Skip to main content Accesibility Help

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

  • Claude Jaupart (a1) and Sylvie Vergniolle (a1)

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 (μl Q2 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.

Hide All
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, 6166.
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, 428440.
Chouet, B., Hamisevicz, N. & McGetchin, T. R., 1974 Photoballistics of volcanic jet activity at Stromboli, Italy. J. Geophys. Res. 79, 49614975.
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, 233257.
Greenland, L. P.: 1987 Composition of gases from the 1984 eruption of Mauna Loa. US Geol. Surv. Prof. Pap. 1350, 781–803.
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, 1371313719.
Huppert, H. E.: 1982 The propagation of two-dimensional and axisymmetric viscous gravity currents over a rigid horizontal surface. J. Fluid Mech. 121, 4358.
Jaupart, C. & Vergniolle, S., 1988 Laboratory models of Hawaiian and Strombolian eruptions. Nature 331, 5860.
Jones, A. F. & Wilson, S. D. R. 1978 The film drainage problem in droplet coalescence. J. Fluid Mech. 87, 263288.
Khan, S. A. & Armstrong, R. C., 1986 Rheology of foams: I: Theory for dry foams. J. Non-Newtonian Fluid Mech. 22, 122.
Kraynick, A. M.: 1988 Foam flows. Ann. Rev. Fluid Mech. 20, 325357.
Kraynick, A. M. & Hansen, M. G., 1987 Foam rheology: a model for viscous phenomena. J. Rheol. 31, 175205.
Lambert, G., LeCloarec, M. F., Ardouin, B. & Leroulley, J. C., 1985 Volcanic emission of radionuclides and magma dynamics. Earth Planet. Sci. Lett. 76, 185192.
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, 44774484.
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, 13751397.
Princen, H. M.: 1979 Highly concentrated emulsions, Part I. J. Colloid Interface Sci. 71, 5566.
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, 150171.
Princen, H. M., Aronson, M. P. & Moser, J. C., 1980 Highly concentrated emulsions, Part II. J. Colloid Interface Sci. 75, 246270.
Rand, P. B. & Kraynick, A. M., 1983 Drainage of aqueous foams: generation pressure and cell-size effects. J. Soc. Pet. Engng 21, 152154.
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, 6988.
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.
Schwartz, L. W. & Princen, H. M., 1987 A theory of extensional viscosity for flowing foams and concentrated emulsions. J. Colloid Interface Sci. 118, 201211.
Schowalter, W. R.: 1978 Mechanics of Non-Newtonian Fluids. Pergamon. 300 pp.
Sibree, J. O.: 1934 The viscosity of froth. Trans. Faraday Soc. 30, 325331.
Singh, S. N. & Birkebak, R. C., 1969 Laminar free convection from a horizontal infinite strip facing downwards. Z. angew. Math. Phys. 20, 454461.
Sparks, R. S. J.: 1978 The dynamics of bubble formation and growth in magmas: a review and analysis. J. Volcanol. Geotherm. Res. 3, 137.
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.
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.
Taylor, G. I.: 1932 The viscosity of a fluid containing small drops of another fluid. Proc. R. Soc. Lond. A 138, 4148.
Thondavadi, N. N. & Lemlich, R., 1985 Flow properties of foam with and without solid particles. Ind. Eng. Chem. Process Des. Dev. 14, 748753.
Thurber, C. H.: 1987 Seismic structure and tectonics of Kilauea volcano. US Geol. Surv. Prof. Pap. 1350, 919–934.
Vergniolle, S. & Jaupart, C., 1986 Separated two-phase flow and basaltic eruptions. J. Geophys. Res. 91, 1284212860.
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, 297313.
Wilson, L. & Head, J. W., 1981 Ascent and eruption of basaltic magma on the Earth and Moon. J. Geophys. Res. 86, 29713001.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed