Volcanic eruptions transfer huge amounts of gas to the atmosphere1,2. In particular, the sulfur released during large silicic explosive eruptions can induce global cooling3. A fundamental goal in volcanology, therefore, is to assess the potential for eruption of the large volumes of crystal-poor, silicic magma that are stored at shallow depths in the crust, and to obtain theoretical bounds for the amount of volatiles that can be released during these eruptions. It is puzzling that highly evolved, crystal-poor silicic magmas are more likely to generate volcanic rocks than plutonic rocks4,5. This observation suggests that such magmas are more prone to erupting than are their crystal-rich counterparts. Moreover, well studied examples of largely crystal-poor eruptions (for example, Katmai6, Taupo7 and Minoan8) often exhibit a release of sulfur that is 10 to 20 times higher than the amount of sulfur estimated to be stored in the melt. Here we argue that these two observations rest on how the magmatic volatile phase (MVP) behaves as it rises buoyantly in zoned magma reservoirs. By investigating the fluid dynamics that controls the transport of the MVP in crystal-rich and crystal-poor magmas, we show how the interplay between capillary stresses and the viscosity contrast between the MVP and the host melt results in a counterintuitive dynamics, whereby the MVP tends to migrate efficiently in crystal-rich parts of a magma reservoir and accumulate in crystal-poor regions. The accumulation of low-density bubbles of MVP in crystal-poor magmas has implications for the eruptive potential of such magmas9,10, and is the likely source of the excess sulfur released during explosive eruptions.
This is a preview of subscription content
Subscribe to Journal
Get full journal access for 1 year
only $3.90 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Get time limited or full article access on ReadCube.
All prices are NET prices.
Wallace, P. J. Volcanic SO2 emissions and the abundance and distribution of exsolved gas in magma bodies. J. Volcanol. Geotherm. Res. 108, 85–106 (2001)
Shinohara, H. Excess degassing from volcanoes and its role on eruptive and intrusive activity. Rev. Geophys. 46, RG4005 (2008)
Self, S. The effects and consequences of very large explosive volcanic eruptions. Phil. Trans. R. Soc. A 364, 2073–2097 (2006)
Halliday, A. N., Davidson, J. P., Hildreth, W. & Holden, P. Modeling the petrogenesis of high Rb/Sr silicic magmas. Chem. Geol. 92, 107–114 (1991)
Hildreth, W. Quaternary magmatism in the Cascades: geological perspectives. US Dept Interior/US Geol. Surv. Prof. Pap. 1744 (2007)
Hildreth, W., Fierstein, J. Katmai volcanic cluster and the great eruption of 1912. Geological Society of America Bulletin 112, 1594–1620 (2000)
Wilson, C. J. N., Rogan, A. M., Smith, I. E. M., Northey, D. J., Nairn, I. A., Houghton, B. F. Caldera volcanoes of the Taupo Volcanic Zone, New Zealand. J. Geophys. Res. Solid Earth 89, 8463–8484 (1984)
Druitt, T. H., Costa, F., Deloule, E., Dungan, M. & Scaillet, B. Decadal to monthly timescales of magma transfer and reservoir growth at a caldera volcano. Nature 482, 77–80 (2012)
Blake, S. Volatile oversaturation during the evolution of silicic magma chambers as eruption trigger. J. Geophys. Res. 89, 8237–8244 (1984)
Huppert, H. E. & Woods, A. W. The role of volatiles in magma chamber dynamics. Nature 420, 493–495 (2002)
Bachl, C. A., Miller, C. F., Miller, J. S. & Faulds, J. E. Construction of a pluton: evidence from an exposed cross-section of the Searchlight pluton, Eldorado Mountains, Nevada. Geol. Soc. Am. Bull. 113, 1213–1228 (2001)
Heise, W., Caldwell, T. G., Bibby, H. M. & Bennie, S. L. Three-dimensional electrical resistivity image of magma beneath an active continental rift, Taupo Volcanic Zone, New Zealand. Geophys. Res. Lett. 37, L10301 (2010)
Cooper, K. M. & Kent, A. J. R. Rapid remobilization of magmatic crystals kept in cold storage. Nature 506, 480–483 (2014)
Bachmann, O. & Bergantz, G. W. On the origin of crystal-poor rhyolites: extracted from batholithic crystal mushes. J. Petrol. 45, 1565–1582 (2004)
