  Laboratory experiments in which synthetic, partially molten rock is subjected
to forced deformation provide a context for testing hypotheses about the
dynamics and rheology of the mantle. Here our hypothesis is that the aggregate
viscosity of partially molten mantle is anisotropic, and that this anisotropy
arises from deviatoric stresses in the rock matrix. We formulate a model of
pipe Poiseuille flow based on theory by Takei and Holtzman [2009a] and Takei
and Katz [2013]. Pipe Poiseuille is a configuration that is accessible to
laboratory experimentation but for which there are no published results. We
analyse the model system through linearised analysis and numerical simulations.
This analysis predicts two modes of melt segregation: migration of melt from
the centre of the pipe toward the wall and localisation of melt into
high-porosity bands that emerge near the wall, at a low angle to the shear
plane. We compare our results to those of Takei and Katz [2013] for plane
Poiseuille flow; we also describe a new approximation of radially varying
anisotropy that improves the self-consistency of models over those of Takei and
Katz [2013]. This study provides a set of baseline, quantitative predictions to
compare with future laboratory experiments on forced pipe Poiseuille flow of
partially molten mantle.
