09:00 to 10:00 Grigorios Pavliotis (Imperial College London)Homogenization methods (1) INI 1 10:00 to 11:00 Grigorios Pavliotis (Imperial College London)Homogenization methods (2) INI 1 11:00 to 11:30 Morning Coffee 11:30 to 12:30 Yasuko Takei (University of Tokyo)Constitutive mechanical relations of a partially molten rock in terms of grain boundary contiguity: an approach with an internal state variable Mechanical and transport properties of a partially molten rock strongly depend on the grain scale melt geometry. To quantify the microstructural effects, constitutive mechanical relations for elasticity (Takei, 1998) and diffusion creep viscosity (Takei and Holtzman, 2009) are derived theoretically by considering a realistic microstructural model. The essential geometrical factor which determines these properties was found to be the grain boundary contiguity’’ which represents the area of grain-to-grain contacts relative to the total surface area of each grain. One of the most striking results is that while contiguity affects both elasticity and viscosity, the effect on viscosity is about 100 times larger than that on elasticity. When partially molten rock is texturally equilibrated, contiguity is determined as a function of melt fraction and dihedral angle. However, when it is deformed under a deviatoric stress, contiguity deviates from the equilibrium value an d evolves, resulting in a significant change in the matrix viscosity. Possible consequences of these microstructural evolution on the macroscopic dynamics can be studied within the framework of continuum mechanics by solving the governing equations of two phase flow together with the viscous constitutive relation which includes contiguity as an internal state variable. By applying this approach to the formation of stress-driven, melt-enriched channels, I will demonstrate the important role of microstructural processes in the macroscopic dynamics. INI 1 12:30 to 13:30 Lunch @ Wolfson Court 13:30 to 14:30 Ulrich Faul (Massachusetts Institute of Technology)Experimental constraints on melt distribution and its effect on the rheology and seismic properties of polycrystalline olivine Coauthors: Gordana Garapić (SUNY New Paltz), Ian Jackson (Australian National University) Bulk properties of partially molten rocks are significantly affected by the melt distribution and geometry. Surface energy minimisation determines the melt geometry, both locally at the junction of two grains and melt (dihedral angle), and for the aggregate as whole, in the form of grain growth. Grain growth is a continuous process and partially molten rocks therefore constitute a dynamic system. This contrasts with the assumptions of the model melt distribution in a static system with isotropic grains of a single size that can be fully characterised by measuring dihedral angles. In the dynamic system the local melt geometry is not always in its minimum energy configuration, as grain growth continuously creates new neighbours that need to adjust their grain boundary plane orientations. In this dynamic system, the melt distribution can not be characterised by only measuring dihedral angles.  As a somewhat more comprehensive assessment of the melt distribution, we measure the proportion of grain boundaries wetted by melt (grain boundary wetness/contiguity). While deformation experiments in the diffusion creep regime by necessity need to be carried out on fine-grained samples, the melt distribution can be determined on significantly more coarse-grained samples, hot-pressed at high temperatures up to two weeks in a piston cylinder apparatus. The wetness data from these samples, obtained at suitably high resolution, allows augmentation of the experimentally measured diffusion creep rheology. For the direct experimental determination of the effect of small amounts of melt on both large-strain rheology and seismic properties it is important to characterise genuinely melt-free materials for reference. For this reason we use synthetic Fo90 olivine aggregates that contain no melt or trace elements, unless deliberately added. Experiments with melt-bearing samples show that both the large strain rheology and seismic properties are substantially affected by small amounts of melt, consistent with the observations of the melt distribution described above. For seismic properties the presence of melt affects both the shear modulus and attenuation in the seismic frequency band. Important for the effect of melt on seismic properties are wetted grain boundaries with sufficiently low aspect ratio for local fluid flow to take place (i.e. on the scale of a single grain, ’melt squirt’). Similar materials are also used to determine the effect of water (hydroxyl) on the rheology and seismic properties of olivine. This allows comparison of the relative effects of water and melt in the upper mantle. INI 1 14:30 to 15:30 Sash Hier-Majumder (Royal Holloway, University of London)Cross Scale Modeling of Melt Migration The migration of melt over length scales of hundreds of kms takes place through grain edge tubules and films with typical dimensions of a few hundred nanometers to a few microns. The volume fraction, shape, and distribution of these tubules and films exert a strong influence on the effective physical properties, anisotropy, and the trajectory of melt migration in the mantle. In this talk, I will outline new techniques for modeling the microstructure in partially molten rocks,their influence on the effective physical properties, and the implications for large scale magma flow. INI 1 15:30 to 16:00 Afternoon Tea 16:00 to 17:00 Leila Hashim (Université d'Orléans)Reconciling macroscopic olivine grain growth with the microscopic physical properties of the intergranular medium Co-authors: Gardés Emmanuel (CNRS - Université Caen), Sifré David (CNRS - Université d'Orléans), Morales Luiz F.G. (GFZ Potsdam), Précigout Jacques (CNRS - Université d'Orléans), Gaillard Fabrice (CNRS - Université d'Orléans)Grain size is a critical parameter for the understanding of our planet’s mantle since it has considerable impact on seismological properties, on the permeability of mantle rocks and therefore on melt migration characteristics of Earth’s interior. Grain growth therefore becomes an important process that should be meticulously determined in order to better understand the dynamics of our planet’s interior.Olivine grain growth has therefore been experimentally determined by a wide number of grain growth studies where different effects have been considered (water, fO2, melt, secondary phases). However, no clear consensus on the values of the different material-dependent parameters in the empirical law has been reached. To increase the existing database on olivine grain growth, we experimentally investigated the effect of melt (from nominally melt-free to 12 wt.