Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-20T09:51:42.838Z Has data issue: false hasContentIssue false
  • English
  • Français

The generation and collapse of a foam layer at the roof of a basaltic magma chamber

Published online by Cambridge University Press:  26 April 2006

Claude Jaupart  and
Sylvie Vergniolle
Claude Jaupart
Affiliation:
Laboratoire de Dynamique des Systèmes Géologiques, Université Paris 7 et Institut de Physique du Globe, 4 place Jussieu, 75252 Paris, Cedex 05, France
Sylvie Vergniolle
Affiliation:
Laboratoire de Dynamique des Systèmes Géologiques, Université Paris 7 et Institut de Physique du Globe, 4 place Jussieu, 75252 Paris, Cedex 05, France
Get access Rights & Permissions [Opens in a new window]

Abstract

Basaltic volcanoes erupt in several different regimes which have not been explained. At Kilauea (Hawaii), eruption can take the form of either fire fountaining, where gas-rich jets propel lava clots to great heights in the atmosphere, or quiet effusive outflow of vesicular lava. Another regime is commonly observed at Stromboli, where large gas slugs burst intermittently at the vent. In an attempt to provide a unifying framework for these regimes, we investigate phenomena induced by degassing in a reservoir which empties into a small conduit. Laboratory experiments are done in a cylindrical tank topped by a thin vertical tube. Working liquids are silicone oils and glycerol solutions to investigate a range of viscosity and surface tension. Gas bubbles are generated at the tank bottom with known bubble diameter and total gas flux. The bubbles rise through the tank and accumulate in a foam layer at the roof. Depending on the behaviour of this foam layer, three different regimes can be distinguished: (i) steady horizontal flow of the foam leading to bubbly flow in the conduit; (ii) alternating regimes of foam build-up and collapse leading to the eruption of a single, large gas pocket; (iii) flow of the foam partially coalesced into larger gas pockets leading to intermittent slug flow in the conduit. These regimes have natural counterparts in basaltic volcanoes.

