Viscous constitutive relations of solid‐liquid composites in terms of grain boundary contiguity: 1. Grain boundary diffusion control model

Takei, Yasuko; Holtzman, B. K.

doi:10.1029/2008jb005850

Cited by 112 publications

(267 citation statements)

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“…These dependencies themselves vary as a function of the mode of deformation. New evidence from analogue experiments [Takei, 2010] and homogenization theory [Takei and Holtzman, 2009a, 2009b, 2009c suggest that the mantle is viscously anisotropic. While these complexities could have significant consequences for coupled magma/mantle dynamics, to keep models relatively simple here, I capture the only the leading-order variation in mantle viscosity, which is isotropic.…”

Section: Rheologymentioning

confidence: 99%

Porosity‐driven convection and asymmetry beneath mid‐ocean ridges

Katz

2010

Geochem Geophys Geosyst

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[1] Seismic tomography of the asthenosphere beneath mid-ocean ridges has produced images of wave speed and anisotropy that are asymmetric across the ridge axis. These features have been interpreted as resulting from an asymmetric distribution of upwelling and melting. Using computational models of coupled magma/mantle dynamics beneath mid-ocean ridges, I show that such asymmetry should be expected if buoyancy forces contribute to mantle upwelling beneath ridges. The sole source of buoyancy considered here is the dynamic retention of less dense magma within the pores of the mantle matrix. Through a scaling analysis and comparison with a suite of simulations, I derive a quantitative prediction of the contribution of such buoyancy to upwelling; this prediction of convective vigor is based on parameters that, for the Earth, can be constrained through natural observations and experiments. I show how the width of the melting region and the crustal thickness, as well as the susceptibility to asymmetric upwelling, are related to convective vigor. I consider three causes of symmetry breaking: gradients in mantle potential temperature and composition and ridge migration. I also report that in numerical experiments performed for this study, the fluid dynamical instability associated with porosity/shear band formation is not observed to occur.

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Section: Rheologymentioning

confidence: 99%

Porosity‐driven convection and asymmetry beneath mid‐ocean ridges

Katz

2010

Geochem Geophys Geosyst

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“…This disagreement between models and experiments found a possible resolution by the incorporation of anisotropic viscosity arising from coherent alignment of melt pockets between grains [i.e., melt-preferred orientation (MPO)] in response to a deviatoric stress (10)(11)(12)(13).…”

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confidence: 99%

“…Under deviatoric stress, melt pockets in the REV coherently align normal to the σ 3 direction and the timescale for the diffusive response to stress is reduced in this direction. If the dominant deformation mechanism of the aggregate is diffusion creep, this rapid response imparts a reduction of the continuum viscosity in the σ 3 direction (10,16). Likewise, the change in grain contiguity associated with σ 1 increases the viscosity in that direction.…”

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confidence: 99%

“…Fig. 1A illustrates how anisotropy in grain/melt microstructure (i.e., MPO) produces viscous anisotropy through the mechanics of diffusion creep (10). For a representative grain in an aggregate subjected to a deviatoric stress, the contact area with neighboring grains decreases for grain boundaries that are normal to the direction of the minimum principal stress σ 3 (the minimum eigenvalue of the deviatoric stress tensor, compression positive).…”

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confidence: 99%

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Experimental test of the viscous anisotropy hypothesis for partially molten rocks

Kohlstedt

Katz

et al. 2015

Proc. Natl. Acad. Sci. U.S.A.

