢ┦㛵ࡀ࠶ࡿࡇᅗ 9 ࡟ࡣ㸪ᘧ (11)࡛୚࠼ࡽࢀࡿ㸪ࢾࢵࢭࣝࢺᩘ Nu ࡢ㸪࡜ࡀ♧ࡉࢀࡓ㸬ࡲࡓほᐹ࡟ࡼࡾ㸪࣐࢖ࢡࣟࣂࣈࣝࡀ␯Ỉ࣐࢖ࢡࣟࣂࣈࣝࢆྵࡲ࡞࠸ὶయࡢࢾࢵࢭࣝࢺᩘ Nuw ࡟ᛶ࢖ࣥࢡࡢ⾲㠃࡟྾╔ࡍࡿࡇ࡜ࡀࢃ࠿ࡗࡓ㸬࣐࢖ࢡࣟࣂ

ᑐࡍࡿẚ HTR ࢆ♧ࡍ㸬᭱኱᢬ᢠపῶ⋡࡜ẚ࡭࡚㸪᭱኱ࣈࣝࡣ㸪⁐ᏑẼయࡢ྾཰࡜㸪௚ࡢ࣐࢖ࢡࣟࣂࣈࣝ࡜ࡢྜ⇕ఏ㐩ᢚไ⋡ࡣ⣙ 22㹼35%኱ࡁ࠸ࡇ࡜ࡀࢃ࠿ࡿ㸬࡞࠾㸪ే࡟ࡼࡗ࡚ࡑࡢ┤ᚄࢆቑ኱ࡉࡏࡿࡇ࡜ࡀぢࡽࢀࡓ㸬ࡋࡓࡇࢀࡽࡢపῶ⋡㸦ᢚไ⋡㸧ࡣ㸪᢬ᢠ࡟ࡘ࠸࡚ࡣ⟶᢬ᢠಀࡀࡗ࡚㸪Ὑίࡍࡿ≀㉁࡟྾╔ࡋࡓ࣐࢖ࢡࣟࣂࣈࣝࡀ㸪┤ᩘ㸪⇕ఏ㐩࡟ࡘ࠸࡚ࡣ⇕ఏ㐩⋡࡛ィ⟬ࡉࢀ࡚࠸ࡿࡓࡵ㸪ᚄࡀὙί≀㉁ୖ࡛ቑ኱ࡍࡿࡇ࡜࡟క࠺ᾋຊࡢቑຍ࡟ࡼࡗ

඲ࡃྠࡌᇶ‽ࡢホ౯࡛ࡣ࡞࠸㸬ࡋࡓࡀࡗ࡚㸪୧⪅ࡢᐃ㔞࡚๤㞳ࡍࡿࡢ࡟క࠸㸪␯Ỉᛶ࢖ࣥࢡࡀὙίࡉࢀࡿࡇ࡜ࡀ㸪ⓗ࡞ẚ㍑ࡣᚲࡎࡋࡶྍ⬟࡛ࡣ࡞࠸㸬Ὑίᶵᵓࡢᮏ㉁ⓗ࡞ᶵᵓ࡛࠶ࡿ࡜᥎ ࡋ࡚࠸ࡿ㸬ࡇࡢ᝿ ࢃࢀࢃࢀࡢᐇ㦂ࡣ࠸ࢃࡺࡿᙉไ⇕ఏ㐩࡟㛵ࡍࡿ◊✲࡛ᐃࡢᶍᘧᅗࢆᅗ 10 ࡟♧ࡍ㸬ࡇࡢᶵᵓࡣ㸪࣐࢖ࢡࣟࣂࣈࣝ࠶ࡿࡀ㸪⮬↛ᑐὶ࡟ࡼࡿ⇕ఏ㐩࡛ࡣ㸪ࡇࢀ࡜ࡣ࠿࡞ࡾ␗࠾ࡼࡧὙί≀㉁⾲㠃ࡢ≀ᛶ࡟ࡘ࠸࡚ࡉࡽ࡟⌮ゎࡀ㐍ࡵࡤ㸪࡞ࡗࡓ⤖ᯝࡀᚓࡽࢀ࡚࠸ࡿ㸬Kitagawa et al. 20) ࡟ࡼࡿ㖄௚ࡢᵝࠎ࡞ศ㔝࡟ᛂ⏝࡛ࡁࡿ࡜⪃࠼࡚࠸ࡿ㸬柳瀬眞一郎・松浦宏治361

