The Viscosities of Partially Molten Materials Undergoing Diffusion Creep

Abstract

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.