The viscous constitutive relations of partially molten rocks developed here show that an anisotropy in grain-scale melt distribution can lead to a strong anisotropy in the viscosity of the solid framework. With anisotropic viscosity, a direct coupling between shear and isotropic components of stress occurs, and hence, the role of shear deformation in melt migration significantly increases. We demonstrate the significant effects of viscous anisotropy on melt migration dynamics by solving the solid-liquid two-phase dynamics for two simple cases. First, in rotary shear deformation, an anisotropy creates a driving force for melt migration up stress gradients in the solid matrix, which does not exist with isotropic viscosity. Second, in uniform simple shear deformation, melt segregates spontaneously into low-angle bands due to anisotropic melt alignment, in close agreement with experimental observations. Our results indicate that stress-induced melt alignment at the grain scale drives further melt redistribution over distances much longer than the grain scale. The development of such "multiscale anisotropy'' is demonstrated by "forward'' or ab initio approaches based on the equations of two-phase dynamics, in which the viscous constitutive relation is based on observed microstructure and realistic rheology. When applied to a simple approximation of flow in the mantle beneath ridge and subduction zone, the anisotropic constitutive relation significantly affects melt migration patterns.
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