 ࣐࢖ࢡࣟࣂࣈࣝ࡟ࡼࡿὙίᢏ⾡ࡢṑᏛ࣭་Ꮫศ㔝࡬ࡢㅰ㎡㸸᭱ึ࡟㸪ᑐ㠃ᆺ࣐࢖ࢡࣟࣂࣈࣝⓎ⏕⿦⨨ࢆ㛤Ⓨᛂ⏝ࡶ㐍ࡵࡽࢀ࡚࠸ࡿ㸬౛࠼ࡤ㸪ᒀ㐨࢝ࢸ࣮ࢸࣝෆࡸཱྀࡋ㸪◊✲ᐊ࡟࣐࢖ࢡࣟࣂࣈࣝ◊✲ࡢࡁࡗ࠿ࡅࢆᑟධࡋ࡚⭍ෆ࡟ᙧᡂࡍࡿࣂ࢖࢜ࣇ࢕࣒ࣝࡀ㸪་Ꮫⓗ࡟ㄢ㢟࡜࡞ࡗ࠸ࡓࡔ࠸ࡓ㸪ᒣᮏᜤ஧ᒸᒣ኱Ꮫྡ㄃ᩍᤵ࡟῝ࡃឤㅰࡍࡿ㸬࡚࠸ࡿ㸬ᐇ㝿㸪┤ᚄ 1 mm ௨ୗࡢὶ㊰➼ࡢᚤ⣽✵㛫ෆ࡟㸪ࡲࡓ㸪┤⟶㸪࣊ࣜ࢝ࣝ⟶ࡢඃࢀࡓᐇ㦂ࢆ⾜ࡗࡓ Shatat ༤ࣂ࢖࢜ࣇ࢕࣒ࣝࡀᙧᡂࡉࢀࡿ㸬ࡇࡢࡼ࠺࡞ࣂ࢖࢜ࣇ࢕ࣝኈ㸪࣐࢖ࢡࣟࣂࣈࣝὙίᐇ㦂࡟ᦠࢃࡗࡓᑠᒣ࿴᫭㸪ᑠᕝ࣒ࢆὙί࣭ẅ⳦ࡍࡿࡓࡵ࡟㸪࣐࢖ࢡࣟࣂࣈࣝࡀ฼⏝࡛ࡁ្㸪➟ᮌಙဢྩ㸪࣐࢖ࢡࣟࣂࣈࣝࡢ᢬ᢠపῶຠᯝࡢ෌⌧ࡿ࡜⪃࠼ࡽࢀࡿ㸬ࡑࡇ࡛㸪ࢃࢀࢃࢀࡢࢢ࣮ࣝࣉ࡛ࡣ㸪ᅗᐇ㦂࡟ࡼࡾ㸪ᐇ㦂⤖ᯝ࡟ಖ㞀ࢆ୚࠼ࡓἙෆಇ᠇༤ኈ࡟ឤ

3 ࡢ࣐࢖ࢡࣟࣂࣈࣝⓎ⏕⿦⨨ࢆ⏝࠸࡚㸪ᅵተࡸከᵝ࡞Ỉㅰࡍࡿ㸬࡞࠾㸪ᮏ◊✲ࡣ᪥ᮏᏛ⾡᣺⯆఍⛉Ꮫ◊✲⿵ຓ㔠㸪⣔࡟ᗈࡃศᕸࡍࡿ୍⯡ⓗ࡞⣽⳦ࡢ୍✀࡛࠶ࡿᇶ┙◊✲㸦C24560196㸧㸪2012 ᖺᗘ⣊㣗◊✲఍◊✲࡟ࡼ

