Rheological flow laws for multiphase magmas: An empirical approach

Abstract

The physical properties of magmas play a fundamental role in controlling the eruptive dynamics of volcanoes. Magmas are multiphase mixtures of crystals and gas bubbles suspended in a silicate melt and, to date, no flow laws describe their rheological behaviour. In this study we present a set of equations quantifying the flow of high-viscosity (>105Pa·s) silica-rich multiphase magmas, containing both crystals (24–65vol.%) and gas bubbles (9–12vol.%). Flow laws were obtained using deformation experiments performed at high temperature (673–1023K) and pressure (200–250MPa) over a range of strain-rates (5·10−6s−1 to 4·10−3s−1), conditions that are relevant for volcanic conduit processes of silica-rich systems ranging from crystal-rich lava domes to crystal-poor obsidian flows. We propose flow laws in which stress exponent, activation energy, and pre-exponential factor depend on a parameter that includes the volume fraction of weak phases (i.e. melt and gas bubbles) present in the magma. The bubble volume fraction has opposing effects depending on the relative crystal volume fraction: at low crystallinity bubble deformation generates gas connectivity and permeability pathways, whereas at high crystallinity bubbles do not connect and act as “lubricant” objects during strain localisation within shear bands. We show that such difference in the evolution of texture is mainly controlled by the strain-rate (i.e. the local stress within shear bands) at which the experiments are performed, and affect the empirical parameters used for the flow laws. At low crystallinity (<44vol.%) we observe an increase of viscosity with increasing strain-rate, while at high crystallinity (>44vol.%) the viscosity decreases with increasing strain-rate. Because these behaviours are also associated with modifications of sample textures during the experiment and, thus, are not purely the result of different deformation rates, we refer to “apparent shear-thickening” and “apparent shear-thinning” for the behaviours observed at low and high crystallinity, respectively. At low crystallinity, increasing deformation rate favours the transfer of gas bubbles in regions of high strain localisation, which, in turn, leads to outgassing and the observed increase of viscosity with increasing strain-rate. At high crystallinity gas bubbles remain trapped within crystals and no outgassing occurs, leading to strain localisation in melt-rich shear bands and to a decrease of viscosity with increasing strain-rate, behaviour observed also in crystal-bearing suspensions.Increasing the volume fraction of weak phases induces limited variation of the stress exponent and pre-exponential factor in both apparent shear-thickening and apparent shear-thinning regimes; conversely, the activation energy is strongly dependent on gas bubble and melt volume fractions. A transient rheology from apparent shear-thickening to apparent shear-thinning behaviour is observed for a crystallinity of 44vol.%. The proposed equations can be implemented in numerical models dealing with the flow of crystal- and bubble-bearing magmas. We present results of analytical simulations showing the effect of the rheology of three-phase magmas on conduit flow dynamics, and show that limited bubble volumes (<10vol.%) lead to strain localisation at the conduit margins during the ascent of crystal-rich lava domes and crystal-poor obsidian flows.