Rheology, eruption, and flow of three-phase magma

A model is developed for the rheology of a three-phase suspension of bubbles and particles in a Newtonian liquid undergoing steady flow. An `effective-medium' approach is adopted, which treats the bubbly liquid as a continuous medium which suspends the particles. The resulting three-phase model combines separate two-phase models for bubble suspension rheology and particle suspension rheology, which are taken from the literature. The model is validated against new 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 ≤ φp ≤ 0.5) and bubble volume fraction (0 ≤ φb ≤ 0.3). Consistent with model predictions, experimental results demonstrate that adding bubbles to a dilute particle suspension at low capillarity increases its viscosity, whilst adding bubbles to a concentrated particle suspension decreases its viscosity. The model accounts for particle anisometry and is easily extended to account for variable capillarity, and bubbles which are larger than the particles, but has not been experimentally validated for these cases. This model is a significant step forward, because it allows the viscosity of many magmas and lavas - which typically contain both crystals and bubbles - to be calculated more accurately. The model is then used to explain three volcanological problems. Firstly, it is proposed that in a jammed magma mush, the pervasive formation and growth of bubbles of magmatic gas can push the crystals apart, unjamming the mush. Further bubble growth would then lead to a dramatic reduction in viscosity. This concept is tested using analogue suspensions, and it is demonstrated that the growth of bubbles alone is sufficient to mobilize an initially jammed particle suspension. Secondly, lava morphologies found in the crystal-rich 1780 flow field on Volcán Llaima, Chile, are described. Within the 1780 flow field, occur: well-developed `a`ā, with broad, leveed channels; well-developed pāhoehoe; slabby pāhoehoe with transitions to and from `a`ā; and a cluster of features that have been termed "`a`ā mounds", which are interpreted to be higher viscosity analogues of rootless shields found on Hawai'i, and comparable to megatumuli and terraces found on Mount Etna. It is proposed that this crystal-rich lava was able to flow as pāhoehoe because bubbles lowered its viscosity. Thirdly, a recent lava flow from Kīlauea is analysed, and the various factors that control viscosity quantified. These include bubble and crystal fractions, crystal shapes, and dissolved volatile contents. These factors are then used to understand down-flow changes in morphology. In each of these volcanological problems, understanding the three-phase rheology is important for understanding the problem, and the related flow behaviour and hazards