Micrococcus Luteus ࡢࣂ࢖࢜ࣇ࢕࣒ࣝὙίᐇ㦂ࢆ⾜ࡗࡓࡗ࡚࠸ࡿ㸬24)㸬ᘬ⏝ᩥ⊩1) ኱ᡂ༤ᩥ㸸࣐࢖ࢡࣟࣂࣈࣝࡢࡍ࡭࡚㸪᪥ᮏᐇᴗฟ∧♫㸪(2006)㸬
ᅗ 10 ␯Ỉᛶ࢖ࣥࢡὙίᐇ㦂࡛ぢฟࡋࡓ㸪࣐࢖ࢡࣟࣂࣈࣝࢆ⏝࠸ࡓὙίᶵᵓࡢᶍᘧᅗ㸬ᖹ⾜ᅄ㎶ᙧࡀ␯Ỉᛶ࢖ࣥࢡࢆ㸪୸࠸⢏Ꮚࡀ࣐࢖ࢡࣟࣂࣈࣝࢆ♧ࡍ㸬ࢫࣛ࢖ࢻ࢞ࣛࢫୖ࡟ࣂ࢖࢜ࣇ࢕࣒ࣝࢆస〇ࡋ㸪ᅗ㸱࡟♧ࡍⓎ⏕⿦⨨࠿ࡽⓎ⏕ࡍࡿ࣐࢖ࢡࣟࣂࣈࣝࢆ⏝࠸࡚ࣂ࢖࢜ࣇ࢕࣒ࣝࡢ㝖ཤྍ⬟ᛶࢆ᳨ウࡋࡓ㸬࣐࢖ࢡࣟࢫࢥ࣮ࣉほᐹ࡟ࡼࡾ㸪ࡇࡢࣂ࢖࢜ࣇ࢕࣒ࣝ࡟࣐࢖ࢡࣟࣂࣈࣝࡀ྾╔ࡍࡿࡇ࡜ࢆ☜ㄆࡋࡓ㸬ࡲࡓ㸪ᐇ㦂ᚋࡢࣂ࢖࢜ࣇ࢕࣒ࣝ
ࢆ Cristal Violet ࡛ᰁⰍࡋࡓ࡜ࡇࢁ㸪30 ศ㛫ฎ⌮ࡋࡓᚋࡢヨᩱ࡟࠾࠸࡚ࡣࡑࡢ㍤ᗘࡀపୗࡋ࡚࠸ࡓࡇ࡜࠿ࡽ㸪ࣂ࢖࢜ࣇ࢕࣒ࣝᒙࡢཌࡳࢆῶࡽࡍຠᯝࡀ࠶ࡿ࡜⪃࠼࡚࠸ࡿ㸬ࡇࡢ࣐࢖ࢡࣟࣂࣈࣝ࡟ࡼࡿὙίຠᯝ࡜ẅ⳦๣ࢆే⏝ࡍࡿࡇ࡜࡟ࡼࡗ࡚㸪ࣂ࢖࢜ࣇ࢕࣒ࣝෆࡢ⳦ࢆຠ⋡ⓗ࡟ẅ⳦࡛ࡁࡿྍ⬟ᛶࡀ⪃࠼ࡽࢀࡿ㸬7 ⤖ゝ ⴭ⪅ࡽࡢ◊✲࡟ᇶ࡙࠸࡚㸪࣐࢖ࢡࣟࣂࣈࣝࢆྵࡴὶࢀ࡟ࡼࡿ᢬ᢠపῶ㸪⇕ఏ㐩ᢚไຠᯝ࡟㛵ࡍࡿᐇ㦂⤖ᯝࢆ㏙࡭㸪࣐࢖ࢡࣟࣂࣈࣝࢆྵࡴỈ࡟ࡼࡿ㸪␯ỈᛶởࢀࡢὙίຠᯝࢆ⤂௓ࡋࡓ㸬ࡇࢀࡽࡣ㏆ᖺ㠀ᖖ࡟ὀ┠ࡉࢀ࡚࠸ࡿࢸ࣮࣐࡛࠶ࡾ㸪኱Ꮫ㸪௻ᴗ࡟ࡼࡿከࡃࡢ◊✲ࡀሗ࿌ࡉࢀ࡚࠸ࡿࡀ㸪ࢹ࣮ࢱࡢཝᐦ࡞᳨ᐃࢆకࡗࡓ◊✲ࡣࡲࡔࡑࢀ࡯࡝ከࡃ࡞࠸㸬⌧᫬Ⅼ࡛ࡣ㸪࣐࢖ࢡࣟࣂࣈࣝỈࡢ࣑ࢡࣟ࡞
≀⌮ⓗ㸪໬Ꮫⓗ㸪ຊᏛⓗᶵᵓ࡟ࡣ୙᫂࡞Ⅼࡀከ࠸ࡀ㸪ⴭ⪅ࡽࡢ୍㐃ࡢ◊✲ࡢ⤖ᯝ࠿ࡽ㸪࣐࢖ࢡࣟࣂࣈࣝࡀከࡃࡢᕤᴗⓗᛂ⏝ࡢྍ⬟ᛶࢆෆໟࡋ࡚࠸ࡿࡇ࡜ࡀ᫂ࡽ࠿࡜࡞ࡗ
ࡓ㸬㏆࠸ᑗ᮶㸪ྛศ㔝࡟ࢃࡓࡗ࡚ከᙬ࡞ᡂᯝࢆ⏕ࡴࡇ࡜ࡀᮇᚅࡉࢀࡿ㸬2) Ọᯇဴ㑻௚㸸㟷㞼୸ࢆ⏝࠸ࡓ࣐࢖ࢡࣟࣂࣈࣝࡢᦶ᧿᢬ᢠపῶᐇ⯪ᐇ㦂୍ᚋ⦅㸸ᐇ⯪ᐇ㦂୍㸪᪥ᮏ㐀⯪Ꮫ఍ㄽᩥ㞟 192(2002)15-28㸬
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ീゎᯒ㸧㸪ᒸᒣ኱Ꮫ⮬↛⛉Ꮫ◊✲⛉༤ኈ๓ᮇㄢ⛬ᶵᲔࢩࢫࢸ࣒ᕤᏛᑓᨷ㸦ᶵᲔ⣔㸧2010 ᖺᗘಟኈㄽᩥ(2011)㸬
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