Hildreth, W. S. Volcanological perspectives on Long Valley, Mammoth Mountain, and Mono Craters: several contiguous but discrete systems. J. Volcanol. Geotherm. Res. 136, 169–198 (2004)
Huber, C., Bachmann, O. & Manga, M. Homogenization processes in silicic magma chambers by stirring and mushification (latent heat buffering). Earth Planet. Sci. Lett. 283, 38–47 (2009)
Faroughi, S. A. & Huber, C. A generalized equation for rheology of emulsions and suspensions of deformable particles subjected to simple shear at low Reynolds number. Rheol. Acta 54, 85–108 (2015)
Faroughi, S. A. & Huber, C. Unifying the settling velocity in suspensions and emulsions of non-deformable particles. Geophys. Res. Lett. 42, 53–59 (2015)
Lenormand, R., Touboul, E. & Zarcone, C. Numerical models and experiments on immiscible displacements in porous media. J. Fluid Mech. 189, 165–187 (1988)
Huber, C., Bachmann, O., Vigneresse, J-L., Dufek, J. & Parmigiani, A. A physical model for metal extraction and transport in shallow magmatic systems. Geochem. Geophys. Geosys . 13, Q08003 (2012)
Parmigiani, A., Huber, C., Chopard, B. & Bachmann, O. Pore-scale mass and reactant transport in multiphase porous media flows. J. Fluid Mech. 686, 40–76 (2011)
Holtzman, R., Szulczewski, M. L. & Juanes, R. Capillary fracturing in granular media. Phys. Rev. Lett. 108, 264504 (2012)
Oppenheimer, J., Rust, A. C., Cashman, K. V. & Sandnes, B. Gas migration regimes and outgassing in particle-rich suspensions. Front. Phys. 3, 60 (2015)
Philpotts, A. R., Shi, J. & Brustman, C. Role of plagioclase crystal chains in the differentiation of partly crystallized basaltic magma. Nature 395, 343–346 (1998)
Jain, A. K. & Juanes, R. Preferential mode of gas invasion in sediments: grain-scale mechanistic model of coupled multiphase fluid flow and sediment mechanics. J. Geophys. Res. 114, B08101 (2009)
Christiansen, R. L. The quaternary and Pliocene Yellowstone plateau volcanic field of Wyoming, Idaho, and Montana. U.S. Geol. Surv. Prof. Pap. 729-G (2001)
Graham, I. J., Cole, J. W., Briggs, R. M., Gamble, J. A. & Smith, I. E. M. Petrology and petrogenesis of volcanic rocks from the Taupo Volcanic Zone: a review. J. Volcanol. Geotherm. Res. 68, 59–87 (1995)
Lipman, P. W. & Bachmann, O. Ignimbrites to batholiths: integrating perspectives from geological, geophysical, and geochronological data. Geosphere 11, 705–743 (2015)
Sillitoe, R. H. Porphyry copper systems. Econ. Geol. 105, 3–41 (2010)
Devine, J. D., Sigurdsson, H., Davis, A. N. & Self, S. Estimates of sulfur and chlorine yield to the atmosphere from volcanic eruptions and potential climatic effects. J. Geophys. Res. 89, 6309–6325 (1984)
Gerlach, T. M., Westrich, H. R., Casadevall, T. J. & Finnegan, D. L. Vapor saturation and accumulation in magmas of the 1989–1990 eruption of Redoubt Volcano, Alaska. J. Volcanol. Geotherm. Res. 62, 317–337 (1994)
Sigurdsson, H., Carey, S., Palais, J. M. & Devine, J. Pre-eruption compositional gradients and mixing of andesite and dacite magma erupted from Nevado del Ruiz, Colombia in 1985. J. Volcanol. Geotherm. Res. 41, 127–151 (1990)
Walker, B. J., Miller, C. F., Lowery, L. E., Wooden, J. L. & Miller, J. S. Geology and geochronology of the Spirit Mountain batholith, southern Nevada: implications for timescales and physical processes of batholith construction. J. Volcanol. Geoth. Res. 167, 239−262 (2007)
Dufek, J. & Bachmann, O. Quantum magmatism: magmatic compositional gaps generated by melt-crystal dynamics. Geology 38, 687–690 (2010)
Wallace, P. J. Volatiles in subduction zone magmas: concentration and fluxes based on melt inclusion and volcanic gas data. J. Volcanol. Geotherm. Res. 140, 217–240 (2005)
Gerlach, T. M., Westrich, H. R. & Symonds, R. B. in Fire and Mud: Eruptions and Lahars of Mt. Pinatubo, Philippine 415−433 (Univ. Washington Press, 1996)
Costa, F., Scalliet, B. & Gourgaud, A. Massive atmospheric sulfur loading of the AD 1600 Huaynaputina eruption and implications for petrological sulfur estimates. Geophys. Res. Lett. 30, 1068 (2003)
