The Rheology of Three-Phase Basaltic Magma

Abstract:

The transport of magma is controlled by its rheology which, in turn, is a function of its crystal and bubble content. We develop the first empirically-validated model for the rheology of a three-phase magma (i.e. one containing both bubbles and crystals). The model is valid at low bubble capillary number (where bubble deformation is small) which is typical of basaltic magma. We adopt an ‘effective-medium’ approach in which the bubbly melt is treated as a continuous medium which suspends the crystals. The resulting three-phase model combines separate two-phase models for bubble suspension rheology and crystal suspension rheology, which are taken from the literature. The model is validated against new analogue experimental data for three-phase suspensions of bubbles and spherical particles, collected in the low bubble capillary number regime. Good agreement is found across the experimental range of particle volume fraction (0 ≤ Фp ≤0.5) and bubble volume fraction (0 ≤ Фb ≤ 0.3). Consistent with model predictions, experimental results demonstrate that, at low capillarity, bubble growth in a crystal-poor magma increases its viscosity, whilst bubble growth in a crystal-rich magma decreases its viscosity.

The validity range of the model makes it particularly applicable to the transport of magma in the sub-volcanic plumbing system. The model is trivially extended to account for variations in crystal shape, and for the high capillarity regime; these extended models await experimental validation.