  Grain size is an important control on mantle viscosity and permeability, but
is difficult or impossible to measure in situ. We construct a two-dimensional,
single phase model for the steady-state mean grain size beneath a mid-ocean
ridge. The mantle rheology is modelled as a composite of diffusion creep,
dislocation creep, dislocation accommodated grain boundary sliding, and a
plastic stress limiter. The mean grain size is calculated by the piezometric
relationship of Austin and Evans [2007]. We investigate the sensitivity of our
model to global variations in grain growth exponent, potential temperature,
spreading-rate, and mantle hydration. We interpret the mean mean grain-size
field in the context of permeability. The permeability structure due to mean
grain size may be approximated as a high permeability region beneath a low
permeability region. The transition between high and low permeability regions
forms a boundary that is steeply sloped toward the ridge axis. We hypothesise
that such a permeability structure generated from the variability of the mean
grain size may be able to focus melt towards the ridge axis, analogous to a
Sparks and Parmentier [1991]-type focusing. This focusing may, in turn,
constrain the region where significant melt fractions are observed by seismic
or magnetotelluric surveys. This interpretation of melt focusing via the
grain-size permeability structure is consistent with MT observation of the
asthenosphere beneath the East Pacific Rise [Baba et al., 2006, Key et al.,
2013].