Shan, X. & Chen, H. Lattice Boltzmann model for simulation of flows with multiple phases and components. Phys. Rev. E 47, 1815 (1993)
Porter, M. L., Coon, E. T., Kang, Q., Moulton, J. D. & Carey, J. W. Multicomponent interparticle-potential lattice Boltzmann model for fluids with large viscosity ratios. Phys. Rev. E 86, 036701 (2012)
Huber, C., Parmigiani, A., Latt, J. & Dufek, J. Channelization of buoyant non-wetting fluids in saturated porous media. Wat. Resour. Res. 49, 6371–6380 (2013)
Gauglitz, P. A., St. Laurent, C. M. & Radke, C. J. Experimental determination of gas-bubble break-up in constricted cylindrical capillary. Ind. Eng. Chem. Res. 27, 1282–1291 (1988)
Guillot, P. & Colin, A. Stability of a jet in confined pressure-driven biphasic flows at low Reynolds number in various geometries. Phys. Rev. E 78, 016307 (2008)
Beresnev, I. A., Li, W. & Vigil, R. D. Condition for break-up of non-wetting fluid in sinusoidally constricted capillary channels. Transp. Porous Media 80, 581–604 (2009)
Clift, R., Grace, J. R. & Weber, M. E. Bubbles, Drops, and Particles. (Courier Dover Publications, 1975)
Batchelor, G. K. An Introduction to Fluid Dynamics. (Cambridge Univ. Press, 1967)
Sonshine, R. M., Cox, R. G. & Brenner, H. The Stokes translation of a particle of arbitrary shape along the axis of a circular cylinder. Appl. Sci. Res. 16, 273–300 (1966)
Ruprecht, P., Bergantz, G.W. & Dufek, J. Modeling of gas-driven magmatic overturn: tracking of phenocryst dispersal and gathering during magma mixing. Geochem. Geophys. Geosys. 9, Q07017 (2008)
Martin, D. & Nokes, R. Crystal settling in a vigorously convecting magma chamber. Nature 332, 534–536 (1988)
Higuera, F. J. Injection and coalescence of bubbles in a very viscous liquid. J. Fluid Mech. 530, 369–378 (2005)
Gerlach, D., Alleborn, N., Buwa, V. & Durst, F. Numerical simulation of periodic bubble formation at a submerged orifice with constant gas flow rate. Chem. Eng. Sci. 62, 2109–2125 (2007)
Quan, S. & Hua, J. Numerical studies of bubble necking in viscous liquids. Phys. Rev. E 77, 066303 (2008)
He, X. & Luo, L. S. A priori derivation of the lattice Boltzmann equation. Phys. Rev. E 55, R6333–R6336 (1997)
Shan, X., Yuan, X. F. & Chen, H. Kinetic theory representation of hydrodynamics: a way beyond the Navier-Stokes equation. J. Fluid Mech. 550, 413–441 (2006)
Shan, X. & Doolen, G. D. Multicomponent Lattice Boltzmann model with interparticle interaction. J. Stat. Phys. 81, 379 (1995)
Coon, E. T., Porter, M. L. & Kang, Q. Taxila LBM: a parallel, modular lattice Boltzmann framework for simulating pore-scale flow in porous media. Comput. Geosci. 18, 17–27 (2014)
He, X., Chen, S. & Doolen, G. D. A novel thermal model for the lattice Boltzmann method in incompressible limit. J. Comput. Phys. 146, 282–300 (1998)
D’Humieres, D., Ginzburg, I., Krafzcyk, M., Lallemand, P. & Luo, L. S. Multiple-relaxation-time lattice Boltzmann models in three dimensions. Phil. Trans. R. Soc. Lond. A 360, 437–451 (2002)
Sbragaglia, M. et al. Generalized lattice Boltzmann method with multirange pseudopotential. Phys. Rev. E 75, 026702 (2007)
Huang, H., Thorne, D. T., Schaap, M. G. & Sukop, M. C. Proposed approximation for contact angles in the Shan-and-Chen type multicomponent multiphase lattice Boltzmann models. Phys. Rev. E 76, 066701 (2007)
Discussion of an early version of the paper with A. Burgisser, P. W. Lipman, O. Malaspinas, M. Lupi and W. Degruyter helped us to clarify some concepts. We also thank O. Malaspinas and the rest of the Palabos team, as well as M. L. Porter for discussing how to implement lattice Boltzmann algorithms. We thank J. Bourquin for help with redrafting several figures. A.P. and O.B. acknowledge support from the Swiss National Science Foundation (Ambizione grant no. 154854 to A.P., and project no. 200021-103441 to O.B.). S.F., C.H. and Y.S. acknowledge funding from a National Science Foundation CAREER grant (1454821; awarded to C.H.). This work was also supported by grants from the Swiss National Supercomputing Centre (CSCS) under projects s479 and s597, and the Euler Supercomputer from ETHZ.
