Abstract:The processes that are involved in migration and extraction of melt from the mantle are not yet fully understood. Gaining a better understanding of material properties of partially molten rock could help shed light on the behavior of melt on larger scales in the mantle. In this study, we simulate threedimensional torsional deformation of a partially molten rock that contains a rigid, spherical inclusion. We compare the computed porosity patterns to those found in recent laboratory experiments. The laboratory e… Show more
“…The growth-rate of melt bands also depends on the ratio of bulk to shear viscosity. The rheological laws here suggest the bulk viscosity is comparable in magnitude to the shear viscosity, as also recently argued by Alisic, Rhebergen, Rudge, Katz, and Wells (2016) on the basis of a comparison of numerical models of melt bands with the laboratory experiments by Qi, Zhao, and Kohlstedt (2013). A bulk viscosity comparable to the shear viscosity was also inferred in four-point bending experiments by Cooper (1990), who found ζ/η = 1.9, not too dissimilar the value of ζ/η = 5 3 = 1.67 predicted for Coble creep.…”
Partially molten materials resist shearing and compaction. This resistance is described by a fourth‐rank effective viscosity tensor. When the tensor is isotropic, two scalars determine the resistance: an effective shear and an effective bulk viscosity. Here calculations are presented of the effective viscosity tensor during diffusion creep for a 2‐D tiling of hexagonal unit cells and a 3‐D tessellation of tetrakaidecahedrons (truncated octahedrons). The geometry of the melt is determined by assuming textural equilibrium. The viscosity tensor for the 2‐D tiling is isotropic but that for the 3‐D tessellation is anisotropic. Two parameters control the effect of melt on the viscosity tensor: the porosity and the dihedral angle. Calculations for both Nabarro‐Herring (volume diffusion) and Coble (surface diffusion) creep are presented. For Nabarro‐Herring creep the bulk viscosity becomes singular as the porosity vanishes. This singularity is logarithmic, a weaker singularity than typically assumed in geodynamic models. The presence of a small amount of melt (0.1% porosity) causes the effective shear viscosity to approximately halve. For Coble creep, previous modeling work has argued that a very small amount of melt may lead to a substantial, factor of 5, drop in the shear viscosity. Here a much smaller, factor of 1.4, drop is obtained for tetrakaidecahedrons. Owing to a Cauchy relation symmetry, the Coble creep bulk viscosity is a constant multiple of the shear viscosity when melt is present.
“…The growth-rate of melt bands also depends on the ratio of bulk to shear viscosity. The rheological laws here suggest the bulk viscosity is comparable in magnitude to the shear viscosity, as also recently argued by Alisic, Rhebergen, Rudge, Katz, and Wells (2016) on the basis of a comparison of numerical models of melt bands with the laboratory experiments by Qi, Zhao, and Kohlstedt (2013). A bulk viscosity comparable to the shear viscosity was also inferred in four-point bending experiments by Cooper (1990), who found ζ/η = 1.9, not too dissimilar the value of ζ/η = 5 3 = 1.67 predicted for Coble creep.…”
Partially molten materials resist shearing and compaction. This resistance is described by a fourth‐rank effective viscosity tensor. When the tensor is isotropic, two scalars determine the resistance: an effective shear and an effective bulk viscosity. Here calculations are presented of the effective viscosity tensor during diffusion creep for a 2‐D tiling of hexagonal unit cells and a 3‐D tessellation of tetrakaidecahedrons (truncated octahedrons). The geometry of the melt is determined by assuming textural equilibrium. The viscosity tensor for the 2‐D tiling is isotropic but that for the 3‐D tessellation is anisotropic. Two parameters control the effect of melt on the viscosity tensor: the porosity and the dihedral angle. Calculations for both Nabarro‐Herring (volume diffusion) and Coble (surface diffusion) creep are presented. For Nabarro‐Herring creep the bulk viscosity becomes singular as the porosity vanishes. This singularity is logarithmic, a weaker singularity than typically assumed in geodynamic models. The presence of a small amount of melt (0.1% porosity) causes the effective shear viscosity to approximately halve. For Coble creep, previous modeling work has argued that a very small amount of melt may lead to a substantial, factor of 5, drop in the shear viscosity. Here a much smaller, factor of 1.4, drop is obtained for tetrakaidecahedrons. Owing to a Cauchy relation symmetry, the Coble creep bulk viscosity is a constant multiple of the shear viscosity when melt is present.
“…Alisic et al. (2016) provides a three-dimensional analysis for torsion in cylindrical coordinates, but this adds mathematical complexity without additional physical insight. Figure 4.Growth rate of sinusoidal perturbations under a simple-shear flow from (4.17).…”
Section: Discussionmentioning
confidence: 99%
“…The procedure is a standard linearised stability analysis, detailed in Katz (2022, Chapter 7) and sketched in the next paragraph. Alisic et al (2016) provides a three-dimensional analysis for torsion in cylindrical coordinates, but this adds mathematical complexity without additional physical insight.…”
Section: Simple Shear Between Parallel Platesmentioning
Partially molten rock is a densely packed, melt-saturated, granular medium, but it has seldom been considered in these terms. In this paper we extend the continuum theory of partially molten rock to incorporate the physics of granular media. Our formulation includes dilatancy in a viscous constitutive law and introduces a non-local fluidity. We analyse the resulting poro-viscous–granular theory in terms of two modes of liquid–solid segregation that are observed in published torsion experiments: localisation of liquid into high-porosity sheets and radially inward liquid flow. We show that the newly incorporated granular physics brings the theory into agreement with experiments. We discuss these results in the context of grain-scale physics across the nominal jamming fraction at the high homologous temperatures relevant in geological systems.
Summary
It is generally accepted that melt extraction from the mantle at mid-ocean ridges is concentrated in narrow regions of elevated melt fraction called channels. Two feedback mechanisms have been proposed to explain why these channels grow by linear instability: shear flow of partially molten mantle and reactive flow of the ascending magma. These two mechanisms have been studied extensively, in isolation from each other, through theory and laboratory experiments as well as field and geophysical observations. Here, we develop a consistent theory that accounts for both proposed mechanisms and allows us to weigh their relative contributions. We show that interaction of the two feedback mechanisms is insignificant and that the total linear growth rate of channels is well-approximated by summing their independent growth rates. Furthermore, we explain how their competition is governed by the orientation of channels with respect to gravity and mantle shear. By itself, analysis of the reaction-infiltration instability predicts the formation of tube-shaped channels. We show that with the addition of even a small amount of extension in the horizontal, the combined instability favours tabular channels, consistent with the observed morphology of dunite bodies in ophiolites. We apply the new theory to mid-ocean ridges by calculating the accumulated growth and rotation of channels along streamlines of the solid flow. We show that reactive flow is the dominant instability mechanism deep beneath the ridge axis, where the most unstable orientation of high-porosity channels is sub-vertical. Channels are then rotated by the solid flow away from the vertical. The contribution of the shear-driven instability is confined to the margins of the melting region. Within the limitations of our study, the shear-driven feedback does not appear to be responsible for significant melt focusing or for the shallowly dipping seismic anisotropy that has been obtained by seismic inversions.
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