Spontaneous Small-scale Melt Segregation in Partial Melts Undergoing Deformation

A partial melt undergoing large scale deformation is shown to be unstable with respect to small scale redistribution of melt, provided the shear viscosity of the matrix depends on melt fraction. In the physically realistic case where melt "softens" the matrix, melt migrates along the direction parallel to the axis of minimum compressive stress and accumulates in "veins" (melt-rich lenses). The maximum growth rate of the instability is of order -f.0 dIn 1J / df (f.0 = largest component of the principal strain tensor, 1J = shear viscosity, f =melt fraction), and plausibly fast enough to invalidate the conventional applications of Darcy's law (e.g., mid-ocean ridges, subduction zones) since melt migrates into veins in preference to being pervasively flushed vertically. The preferred lengthscale of the instability is poorly determined but probably ~meters. Veins may eventually form an interconnected drainage networlc, allowing rapid vertical flushing of melt.