A simple theory is proposed to explain regimes (i) and (ii). The bubbles in contact with the roof deform under the action of buoyancy forces, developing flat contact areas whose size increases as a function of foam thickness. Maximum deformation corresponds to a critical thickness hc = 2σ/ερlgR, where σ is the coefficient of surface tension, ρl the liquid density, g the acceleration due to gravity, R the bubble radius and ε the gas volume fraction in the foam. The foam thickness is determined by a balance between the input of bubbles from below and the output into the conduit, and is proportional to (μlQ/ε2 ρlg)¼, where μl is the liquid viscosity and Q the gas flux. A necessary and sufficient condition for collapse is that it exceeds the critical value hc. In a liquid of given physical properties, this occurs when the gas flux exceeds a critical value which depends on viscosity, surface tension and bubble size. Experimental determinations of the critical gas flux and of the time between two events of foam collapse are in agreement with this simple theory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 203 , June 1989 , pp. 347 - 380
Copyright
© 1989 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Batchelor, G. K.: 1967 An Introduction to Fluid Dynamics. Cambridge University Press. 615 pp.
Beckett, P. M. & Poots, G., 1975 Laminar film condensation on horizontal flat plates. Mech. Res. Commun. 2, 61–66.Google Scholar
Bikerman, J. J.: 1973 Foams. Springer. 337 pp.
Blackburn, E. A., Wilson, L. & Sparks, R. S. J. 1976 Mechanisms and dynamics of Strombolian activity. J. Geol. Soc. Lond. 132, 428–440.Google Scholar
Chouet, B., Hamisevicz, N. & McGetchin, T. R., 1974 Photoballistics of volcanic jet activity at Stromboli, Italy. J. Geophys. Res. 79, 4961–4975.Google Scholar
Clift, R., Grace, J. R. & Weber, M. E., 1978 Bubbles, Drops and Particles. Academic Press. 380 pp.
Drew, D. A. & Segel, L. A., 1971 Analysis of fluidized beds and foams using averaged equations. Stud. Appl. Math 50, 233–257.Google Scholar
Greenland, L. P.: 1987 Composition of gases from the 1984 eruption of Mauna Loa. US Geol. Surv. Prof. Pap. 1350, 781–803.Google Scholar
Head, J. W. & Wilson, L., 1987 Lava fountains height at Pu'u'Oo, Kilauea, Hawaii: indicators of amounts and variations of exsolved magma volatiles. J. Geophys. Res. 92, 13713–13719.Google Scholar
Huppert, H. E.: 1982 The propagation of two-dimensional and axisymmetric viscous gravity currents over a rigid horizontal surface. J. Fluid Mech. 121, 43–58.Google Scholar
Jaupart, C. & Vergniolle, S., 1988 Laboratory models of Hawaiian and Strombolian eruptions. Nature 331, 58–60.Google Scholar
Jones, A. F. & Wilson, S. D. R. 1978 The film drainage problem in droplet coalescence. J. Fluid Mech. 87, 263–288.Google Scholar
Khan, S. A. & Armstrong, R. C., 1986 Rheology of foams: I: Theory for dry foams. J. Non-Newtonian Fluid Mech. 22, 1–22.Google Scholar
Kraynick, A. M.: 1988 Foam flows. Ann. Rev. Fluid Mech. 20, 325–357.Google Scholar
Kraynick, A. M. & Hansen, M. G., 1987 Foam rheology: a model for viscous phenomena. J. Rheol. 31, 175–205.Google Scholar
Lambert, G., LeCloarec, M. F., Ardouin, B. & Leroulley, J. C., 1985 Volcanic emission of radionuclides and magma dynamics. Earth Planet. Sci. Lett. 76, 185–192.Google Scholar
LeCloarec, M. F., Pennisi, M., Ardouin, B., Leroulley, J. C. & Lambert, G., 1988 Relationship between gases and volcanic activity at Mount Etna in 1986. J. Geophys. Res. 93, 4477–4484.Google Scholar
Lee, J. C. & Hodgson, T. D., 1968 Film flow and coalescence: I: Basic relations, film shape and criteria for interface mobility. Chem. Engng Sci. 23, 1375–1397.Google Scholar
Princen, H. M.: 1979 Highly concentrated emulsions, Part I. J. Colloid Interface Sci. 71, 55–66.Google Scholar
Princen, H. M.: 1985 Rheology of foams and highly concentrated emulsions. II. Experimental study of the yield stress and wall effects for concentrated oil-in-water emulsions. J. Colloid Interface Sci. 105, 150–171.Google Scholar
Princen, H. M., Aronson, M. P. & Moser, J. C., 1980 Highly concentrated emulsions, Part II. J. Colloid Interface Sci. 75, 246–270.Google Scholar
Rand, P. B. & Kraynick, A. M., 1983 Drainage of aqueous foams: generation pressure and cell-size effects. J. Soc. Pet. Engng 21, 152–154.Google Scholar
Rosner, D. R. & Epstein, M., 1972 Effects of interface kinetics, capillarity and solution diffusion on bubble growth rates in highly supersaturated liquids. Chem. Engng Sci. 27, 69–88.Google Scholar
Ryan, M. P.: 1987 Elasticity and contractancy of Hawaiian olivine tholeiite and its role in the stability and evolution of subcaldera magma reservoirs and rift systems. US Geol Surv. Prof. Pap. 1350, 1395–1447.Google Scholar
Schwartz, L. W. & Princen, H. M., 1987 A theory of extensional viscosity for flowing foams and concentrated emulsions. J. Colloid Interface Sci. 118, 201–211.Google Scholar
Schowalter, W. R.: 1978 Mechanics of Non-Newtonian Fluids. Pergamon. 300 pp.
Sibree, J. O.: 1934 The viscosity of froth. Trans. Faraday Soc. 30, 325–331.Google Scholar
Singh, S. N. & Birkebak, R. C., 1969 Laminar free convection from a horizontal infinite strip facing downwards. Z. angew. Math. Phys. 20, 454–461.Google Scholar
Sparks, R. S. J.: 1978 The dynamics of bubble formation and growth in magmas: a review and analysis. J. Volcanol. Geotherm. Res. 3, 1–37.Google Scholar
Swanson, D. A., Duffield, W. A., Jackson, D. B. & Peterson, D. W., 1979 Chronological narrative of the 1969–71 Mauna-Ulu eruption of Kilauea volcano, Hawaii. US Geol. Surv. Prof. Pap. 1956. 59 pp.Google Scholar
Tait, S. R., Jaupart, C. & Vergniolle, S., 1989 Pressure, gas content and eruption periodicity of a shallow crystallising magma chamber. Earth Plant. Sci. Lett. in press.Google Scholar
Taylor, G. I.: 1932 The viscosity of a fluid containing small drops of another fluid. Proc. R. Soc. Lond. A 138, 41–48.Google Scholar
Thondavadi, N. N. & Lemlich, R., 1985 Flow properties of foam with and without solid particles. Ind. Eng. Chem. Process Des. Dev. 14, 748–753.Google Scholar
Thurber, C. H.: 1987 Seismic structure and tectonics of Kilauea volcano. US Geol. Surv. Prof. Pap. 1350, 919–934.Google Scholar
Vergniolle, S. & Jaupart, C., 1986 Separated two-phase flow and basaltic eruptions. J. Geophys. Res. 91, 12842–12860.Google Scholar
Williams, H. & McBirney, A. R., 1979 Volcanology. Freeman Cooper. 397 pp.
Wilson, L.: 1980 Relationships between pressure, volatile content and ejecta velocity in three types of volcanic eruptions. J. Volcanol. Geotherm. Res. 8, 297–313.Google Scholar
Wilson, L. & Head, J. W., 1981 Ascent and eruption of basaltic magma on the Earth and Moon. J. Geophys. Res. 86, 2971–3001.Google Scholar