  In this paper a model for partial melts is constructed using two-scale
homogenization theory. While this technique is well known to the mathematics
and materials communities, it is relatively novel to problems in the solid
Earth. This approach begins with a grain scale model of the medium, coarsening
it into a macroscopic one. The emergent model is in good agreement with
previous work, including D. McKenzie's, and serves as verification. This
methodology also yields a series of Stokes problems whose solutions provide
constitutive relations for permeability and viscosity. A numerical
investigation of these relations appears in a companion paper.
