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Bubble accumulation and its role in the evolution of magma reservoirs in the upper crust


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.

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Figure 1: Transport of a buoyant, non-wetting MVP in crystal-rich and crystal-poor magmas.
Figure 2: Transport of a buoyant, non-wetting MVP in magmas with different crystal contents.
Figure 3: MVP behaviour at the transition from crystal-rich to crystal-poor magma.
Figure 4: Geological evidence for MVP accumulation in high-SiO2, crystal-poor caps.


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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.

Author information

Authors and Affiliations



C.H., O.B. and A.P. conceived the research. C.H. and, to a lesser extent, A.P. developed the physical model. A.P. performed the numerical modelling and analysed the results. S.F. developed the laboratory experiments and theoretical model for the transport of volatiles in crystal-poor magmas. Y.S. led the discussion on excess sulfur. C.H., O.B. and A.P. all wrote the manuscript.

Corresponding author

Correspondence to A. Parmigiani.

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The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Hindrance function.

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)).

Extended Data Figure 2 Confinement effect and MVP percolation.

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.

Extended Data Figure 3 Experimental study of bubble separation in suspensions.

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)).

Extended Data Figure 4 Residence time of bubbles in convecting crystal-poor magmas.

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.

Extended Data Figure 5 Bubble accumulation in convecting magma.

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.

Extended Data Figure 6 Pinch-off dynamics.

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.

ac, 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. dg, 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).

Supplementary information

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)

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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).

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