Reactive transport in a partially molten system with binary solid solution

Abstract

Melt extraction from the Earth's mantle through high‐porosity channels is required to explain the composition of the oceanic crust. Feedbacks from reactive melt transport are thought to localize melt into a network of high‐porosity channels. Recent studies invoke lithological heterogeneities in the Earth's mantle to seed the localization of partial melts. Therefore, it is necessary to understand the reaction fronts that form as melt flows across the lithological interface between the heterogeneity and the ambient mantle. Here we present a chromatographic analysis of reactive melt transport across lithological boundaries, using the theory of hyperbolic conservation laws. This is an extension of linear trace element chromatography to the coupling of major elements and energy transport. Our analysis allows the prediction of the nonlinear feedbacks that arise in reactive melt transport due to changes in porosity. This study considers the special case of a partially molten porous medium with binary solid solution. As melt traverses a lithological contact, binary solid solution leads to the formation of a reacted zone between an advancing reaction front and the initial contact. The analysis also shows that the behavior of a fertile heterogeneity depends on its absolute concentration, in addition to compositional differences between itself and the refractory background. We present a regime diagram that predicts if melt emanating from a fertile heterogeneity localizes into high‐porosity channels or develops a zero porosity shell. The theoretical framework presented here provides a useful tool for understanding nonlinear feedbacks in reactive melt transport, because it can be extended to more complex and realistic phase behaviors.

Physics of Melt Extraction from the Mantle: Speed and Style

“…A comparison of the contributions of ΓR and ΓT indicates that, for the case of a heterogeneity with a significant solidus difference from the ambient mantle, the melting powered by thermal diffusion plays a larger role than that by chemical reaction. Jordan & Hesse (2015) showed that two-component, solid-solution petrology can also capture the case of melts from a heterogeneity that reactively crystallises to create an impermeable shell. As discussed above, this behaviour is expected for quartz-normative pyroxenite enclaves.…”

“…Lundstrom et al (2000) argued that the products of this reactive crystallisation would, at lower pressure, be preferentially melted and drive channelisation. It remains unclear, however, if/how the behaviour predicted in the context of highly simplified petrology Jordan & Hesse 2015;Keller & Katz 2016) is consistent with more realistic petrological models and, indeed, with the natural system.…”

Thermal Evolution of the Impact‐Induced Cryomagma Chamber Beneath Occator Crater on Ceres

“…To derive an evolution equation for the multiphase medium that includes the latent heat of the phase transformation, we use an enthalpy method (Jordan & Hesse, 2015;Katz et al, 2006). With the assumption outlined above, this approach leads to an effective heat equation, similar to those commonly used in thermal modeling of asteroids (Levin, 1962;Merk et al, 2002;Neumann et al, 2012); see supplementary materials for derivation.…”

Influence of Lithology on Reactive Melt Flow Channelization

“…Nonetheless, the dunites appear to represent an important melt migration feature in the upper mantle and as such have been the focus of several experimental investigations (Daines & Kohlstedt, 1994; Lundstrom, 2003; Morgan & Liang, 2003, 2005; Van Den Bleeken et al, 2010) and numerical modeling studies (e.g. Baltzell et al, 2015; Hesse et al, 2011; Jordan & Hesse, 2015; Liang & Guo, 2003; Liang et al, 2010, 2011; Rees Jones & Katz, 2018; Spiegelman & Kelemen, 2003; Schiemenz et al, 2011; Spiegelman et al, 2001).…”