Rheological state variables: A framework for viscosity parametrization in crystal-rich magmas

Abstract

Igneous processes involve multiphase magmas, and the rate at which these processes operate is tightly controlled by multiphase rheology. The rheology of magmatic suspensions containing irregular-shaped crystals is complex, and this complexity is illustrated by the strong non-linear response to deformation and the lack of apparent self-similarity when comparing the results of experiments conducted under different shear conditions. Structural and empirical models have been developed to describe the experimental data. However, they are not predictive due to presence of several tuning parameters and their strong dependence on the flow variables and suspension characteristics. The current study proposes a state variable framework that restores self-similarity in the rheology of crystal-rich magmas. This framework only uses two rheological state variables and defines a universal rheological model to explain the relative viscosity of magmatic suspensions while considering microstructural changes such as crystals’ orientation, deformation, and comminution as well as shear-induced heterogeneities. We show that the viscosity of crystal-rich magmas as function of crystal content obeys the well-known monotonic and divergent behavior documented for suspensions of solid particles. This is achieved when the appropriate state of crystal dispersion is obtained using a unique product of the two rheological state variables. This theoretical approach, compared to empirical models, is as powerful for fitting, and can be also extrapolated beyond experimental data used in the fitting procedure. Hence, the state variable framework can be generalized to form a unified law with predictive power. At low shear rates, this framework is fully predictive as we can directly constrain both variables and their unique product. At high shear rates, one of the variables must be computed and measured independently. It is also shown that the proposed model can be used to detect the presence of anomalies, e.g., crystal breakage and shear-induced heterogeneities, in experimental data.