リケラボ論文検索は、全国の大学リポジトリにある学位論文・教授論文を一括検索できる論文検索サービスです。

リケラボ 全国の大学リポジトリにある学位論文・教授論文を一括検索するならリケラボ論文検索大学・研究所にある論文を検索できる

リケラボ 全国の大学リポジトリにある学位論文・教授論文を一括検索するならリケラボ論文検索大学・研究所にある論文を検索できる

大学・研究所にある論文を検索できる 「マグマ中の気泡合体の理論的研究」の論文概要。リケラボ論文検索は、全国の大学リポジトリにある学位論文・教授論文を一括検索できる論文検索サービスです。

コピーが完了しました

URLをコピーしました

論文の公開元へ論文の公開元へ
書き出し

マグマ中の気泡合体の理論的研究

丸石, 崇史 MARUISHI, Takafumi マルイシ, タカフミ 九州大学

2023.03.20

概要

九州大学学術情報リポジトリ
Kyushu University Institutional Repository

Theoretical study of coalescence of bubbles in
magma
丸石, 崇史

https://hdl.handle.net/2324/6787419
出版情報:Kyushu University, 2022, 博士(理学), 課程博士
バージョン:
権利関係:

(様式3)





:丸石

崇史

論 文 名

: Theoretical study of coalescence of bubbles in magma
(マグマ中の気泡合体の理論的研究)























The coalescence of ascending bubbles driven by buoyancy leads to the spatial heterogeneity of
volatile in basaltic magma, to control the style and dynamics of basaltic eruptions.
It is essential to quantitatively know what factors and how they control bubble size
distribution (BSD), because the BSD controls the coalescence process through approaching
velocity between two bubbles, and in turn, the coalescence process entirely changes the BSD.
First, we derive the effective cross-section for bubble coalescence, including hydrodynamic
interaction between bubbles. As a result, it is found that our newly-derived effective
cross-section is proportional to the product of the radii, although the geometrical cross-section
is proportional to the square of the sum of the radii. Next, using both cross-sections, we
numerically calculate the evolution of BSD for the initial distribution with a narrow size range.
For the geometrical cross-section, the BSD shows power-law with exponent -1.3 for larger
bubbles. For our effective cross-section, the BSD shows power-law with exponent -2.2 for
smaller bubbles. The exponent of -2.2 is close to the exponent of -2.0 for basaltic lava (Gaonach
et al., 1996). Our calculation of BSD allows us to estimate the timescale of formation of
power-law, as sometimes recorded in natural samples. For both cross-sections, the power-law
region extends with time and covers all the sizes at a finite time, which can be interpreted as a
rapid formation of large bubbles. This result may explain the formation of large bubbles
observed in lava lakes and Strombolian eruptions.

参考文献

[1] Atsushi Toramaru. Numerical study of nucleation and growth of bubbles in

viscous magmas. Journal of Geophysical Research: Solid Earth, 100:1913–

1931, 2 1995.

[2] T. Shimano and S. Nakada. Vesiculation path of ascending magma in the

1983 and the 2000 eruptions of miyakejima volcano, japan. Bulletin of Volcanology, 68:549–566, 5 2006.

[3] C. Klug, K. Cashman, and C. Bacon. Structure and physical characteristics of pumice from the climactic eruption of mount mazama (crater lake),

oregon. Bulletin of Volcanology, 64:486–501, 10 2002.

[4] H´el`ene Gaonac’h, Shaun Lovejoy, and Daniel Schertzer. Scaling vesicle

distributions and volcanic eruptions. Bulletin of Volcanology, 67:350–357, 4

2005.

[5] Drok L Sahagian, Alfred T Anderson, and Brian Ward. Vold fi ology numerical model with natural examples. 1974:49–56, 1989.

[6] H. Gaonac’h, S. Lovejoy, J. Stix, and D. Scherzter. A scaling growth model

for bubbles in basaltic lava flows. Earth and Planetary Science Letters, 1996.

[7] H Gaonac’h Ay, J Stix, and S Lovejoy. Scaling effects on vesicle shape, size

and heterogeneity of lavas from mount etna, 1996.

[8] S. Lovejoy, H. Gaonac’h, and Daniel Schertzer. Bubble distributions and

dynamics: The expansion-coalescence equation. Journal of Geophysical

Research: Solid Earth, 109:1–16, 2004.

85

[9] Simona Mancini, Louis Forestier-Coste, Alain Burgisser, Franc¸ois James,

and Jonathan Castro. An expansion-coalescence model to track gas bubble

populations in magmas. Journal of Volcanology and Geothermal Research,

313:44–58, 2016.

[10] Michael Manga and H A Stone. Interactions between bubbles in magmas and

lavas: effects of bubble deformation. Journal of Volcanology and Geothermal Research, 63:267–279, 1994.

[11] M. Masotta, H. Ni, and H. Keppler. In situ observations of bubble growth in

basaltic, andesitic and rhyodacitic melts. Contributions to Mineralogy and

Petrology, 167:1–14, 2014.

