[1] This contribution presents a semiempirical model describing the effective relative viscosity of crystalbearing magmas as function of crystal fraction and strain rate. The model was applied to an extensive data set of magmatic suspensions and partially molten rocks providing a range of values for the fitting parameters that control the behavior of the relative viscosity curves as a function of the crystal fraction in an intermediate range of crystallinity (30-80 vol % crystals). The analysis of the results and of the materials used in the experiments allows for evaluating the physical meaning of the parameters of the proposed model. We show that the model, by varying the parameters within the ranges obtained during the fitting procedure, is able to describe satisfactory the effective relative viscosity as a function of crystal fraction and strain rate for suspensions having different geometrical characteristics of the suspended solid fraction.Components: 6984 words, 4 figures, 1 table.Keywords: melts; concentrated suspensions; viscosity; strain rate. Caricchi, and N. Bagdassarov (2009), A model for the rheology of particle-bearing suspensions and partially molten rocks, Geochem. Geophys. Geosyst., 10, Q03010,

[1] The relationship between permeability and porosity is reviewed and investigated. The classical Kozeny-Carman approach and a fractal pore-space geometry assumption are used to derive a new permeability-porosity equation. The equation contains only two fitting parameters: a Kozeny coefficient and a fractal exponent. The strongest features of the model are related to its simplicity and its capability to describe measured permeability values of different non-granular porous media better than other models.Citation: Costa, A. (2006), Permeability-porosity relationship: A reexamination of the Kozeny-Carman equation based on a fractal pore-space geometry assumption, Geophys. Res. Lett., 33, L02318,

[1] We develop a model to describe ash aggregates in a volcanic plume. The model is based on a solution of the classical Smoluchowski equation, obtained by introducing a similarity variable and a fractal relationship for the number of primary particles in an aggregate. The considered collision frequency function accounts for different mechanisms of aggregation, such as Brownian motion, ambient fluid shear, and differential sedimentation. Although model formulation is general, here only sticking efficiency related to the presence of water is considered. However, the different binding effect of liquid water and ice is discerned. The proposed approach represents a first compromise between the full description of the aggregation process and the need to decrease the computational time necessary for solving the full Smoluchowski equation. We also perform a parametric study on the main model parameters and estimate coagulation kernels and timescales of the aggregation process under simplified conditions of interest in volcanology. Further analyses and applications to real eruptions are presented in the companion paper by Folch et al.