The Viscosities of Partially Molten Materials Undergoing Diffusion 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 2D tiling of hexagonal unit cells and a 3D tessellation of tetrakaidecahedrons (truncated octahedrons). The geometry of the melt is determined by assuming textural equilibrium. The viscosity tensor for the 2D tiling is isotropic, but that for the 3D 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 modelling 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.
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