[12] Takafumi Maruishi and Atsushi Toramaru. Effect of bubble deformation on

the coalescence of two ascending bubbles in a viscous liquid. Physics of

Fluids, 34, 4 2022.

[13] Michael Manga and H A Stone. Collective hydrodynamics of deformable

drops and bubbles in dilute low reynolds number suspensions. Journal of

Fluid Mechanics, 300:231–263, 1995.

[14] David Saintillan, Eric S.G. Shaqfeh, and Eric Darve. The growth of concentration fluctuations in dilute dispersions of orientable and deformable particles under sedimentation. Journal of Fluid Mechanics, 553:347–388, 2006.

[15] J. Rallison. The deformation of small viscous drops and bubbles in shear

flows. Annual Review of Fluid Mechanics, 16:45–66, 1 1984.

[16] S. Haber and G. Hetsroni. The dynamics of a deformable drop suspended

in an unbounded stokes flow. Journal of Fluid Mechanics, 49:257–277, 9

1971.

[17] Michael Manga and H A Stone. Buoyancy-driven interactions between two

deformable viscous drops. Journal of Fluid Mechanics, 256:647–683, 1993.

[18] Alexander Z. Zinchenko, Michael A. Rother, and Robert H. Davis. Cusping, capture, and breakup of interacting drops by a curvatureless boundaryintegral algorithm. Journal of Fluid Mechanics, 391:249–292, 1999.

86

[19] C T Nguyen, H M Gonnermann, Y Chen, C Huber, A A Maiorano, A Gouldstone, and J Dufek. Film drainage and the lifetime of bubbles. Geochem.

Geophys. Geosyst, 14:3616–3631, 2013.

[20] JOSEPH Kushner, MICHAEL A. Rother, and ROBERT H. Davis.

Buoyancy-driven interactions of viscous drops with deforming interfaces.

Journal of Fluid Mechanics, 446:253–269, 2001.

[21] A. Z. Zinchenko. Calculation of the effectiveness of gravitational coagulation of drops with allowance for internal circulation. Journal of Applied

Mathematics and Mechanics, 46:58–65, 1982.

[22] Gesse A. Roure and Robert H. Davis. Modelling of particle capture by expanding droplets. Journal of Fluid Mechanics, 912, 2021.

[23] Gesse A. Roure, Jenna Trost, and Robert H. Davis. Particle capture by expanding droplets: effects of inner diffusion. Journal of Fluid Mechanics,

948, 10 2022.

[24] Man Hoi Lee. On the validity of the coagulation equation and the nature of

runaway growth. Icarus, 143:74–86, 2000.

[25] F Xiao, T Yabe, and T Ito. I-12 computer physics communications, 1996.

[26] F Xiao, T Yabe, and T Ito. Constructing oscillation preventing scheme for

advection equation by rational function, 1996.

[27] S. K. Friedlander and C. S. Wang. The self-preserving particle size distribution for coagulation by brownian motion. Journal of Colloid And Interface

Science, 22:126–132, 1966.

[28] C. Hayashi and Y. Nakagawa. Size distribution of grains growing by thermal

grain-grain collision. Progress of Theoretical Physics, 54:93–103, 1975.

[29] P. G.J. van Dongen and M. H. Ernst. Scaling solutions of smoluchowski’s

coagulation equation. Journal of Statistical Physics, 50:295–329, 1988.

[30] Cueille S and Sire C. Droplet nucleation and smoluchowski’s equation with

growth and injection of particles st´e phane cueille and cl´e ment sire, 1998.

87

[31] N. G. Lensky, O. Navon, and V. Lyakhovsky. Bubble growth during decompression of magma: Experimental and theoretical investigation. Journal of

Volcanology and Geothermal Research, 129:7–22, 2004.

[32] B. F. Houghton, J. Taddeucci, D. Andronico, H. M. Gonnermann, M. Pistolesi, M. R. Patrick, T. R. Orr, D. A. Swanson, M. Edmonds, D. Gaudin,

R. J. Carey, and P. Scarlato. Stronger or longer: Discriminating between

hawaiian and strombolian eruption styles. Geology, 44:163–166, 2 2016.

[33] E. A. Parfitt and L. Wilson. Explosive volcanic eruptions―ix. the transition

between hawaiian‐style lava fountaining and strombolian explosive activity.

Geophysical Journal International, 121:226–232, 1995.

[34] L. Wilson and J. W. Head. Ascent and eruption of basaltic magma on the

earth and moon. Journal of Geophysical Research, 86:2971–3001, 1981.

[35] E. Bouche, S. Vergniolle, T. Staudacher, A. Nercessian, J. C. Delmont,

M. Frogneux, F. Cartault, and A. Le Pichon. The role of large bubbles detected from acoustic measurements on the dynamics of erta ’ale lava lake

(ethiopia). Earth and Planetary Science Letters, 295:37–48, 2010.

88

...

参考文献をもっと見る

全国の大学の
卒論・修論・学位論文

一発検索!

この論文の関連論文を見る