Summary of “ Viscous constitutive relations of solid - liquid composites in terms of grain boundary contiguity , 1 , 2 & 3 ”

Our collaboration has resulted in a series of three papers on a new model for grain boundarydiffusion creep in partially molten rocks. The broad aim is to better understand the physical processes controlling the interactions of deformation, melt distribution and melt migration. Towards this aim, we saw the need for a 3-D, grain-scale model for viscosity in the presence of melt. The constitutive relations resulting from this model enable us to study dynamic processes at longer length scales, based on microand meso-scale textures observed in experimental samples and natural rocks. In this model, grain scale melt geometry is described by grain boundary contiguity. Contiguity is the fraction of the total grain area that is in contact with neighboring grains, and is a useful structural state variable for describing granular media. It can be quantitatively related to melt fraction for specified values of surface energies, for texturally equilibrated materials (e.g. Takei, 2002). This geometric basis is the same as the contiguity model for homogenization of elastic properties of partially molten rocks (Takei, 1998). Thus, the viscous model is an extension of the elastic contiguity model and builds on the original work of Cooper & Kohlstedt (1984) and Cooper et al. (1989) for grain boundary diffusion creep, referred to below as the CK model. In an ab initio approach, we derived viscous constitutive relations by solving the mass and mechanical balances and reaction and diffusion kinetics for each grain, with boundary conditions determined by the 3-D distribution of grain boundary contiguity. The many questions and findings that emerged in the process of developing the model have taken the form of these three companion papers. The first focuses on the general model and its potential applications, the second on the creep behavior at very small melt fractions, and the third on the causes and consequences of viscous anisotropy.