Linear analysis of melt band formation by simple shear

Recent experiments by Holtzman et al. [2003] demonstrate that partially molten aggregates of many mantle materials undergoing simple shear (from ∼ 100−500% strain) will spontaneously develop localized melt-rich bands. These bands develop at small strains but persist at low angles to the plane of shear (∼ 15– 20) even at large shear strains. The melt-rich bands also appear to form localized weak regions that act as strain guides for the solid matrix flow. These experiments provide an opportunity to test the equations governing flow in deformable porous media developed by McKenzie [1984] and others. Here we present linear analysis of these equations for a solid with a porosity weakening viscosity undergoing simple shear. This analysis calculates the growth in porosity of a plane wave perturbation that initiates at an angle θ0 to the plane of shear after some amount of finite strain. For a strain of 300%, the maximum growing melt band initiates at 16.8(but rotates to ∼ 70◦ in the linear analysis). We also calculate the additional solid shear induced by the localized weak regions and show that it develops a sense of shear consistent with observations only for melt bands less that 45. These two results suggest that only low angle bands are favored under shear, consistent with the observations. The linear analysis, however, does not allow the porosity growth and shear to interact which causes the initially low angle bands to be rotated to higher angles by the background simple shear. To follow the further development of the bands requires solutions of the full non-linear equations. Nevertheless, the linear analysis provides useful insights into the development of the shear bands and suggests that the theory is useful for describing partially molten systems.