In this work, we present a comprehensive rheological database including most of the existing data relevant for crystal-bearing magmas collected from the scientific literature, covering the entire range of natural volcanic conditions, in terms of crystal content (1–80%), crystal shape (aspect ratio R from 1 to 13), and strain rate (between 10−7 and 102 s−1). Datasets were collected and discerned as a function of the information which we considered necessary for building a general systematic model describing relative viscosity of crystal-bearing magmas, such as the apparent and melt viscosity, the crystal concentration, crystal shape, and the strain rate. The selected dataset was then used for modelling the relative viscosity of a liquid-solid mixture having different concentrations of particles with different R, subjected to different strain rates. The proposed model allows us to quantitatively describe the rheological behaviour of crystal-bearing magmatic systems.

<p>The eruptive style of a volcanic system and the energy of the eruption depend on a complex interplay among several internal and external factors, as temperature, pressure, volatile composition and content, and geometry of the volcanic system, all of which concur to affect the rheology of the magma and thus the eruptive strength of a volcano.</p><p>The comprehension of the rheological behavior of the mixtures of melt, crystals, and bubbles is necessary to understand the migration of magma within the volcanic system and the modality of eruptions. To date, crystal-bearing magmas and their behavior have been the focus of the majority of investigations by the scientific community.</p><p>The paucity of studies on bubble-bearing magmas may have been partly due to the greater challenges posed by the experimental procedure, mostly related to the outgassing of the gas phase during the experiments. So, while the influence of crystals in magma rheology has been parameterized in detail, a comprehensive model for the rheology of the bubble-bearing magmas has yet to be formulated.</p><p>The aim of this work is to understand the complex dependence of the viscosity on the bubble content and strain rate, by performing suites of in situ degassing experiments on rhyolitic magma at an experimental temperature of 850 °C, followed by uniaxial deformational experiments (constant strain rates of 5 x 10<sup>-5</sup>, 10<sup>-4</sup> and 10<sup>-3</sup> s<sup>-1</sup>) through a vertical uniaxial press at experimental temperatures varying between 720 and 800 °C. Experimental parameters are selected to investigate the rheology under unsteady flow conditions (i.e., prior to equilibrium deformation of bubbles). Such conditions may be very common during explosive volcanic eruptions, where bubbles are not able to relax in the fast-ascending magmas.</p><p>For constant strain rates, results show trends of apparent viscosity as a function of bubble content, consisting of an initial increase of viscosity for low amounts of bubbles (0-20%), followed, above the 20% threshold porosity, by a general viscosity decrease. At fixed porosity, a strain rate dependence of viscosity is also observed, with viscosity decreasing as the strain rate increases. Overall, the sample's apparent viscosity appears to be non-linearly controlled by both ambient conditions (Temperature T<sub>def</sub> and Strain rate ) and sample texture (Porosity and Vesicle Number Density VND), whose interplay concurs to define the degree of flow unsteadiness. We, therefore, discuss the weight of each parameter in determining the apparent viscosity of the magmatic mixture.</p>

<p><span>In this work, we present </span><span>a novel rheological database including most of the existing data relevant for crystal-bearing magmas collected from the scientific literature, covering the entire range of natural volcanic conditions, in terms of crystal content </span><span>(1-80%)</span><span>, crystal shape </span><span>(aspect ratio <em>R</em> from 1 to 13),</span><span> and strain rate </span><span>(between 10<sup>-7</sup> and 10<sup>2</sup> s<sup>-1</sup>)</span><span>. </span></p><p><span>Datasets were collected and discerned as a function of the information which we considered necessary for building a general systematic model describing relative viscosity of crystal-bearing magmas, such as the apparent and melt viscosity, the crystal concentration, crystal shape, and the strain rate. The selected dataset was then used for modelling</span><span> the relative viscosity of a liquid-solid mixture having different concentrations of particles with different <em>R</em>, subjected to different strain rates. The proposed model is based on a generalization of the four parameters semi-empirical formula, proposed by Costa et al. (2009). A new model was calibrated for the novel collected database, allowing us to quantitatively describe the rheological behaviour of crystal-bearing magmatic systems. </span></p>