Experimental test of the viscous anisotropy hypothesis for partially molten rocks

Abstract

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...

Radial Melt Segregation During Extrusion of Partially Molten Rocks

“…For compaction lengths smaller than the sample size, Allwright and Katz (2014) predicted that melt-rich sheets should extend inward from the channel wall inclined at a low angle and antithetic to the imposed flow direction, similar to those predicted and observed for general shear and torsional deformation geometries Holtzman et al, 2003;King et al, 2010;Kohlstedt et al, 2010;Qi et al, 2015;Qi & Kohlstedt, 2018). For compaction lengths smaller than the sample size, Allwright and Katz (2014) predicted that melt-rich sheets should extend inward from the channel wall inclined at a low angle and antithetic to the imposed flow direction, similar to those predicted and observed for general shear and torsional deformation geometries Holtzman et al, 2003;King et al, 2010;Kohlstedt et al, 2010;Qi et al, 2015;Qi & Kohlstedt, 2018).…”

Crystallographic Preferred Orientation of Olivine in Sheared Partially Molten Rocks: The Source of the “a‐c Switch”

“…This orientation map, which is presented in Figure 4a, covers a 6 mm long by 0.2 mm wide section extending from the center to the edge of the sample, with shear strain increasing from 0 to 11.1. Due to base-state melt segregation that occurs in partially molten rocks deformed in torsion , the melt fraction gradually decreases with increasing radius, as demonstrated for sample PT0767 in Figure 4b (for details, see Qi et al, 2015). With the shear stress at the outer radius sðRÞ 108 MPa as calculated by equation (1), s at radius r calculated using equation (4) with n 2.4 is plotted in Figure 4b.…”

Influence of Compaction Length on Radial Melt Segregation in Torsionally Deformed Partially Molten Rocks

“…The premise in the analysis of base‐state melt segregation in two‐phase flow theory is that grain‐scale alignment of melt pockets induces anisotropy in viscosity, the direction of which is described by the angle, Θ, between the normal of the long axes of melt pockets and the shear direction. Θ and the angle of MPO are complementary (Qi et al, , Figure 2), such that the measurement of MPO is important in discussing anisotropic viscosity. For simple shear deformation, the minimum principal stress σ 3 (the minimum eigenvalue of the deviatoric stress tensor with compression positive) is taken to be at 45 ∘ to the shear plane, synthetic to shear direction, and melt is assumed to align perpendicular to σ 3 , as suggested by experiments on an analog material (Takei, ).…”

“…At a strain of γ ( R )≈ 5, r peak is the smallest in samples with the largest normalized compaction length, δ c / R ≈ 10, while r peak is similar in samples with smaller normalized compaction lengths, 1. In a previous study (Qi et al, ), we explained this observation as follows: The magnitude of viscous anisotropy ( α and β ; see Qi et al, , for details) due to MPO is assumed to increase from 0 at γ ( r = 0)= 0 to a maximum value with increasing strain. The maximum value is reached at a radius r peak at which γ ( r peak )= 1.…”