Pipe Poiseuille flow of viscously anisotropic, partially molten rock

Laboratory experiments in which synthetic, partially molten rock is subjected to forced deformation provide a context for testing hypotheses about the dynamics and rheology of the mantle. Here our hypothesis is that the aggregate viscosity of partially molten mantle is anisotropic, and that this anisotropy arises from deviatoric stresses in the rock matrix. We formulate a model of pipe Poiseuille flow based on theory by Takei and Holtzman [2009a] and Takei and Katz [2013]. Pipe Poiseuille is a configuration that is accessible to laboratory experimentation but for which there are no published results. We analyse the model system through linearised analysis and numerical simulations. This analysis predicts two modes of melt segregation: migration of melt from the centre of the pipe toward the wall and localisation of melt into high-porosity bands that emerge near the wall, at a low angle to the shear plane. We compare our results to those of Takei and Katz [2013] for plane Poiseuille flow; we also describe a new approximation of radially varying anisotropy that improves the self-consistency of models over those of Takei and Katz [2013]. This study provides a set of baseline, quantitative predictions to compare with future laboratory experiments on forced pipe Poiseuille flow of partially molten mantle.Comment: 23 pages, 7 figures. Submitted to Geophysical Journal International on 25 April 2014. Revised after reviewer comments and resubmitted on 20 August 201

Consequences of viscous anisotropy in a deforming, two-phase aggregate. Why is porosity-band angle lowered by viscous anisotropy?

In laboratory experiments that impose shear deformation on partially molten aggregates of initially uniform porosity, melt segregates into high-porosity sheets (bands in cross-section). The bands emerge at 15-20 degrees to the shear plane. A model of viscous anisotropy can explain these low angles whereas previous, simpler models have failed to do so. The anisotropic model is complex, however, and the reason that it produces low-angle bands has not been understood. Here we show that there are two mechanisms: (i) suppression of the well-known tensile instability, and (ii) creation of a new, shear-driven instability. We elucidate these mechanisms using linearised stability analysis in a coordinate system that is aligned with the perturbations. We consider the general case of anisotropy that varies dynamically with deviatoric stress, but approach it by first considering uniform anisotropy that is imposed a priori and showing the difference between static and dynamic cases. We extend the model of viscous anisotropy to include a strengthening in the direction of maximum compressive stress. Our results support the hypothesis that viscous anisotropy is the cause of low band-angles in experiments.Comment: 32 pages, 8 figures. Accepted for publication in the Journal of Fluid Mechanics on 4 October 201

Melt-preferred orientation, anisotropic permeability, and melt-band formation in a deforming, partially molten aggregate

Shear deformation of partially molten rock in laboratory experiments causes the emergence of melt-enriched sheets (bands in cross-section) that are aligned at about 15-20 degrees to the shear plane. Deformation and deviatoric stress also cause the coherent alignment of pores at the grain scale. This leads to a melt-preferred orientation that may, in turn, give rise to an anisotropic permeability. Here we develop a simple, general model of anisotropic permeability in partially molten rocks. We use linearised analysis and nonlinear numerical solutions to investigate its behaviour under simple-shear deformation. In particular, we consider implications of the model for the emergence and angle of melt-rich bands. Anisotropic permeability affects the angle of bands and, in a certain parameter regime, it can give rise to low angles consistent with experiments. However, the conditions required for this regime have a narrow range and seem unlikely to be entirely met by experiments. Anisotropic permeability may nonetheless affect melt transport and the behaviour of partially molten rocks in Earth's mantle.Comment: 19 pages, 7 figures, accepted for publication in Geophysical Journal International on 3 September 201

Variations in mid-ocean ridge CO2 emissions driven by glacial cycles

The geological record shows links between glacial cycles and volcanic productivity, both subaerially and at mid-ocean ridges. Sea-level-driven pressure changes could also affect chemical properties of mid-ocean ridge volcanism. We consider how changing sea-level could alter the CO2 emissions rate from mid-ocean ridges, on both the segment and global scale. We develop a simplified transport model for a highly incompatible element through a homogenous mantle; variations in the melt concentration the emission rate of the element are created by changes in the depth of first silicate melting. The model predicts an average global mid-ocean ridge CO2 emissions-rate of 53 Mt/yr, in line with other estimates. We show that falling sea level would cause an increase in ridge CO2 emissions with a lag of about 100 kyrs after the causative sea level change. The lag and amplitude of the response are sensitive to mantle permeability and plate spreading rate. For a reconstructed sea-level time series of the past million years, we predict variations of up to 12% (7 Mt/yr) in global mid-ocean ridge CO2 emissions. The magnitude and timing of the predicted variations in CO2 emissions suggests a potential role for ridge carbon emissions in glacial cycles

Formation of Chimneys in Mushy Layers: Experiment and Simulation

In this fluid dyanmics video, we show experimental images and simulations of chimney formation in mushy layers. A directional solidification apparatus was used to freeze 25 wt % aqueous ammonium chloride solutions at controlled rates in a narrow Hele-Shaw cell (1mm gap). The convective motion is imaged with schlieren. We demonstrate the ability to numerically simulate mushy layer growth for direct comparison with experiments

Volatiles beneath mid-ocean ridges: deep melting, channelised transport, focusing, and metasomatism

Deep-Earth volatile cycles couple the mantle with near-surface reservoirs. Volatiles are emitted by volcanism and, in particular, from mid-ocean ridges, which are the most prolific source of basaltic volcanism. Estimates of volatile extraction from the asthenosphere beneath ridges typically rely on measurements of undegassed lavas combined with simple petrogenetic models of the mean degree of melting. Estimated volatile fluxes have large uncertainties; this is partly due to a poor understanding of how volatiles are transported by magma in the asthenosphere. Here, we assess the fate of mantle volatiles through numerical simulations of melting and melt transport at mid-ocean ridges. Our simulations are based on two-phase, magma/mantle dynamics theory coupled to idealised thermodynamic model of mantle melting in the presence of water and carbon dioxide. We combine simulation results with catalogued observations of all ridge segments to estimate a range of likely volatile output from the global mid-ocean ridge system. We thus predict global MOR crust production of 66-73 Gt/yr (22-24 km3/yr) and global volatile output of 52-110 Mt/yr, corresponding to mantle volatile contents of 100--200~ppm. We find that volatile extraction is limited: up to half of deep, volatile-rich melt is not focused to the axis but is rather deposited along the LAB. As these distal melts crystallise and fractionate, they metasomatise the base of the lithosphere, creating rheological heterogeneity that could contribute to the seismic signature of the LAB.Comment: 42 pages; 8 figures; 2 appendices (incl 1 table); 7 suppl. figures; 1 suppl. tabl

How Much Do Immigration and Trade Affect Labor Market Outcomes?

macroeconomics, trade, labor markets, immigration