A continuum model of multi-phase reactive transport in igneous systems

Multi-phase reactive transport processes are ubiquitous in igneous systems. A challenging aspect of modelling igneous phenomena is that they range from solid-dominated porous to liquid-dominated suspension flows and therefore entail a wide spectrum of rheological conditions, flow speeds, and length scales. Most previous models have been restricted to the two-phase limits of porous melt transport in deforming, partially molten rock and crystal settling in convecting magma bodies. The goal of this paper is to develop a framework that can capture igneous system from source to surface at all phase proportions including not only rock and melt but also an exsolved volatile phase. Here, we derive an n-phase reactive transport model building on the concepts of Mixture Theory, along with principles of Rational Thermodynamics and procedures of Non-equilibrium Thermodynamics. Our model operates at the macroscopic system scale and requires constitutive relations for fluxes within and transfers between phases, which are the processes that together give rise to reactive transport phenomena. We introduce a phase- and process-wise symmetrical formulation for fluxes and transfers of entropy, mass, momentum, and volume, and propose phenomenological coefficient closures that determine how fluxes and transfers respond to mechanical and thermodynamic forces. Finally, we demonstrate that the known limits of two-phase porous and suspension flow emerge as special cases of our general model and discuss some ramifications for modelling pertinent two- and three-phase flow problems in igneous systems.Comment: Revised preprint submitted for peer-reviewed publication: main text with 8 figures, 1 table; appendix with 3 figures and 2 table

On the propagation of a normal shock wave through a layer of incompressible porous material

A novel numerical formulation of the two-phase macroscopic balance equations governing the flow field in incompressible porous media is presented. The numerical model makes use of the Weighted Average Flux (WAF) method and Total Variation Diminishing (TVD) flux limiting techniques, and results in a second-order accurate scheme. A shock tube study was carried out to examine the interaction of a normal shock wave with a thin layer of porous, incompressible cellular ceramic foam. Particular attention was paid to the transmitted and reflected flow fields. The numerical model was used to simulate the experimental test cases, and their results compared with a view to validating the numerical model. A phenomenological model is proposed to explain the behaviour of the transmitted flow field

Nonlinear Viscoelastic Compaction in Sedimentary Basins

In the mathematical modelling of sediment compaction and porous media flow, the rheological behaviour of sediments is typically modelled in terms of a nonlinear relationship between effective pressure $p_e$ and porosity $\phi$, that is $p_e=p_e(\phi)$. The compaction law is essentially a poroelastic one. However, viscous compaction due to pressure solution becomes important at larger depths and causes this relationship to become more akin to a viscous rheology. A generalised viscoelastic compaction model of Maxwell type is formulated, and different styles of nonlinear behaviour are asymptotically analysed and compared in this paper

Deformation-Induced Mechanical Instabilities at the Core-Mantle Boundary

Post-Perovskite: The Last Mantle Phase Transition Our understanding of the core-mantle boundary (CMB) region has improved significantly over the past several years due, in part, to the discovery of the post-perovskite phase. Sesimic data suggest that the CMB region is highly heterogeneous, possibly reflecting chemical and physical interaction between outer core material and the lowermost mantle. In this contribution we present the results of a new mechanism of mass transfer across the CMB and comment on possible repercussions that include the initiation of deep, siderophile-enriched mantle plumes. We view the nature of core-mantle interaction, and the geodynamic and geochemical ramifications, as multiscale processes, both spatially and temporally. Three lengthscales are defined. On the microscale (1-50 km), we describe the effect of loading and subsequent shearing of the CMB region and show how this may drive local flow of outer core fluid upwards into D". We propose that larger scale processes operating on a mesoscale (50-300 km) and macroscale regimes (> 300 km) are linked to the microscale, and suggest ways in which these processes may impact on global mantle dynamics

Early Thermal Evolution of Planetesimals and its Impact on Processing and Dating of Meteoritic Material

Radioisotopic ages for meteorites and their components provide constraints on the evolution of small bodies: timescales of accretion, thermal and aqueous metamorphism, differentiation, cooling and impact metamorphism. Realising that the decay heat of short-lived nuclides (e.g. 26Al, 60Fe), was the main heat source driving differentiation and metamorphism, thermal modeling of small bodies is of utmost importance to set individual meteorite age data into the general context of the thermal evolution of their parent bodies, and to derive general conclusions about the nature of planetary building blocks in the early solar system. As a general result, modelling easily explains that iron meteorites are older than chondrites, as early formed planetesimals experienced a higher concentration of short-lived nuclides and more severe heating. However, core formation processes may also extend to 10 Ma after formation of Calcium-Aluminum-rich inclusions (CAIs). A general effect of the porous nature of the starting material is that relatively small bodies (< few km) will also differentiate if they form within 2 Ma after CAIs. A particular interesting feature to be explored is the possibility that some chondrites may derive from the outer undifferentiated layers of asteroids that are differentiated in their interiors. This could explain the presence of remnant magnetization in some chondrites due to a planetary magnetic field.Comment: 24 pages, 9 figures, Accepted for publication as a chapter in Protostars and Planets VI, University of Arizona Press (2014), eds. H. Beuther, R. Klessen, C. Dullemond, Th. Hennin

Global Scale Impacts

Global scale impacts modify the physical or thermal state of a substantial fraction of a target asteroid. Specific effects include accretion, family formation, reshaping, mixing and layering, shock and frictional heating, fragmentation, material compaction, dilatation, stripping of mantle and crust, and seismic degradation. Deciphering the complicated record of global scale impacts, in asteroids and meteorites, will lead us to understand the original planet-forming process and its resultant populations, and their evolution in time as collisions became faster and fewer. We provide a brief overview of these ideas, and an introduction to models.Comment: A chapter for Asteroids IV, a new volume in the Space Science Series, University of Arizona Press (Patrick Michel, Francesca E. DeMeo, William F. Bottke, Eds.