RHEOLOGY OF PARTIALLY MOLTEN ROCKS

Partially molten rocks are characterized by specific and apparently antagonist behaviours. For instance, large-scale structures in a migmatite body are concordant with those in surrounding rocks. By contrast, strain partitioning and heterogeneous distribution of melting and small-scale deformation instabilities can be noted in the same migmatite body. The two- fold information cannot be explained in terms of a continuous transition from a liquid-like to a solid-like rheology, as many averaging processes implicitly assume. We develop a full analysis, considering the free energy of partially molten rocks in terms of stress and strain rate, and the relative proportion of melt and solid phases. The mixing of a Newtonian melt, i.e. with a constant viscosity, within a matrix that deforms according to a power law, implies that the viscosity contrast between the two phases varies with strain rate. The surface describing viscosity in a 3D (strain rate-amount of phase-viscosity) diagram presents a cusp shape. The diagram depicts two types of behaviour and a critical state. At high strain, the viscosity contrast between the two phases is lowest. The rock behaves as a homogeneous body and a continuous description of its rheology may be estimated. At low strain rate, three domains are separated by a critical state. When the proportion of one phase is very small, the material behaves as the other end-member. For intermediate proportions, the cusp indicates three possible viscosity values. Two are metastable, whereas the third is virtual. The viscosity of the mixture continuously jumps from the viscosity of one phase to that of the other. In consequence, the mixture has no given viscosity. Different behaviours result, depending on whether the deformation takes place under a fixed content in each phase or a common stress or a common strain rate. We list several implications for partially molten rocks concerning contact melting between crystals, strain localisation and mineral banding.