  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.