% melt) and water on San Carlos olivine under different pressure-temperature-duration conditions (0.3 GPa < P < 3.0 GPa, 1200°C < T < 1350°C, 1h < t < 360h).By combining the existing database on olivine grain growth and our experimental data, we have succeeded in modeling (i) genuinely dry olivine grain growth aggregates, through grain boundary diffusion-controlled processes, (ii) H2O-oversaturated olivine aggregates and (iii) melt-bearing olivine aggregates, from nominally melt-free to ∼ 50 wt.% melt. Different important parameters have been constrained by using our model, namely the dry effective grain boundary thickness (δ ∼ 6 nm), melt contents in nominally melt-free samples (Φ ≤ 0.5 wt.%) as well as the wetting properties (Ψ) of melt as a function of melt content, pressure and temperature. We expect that our results will not only have considerable implications on the grain size-dependent deformation mechanisms of mantle rocks but also reconcile macroscopic observations to microscopic-scale key processes governing the mantle behavior, particularly in intergranular zones impregnated by low melt content s. INI 1
 10:00 to 11:00 Harro Schmeling (Goethe-Universität Frankfurt)Physics of mantle melting: two-phase flow, variable matrix viscosity and density effects In the introduction different partially molten regions within the earth's mantle will be identified. Then, the governing equations are introduced with emphasis on rheology, melt density, and solution strategies. The melt fraction and its geometrical distribution has an important influence on the shear and bulk viscosity of the matrix. A new semi-analytical model is introduced which may describe the geometrical distribution of the melt phase. Combined with a poro-elastic effective medium approach (Schmeling et al., 2012) effective shear and bulk viscosity can be estimated as a function of melt fraction. Models of 2D porosity waves are shown which use such effective viscosity laws. Another important quantity is the melt density which may be higher than the matrix density at transition zone depths. 1D models of a rising hot partially molten plume show that within a certain parameter regime standing porosity waves may develop. If there is time, I will briefly mention a simple mantle convection benchmark initiative with two-phase flow in its partially molten region. Schmeling, H., J.-P. Kruse, and G. Richard, 2012: Effective shear and bulk viscosity of partially molten rock based on elastic moduli theory of a fluid filled poroelastic medium. Geophys. J. Int., doi: 10.1111/j.1365-246X.2012.05596.x INI 1 11:00 to 11:30 Morning Coffee 11:30 to 12:30 Ralph Showalter (Oregon State University)Multiscale Systems for Flow and Transport An elliptic-parabolic system of partial differential equations describes the flow of a single-phase incompressible fluid and the transport of a dissolved chemical by advection and diffusion through a heterogeneous porous medium.  The objective is to develop an upscaled model of this system which represents the full range of scales observed.  After a review of homogenization results for the traditional low contrast and the $\epsilon^2$-scaled high contrast cases, the new discrete upscaled model based on local affine approximations is constructed. It reproduces the full range of scale contrasts observed in experiments. INI 1 12:30 to 13:30 Lunch @ Wolfson Court 13:30 to 14:30 Claude le Bris (ENPC - École des Ponts ParisTech); (INRIA Paris - Rocquencourt)Stochastic homogenization (1) INI 1 14:30 to 15:30 Claude le Bris (ENPC - École des Ponts ParisTech); (INRIA Paris - Rocquencourt)Stochastic homogenization (2) INI 1 15:30 to 16:00 Afternoon Tea 16:00 to 17:00 Stephen Morris (University of Toronto)The rippling instability of icicles Co-authors: Jake Wells (Dept. of Physics, University of Toronto, Toronto ON Canada M5S 1A7), Alina Barnett (Dept. of Physics, McMaster University of Toronto, Hamilton ON Canada L8S 4M1), Josh Calafato (Dept. of Physics, University of Toronto, Toronto ON Canada M5S 1A7), Ken Liao (Dept. of Physics, University of Toronto, Toronto ON Canada M5S 1A7), Antony Szu-Han Chen (Southern Alberta Institute of Technology, Calgary AB Canada T2M 0L4), John Ladan (Dept. of Physics, University of Toronto, Toronto ON Canada M5S 1A7) Icicles are a common ice formation, familiar to anyone who lives in a cold climate. The shape of an icicle emerges from a delicate dance between solidification, hydrodynamics and heat transport. Many, but not all, natural icicles are observed to be decorated around their circumference by ribs or ripples. These features are presumed to be the result of a morphological instability in the growth process of the ice. The sides of an icicle are covered by a thin supercooled water film which flows down their nearly vertical surface. The wavelength of the ripples, which is always found to be near 1~cm, is surprisingly constant, even under diverse growing conditions. A recent detailed study in which hundreds of icicles were grown in controlled laboratory experiments revealed that trace amounts of impurities are required for the formation of the ripples. Icicles grown from distilled water have no ripples. Ripples appear at a remarkably low concentration of impurity, becoming me asurable above a concentration of just 10−3 weight \% of salt. Thereafter, they grow at a rate which is roughly logarithmic in the concentration of the impurity. These effects are not explained by linear stability theory which does not account for impurities. In this talk, we will discuss our recent experiments in which the concentration and molecular species of the impurity were varied, as well as our progress toward a generalized linear stability analysis of the growing ice surface, which includes the effects of impurities. The theory crucially depends on the boundary conditions on the ice-water interface and the possible presence of a mushy layer near this interface. Related Links http://www.physics.utoronto.ca/Icicle_Atlas/ - Open source data archive http://dx.doi.org/10.1088/1367-2630/15/10/103012 - publication INI 1 19:30 to 22:00 Conference Dinner at Corpus Christi College