The authors declare no competing financial interests.
Extended data figures and tables
The hindrance function, F(Ψ,λ), defined by equation (1), for suspensions of MVP (λ→0) over a wide range of MVP volume fractions (0 ≤ Ψ ≤ 0.6). The inset shows the comparison of F(Ψ,λ→ 0) with experimental data up to MVP volume fractions of 10%. Experimental data are taken from ref. 18 where the method of continuous injection is used, injecting the dispersed phase (water) into the highly viscous ambient phase (silicone oil, resulting in λ= O(10−4)).
a–f, The results of three numerical calculations used to explain the effect of crystal confinement on fingering formation (see video in Supplementary Information). Porosity, ϕ, decreases from left to right. a–c, Three separate initial states, at different porosities; d–f, the corresponding steady states, at the corresponding porosities. At higher crystallinity (1−ϕ), fingers can form and remain stable. g, Results of 78 calculations showing the correlation between the MVP volume fraction, Ψ, and the flux of MVP in the porous medium (the Darcy velocity, UDarcy). At low Ψ, the low mobility of bubbles is such that UDarcy is close to zero. Once continuous fingers are formed (‘connected’; green and blue regions), the MVP flux experiences a strong increase because of the sudden and sharp decrease in the rate of viscous energy dissipation. Conversely, during a waning influx of MVP (moving from right to left in g), an MVP volume fraction of 10% or slightly more can remain trapped in the mush because of capillary and viscous trapping in the mush.
Water droplets are released from localized nozzles at the top and sink into viscous silicon oil, forming bubble trains or plumes initially. The motion of water droplet is captured by a camera and used to test our bubble suspension migration model (equation (1)).
For conditions and parameters consistent with exsolved volatile bubbles (2 mm diameter) in a viscous melt, the detrainment of bubbles over time depends on the initial bubble volume fraction, because of the hindered motion of bubbles in a suspension.
a, b, Bubble residence time (a) and accumulation (b) in a convecting crystal-poor cap of thickness H (100 m). D refers to the average diameter of bubbles; Δρ is the density difference between MVP and the magma; q is the volumetric flux of MVP coming from the mush; and Ψs is the volume fraction of bubbles that can accumulate in the convecting layer.
a, b, Results of numerical calculations that show the transition in transport regime of MVP from a confined medium (crystal-rich mush; left) to an unconfined horizon (crystal-poor cap; right).
Extended Data Figure 7 Validation of the lattice Boltzmann algorithm: cylindrical Poiseuille flow and static contact angles.
a–c, Analytical (equations (8) and (9)) and numerical velocity (lattice Boltzmann algorithm) profiles for a three-dimensional, two-immiscible-phase, cylindrical pipe flow scenario at different viscosity ratios (λ=1/5, 1/10, or 1/20), showing normalized bubble velocity versus pipe radius. A bulk force, Fb, is applied to both fluids. Rin and Rout are the internal and external radius, respectively, for the annular flow. d–g, Different static contact angles obtained with our lattice Boltzmann algorithm. From left to right, we increase the non-wetting potential of the dispersed phase. The bubble contact angle accordingly increases from 90° to 150° (d, 90°; e, 110°; f, 130°; g, 150°). The calculations were done with an MRT collision operator (see Methods).
Video showing the time evolution of the high (left) and low (right) confinement calculations as in Figure 2a.
Thanks to these calculations, we can appreciate the positive effect of the solid confinement on bubble coalescence and fingering formation. The MVP volume fraction is the same for both low and high confinement calculations (~0.15). (AVI 5826 kb)
About this article
Cite this article
Parmigiani, A., Faroughi, S., Huber, C. et al. Bubble accumulation and its role in the evolution of magma reservoirs in the upper crust. Nature 532, 492–495 (2016). https://doi.org/10.1038/nature17401
Finite volume simulations of particle-laden viscoelastic fluid flows: application to hydraulic fracture processes
Engineering with Computers (2022)
Bulletin of Volcanology (2022)
Bulletin of Volcanology (2021)
Journal of Iberian Geology (2021)
Bulletin of Volcanology (2021)