  Shear deformation of partially molten rock in laboratory experiments causes
the emergence of melt-enriched sheets (bands in cross-section) that are aligned
at about 15-20 degrees to the shear plane. Deformation and deviatoric stress
also cause the coherent alignment of pores at the grain scale. This leads to a
melt-preferred orientation that may, in turn, give rise to an anisotropic
permeability. Here we develop a simple, general model of anisotropic
permeability in partially molten rocks. We use linearised analysis and
nonlinear numerical solutions to investigate its behaviour under simple-shear
deformation. In particular, we consider implications of the model for the
emergence and angle of melt-rich bands. Anisotropic permeability affects the
angle of bands and, in a certain parameter regime, it can give rise to low
angles consistent with experiments. However, the conditions required for this
regime have a narrow range and seem unlikely to be entirely met by experiments.
Anisotropic permeability may nonetheless affect melt transport and the
behaviour of partially molten rocks in Earth's mantle.
