Dilatancy and in-situ bubble formation in poro-elastic granular magma
Authors: Petford Nick , Llewellin Ed 
Published: February 2023

The formation of bubbles in magma in response to changes in pressure and temperature exerts a fundamental control on magma properties (Coumans et al., 2020). As contemporary models of magma chambers have moved away from the &#8216;liquid tank&#8217; towards a model of a mush zone comprising a mix of solids and melt, it is important to understand better how magma cam be mobilized from a mostly crystalline matrix (Maguire et al., 2022). Here we propose that in-situ bubble formation may be a key driver.Deformation of a packed, congested magma slurry with melt fraction below around 20% can result in Reynolds dilation of the granular skeleton. Where this happens, the coordination number (Z), defining the minimum number of grain contacts, drops as intergranular space is created. The corresponding pressure drop in the interstitial melt phase for a mush of thickness H with a position-dependent permeability can be estimated as a function of variable strain rate (Petford et al., 2020). For expediency, previous work in dilating magmas regarded the melt phase as incompressible, with the caveat that compressibility could be added as an important refinement to modified Biot&#8217;s equations for poro-elasticity.&#160;We present here initial results combining estimates of melt pressure drop in dilating mafic and silicic magmas with estimates for bubble nucleation and growth derived from experiments and numerical modelling. Using appropriate elastic constants (shear and bulk moduli) and particle diameters (1-5 mm) for mixtures of olivine, plagioclase and quartz, order-of-magnitude comparisons suggest that in-situ deformation of congested granular magma can result in pressure drops in the range 5-10 MPa, consistent with bubble formation (Coumans et al., 2020; Hamling & Kilgour, 2020), provided the local shear strain rate exceeds 10-10 s-1.In-situ pressure drops of this magnitude are equivalent to instantaneous transport of the melt phase several hundreds of metres upwards from their resting level and is enough to trigger bubble formation and growth if certain conditions are met. This solid-fluid coupling offers a novel way to explore how bubble nucleation and growth mechanisms change over time in response to shear-induced (local) variations in melt pressure and should be considered an additional mechanism for promoting instability in crustal mush zones.&#160;ReferencesCoumans, JP, Llewellin, EW, Wadsworth, FB, Humphreys, MCS, Mathias, SA, Yelverton, BM, Gardner, JE, (2020). An experimentally validated numerical model for bubble growth in magma. J. Volc. Geothermal. Res. 402. 107002.Hamling, IJ, Kilgour, G, (2020). Goldilocks conditions required for earthquakes to trigger basaltic eruptions: Evidence from the 2015 Ambrym eruption. Science 6, doi: 10.1126/sciadv.aaz5261.Maguire, R, Schmandt, B, Li, J, Chengxin, J, Guoliang, Li, Justin, W, Chen, M, (2022).&#160; Magma accumulation at depths of prior rhyolite storage beneath Yellowstone Caldera, Science, 1001-1004 doi:10.1126/science.ade0347.Petford, N, Koenders, MA, Clemens, JD, (2020). Igneous differentiation by deformation. Contrib. Min. Pet. 5, 1-21.