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Chemical differentiation of rocky planets occurs by melt segregation away from the region of melting. The mechanics of this process, however, are complex and incompletely understood. In partially molten rocks undergoing shear deformation, melt pockets between grains align coherently in the stress field; it has been hypothesized that this anisotropy in microstructure creates an anisotropy in the viscosity of the aggregate. With the inclusion of anisotropic viscosity, continuum, two-phase-flow models reproduce the emergence and angle of melt-enriched bands that form in laboratory experiments. In the same theoretical context, these models also predict sample-scale melt migration due to a gradient in shear stress. Under torsional deformation, melt is expected to segregate radially inward. Here we present torsional deformation experiments on partially molten rocks that test this prediction. Microstructural analyses of the distribution of melt and solid reveal a radial gradient in melt fraction, with more melt toward the center of the cylinder. The extent of this radial melt segregation grows with progressive strain, consistent with theory. The agreement between theoretical prediction and experimental observation provides a validation of this theory.viscous anisotropy | melt segregation | partial melts | basalt | olivine S hear deformation of partially molten rocks gives rise to melt segregation into sheets (bands in cross-section) that emerge at a low angle to the shear plane. This mode of segregation was predicted with two-phase flow theory (1) and subsequently discovered in experiments (2, 3). It has been proposed that meltenriched bands, if present in the mantle of Earth, would permit rapid extraction of melt (4), produce significant anisotropy in seismic wave propagation (5), and provide a mechanism for the seismic discontinuity that is, in some places, associated with the lithosphere-asthenosphere boundary (6). The emergence (7) and low angle (8) of melt-enriched bands under simple-shear deformation can be reproduced using two-phase flow theory with a non-Newtonian, isotropic viscosity. This theory describes the flow of a low-viscosity liquid (melt) through a permeable and viscously deformable solid matrix (grains) (9). However, an unrealistically strong stress dependence of viscosity was required to match the low angle of bands observed in experiments (8).This disagreement between models and experiments found a possible resolution by the incorporation of anisotropic viscosity arising from coherent alignment of melt pockets between grains [i.e., melt-preferred orientation (MPO)] in response to a deviatoric stress (10-13).Crucially, with the inclusion of viscous anisotropy, two-phase flow theory also predicts a simultaneous but distinct mode of melt segregation driven by large-scale gradients in shear stress. This mode is termed base-state melt segregation (13-15). Base-state melt segregation is not predicted if viscosity is isotropic; thus, its occurrence in experiments represents a test of the hypothesis that M...

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“…Alternatively, it is possible that non-Newtonian rheology leads to lower viscosities in the dehydrated layer, where strain rates are higher, such as above the plume or near the ridge axis (Ito et al, 2010). Another possibility is that the presence of even a small amount of melt in the mantle substantially reduces viscosity to partially negate the effects of dehydration strengthening (Takei and Holtzman, 2009). …”

Section: Crustal Thicknessmentioning

confidence: 99%

The origin of the asymmetry in the Iceland hotspot along the Mid-Atlantic Ridge from continental breakup to present-day

Howell

Ito

Breivik

et al. 2014

Earth and Planetary Science Letters

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The Iceland hotspot has profoundly influenced the creation of oceanic crust throughout the North Atlantic basin. Enigmatically, the geographic extent of the hotspot influence along the Mid-Atlantic Ridge has been asymmetric for most of the spreading history. This asymmetry is evident in crustal thickness along the present-day ridge system and anomalously shallow seafloor of ages ∼49-25 Ma created at the Reykjanes Ridge (RR), SSW of the hotspot center, compared to deeper seafloor created by the nowextinct Aegir Ridge (AR) the same distance NE of the hotspot center. The cause of this asymmetry is explored with 3-D numerical models that simulate a mantle plume interacting with the ridge system using realistic ridge geometries and spreading rates that evolve from continental breakup to present-day. The models predict plume-influence to be symmetric at continental breakup, then to rapidly contract along the ridges, resulting in widely influenced margins next to uninfluenced oceanic crust. After this initial stage, varying degrees of asymmetry along the mature ridge segments are predicted. Models in which the lithosphere is created by the stiffening of the mantle due to the extraction of water near the base of the melting zone predict a moderate amount of asymmetry; the plume expands NE along the AR ∼70-80% as far as it expands SSW along the RR. Without dehydration stiffening, the lithosphere corresponds to the near-surface, cool, thermal boundary layer; in these cases, the plume is predicted to be even more asymmetric, expanding only 40-50% as far along the AR as it does along the RR. Estimates of asymmetry and seismically measured crustal thicknesses are best explained by model predictions of an Iceland plume volume flux of ∼100-200 m 3 /s, and a lithosphere controlled by a rheology in which dehydration stiffens the mantle, but to a lesser degree than simulated here. The asymmetry of influence along the present-day ridge system is predicted to be a transient configuration in which plume influence along the Reykjanes Ridge is steady, but is still widening along the Kolbeinsey Ridge, as it has been since this ridge formed at ∼25 Ma.

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Viscous constitutive relations of solid‐liquid composites in terms of grain boundary contiguity: 1. Grain boundary diffusion control model

Cited by 112 publications

References 35 publications

Porosity‐driven convection and asymmetry beneath mid‐ocean ridges

Porosity‐driven convection and asymmetry beneath mid‐ocean ridges

Experimental test of the viscous anisotropy hypothesis for partially molten rocks

The origin of the asymmetry in the Iceland hotspot along the Mid-Atlantic Ridge from continental breakup to present-day

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