Hydrodynamic modelling of bubble interactions inside conduits: insights for volcanic eruption behaviour

Volatile species in magma forms a discrete bubbles phase in large concentrations due to ascent assisted decompression within volcanic conduits. The evolution of the bubbles within the conduit is important to understand contrasting style of volcanic eruptions. Existing studies converge that such population of dynamic bubbles can generate three different styles of two-phase flow, namely: bubbly, slug and annular flows inside a conduit. In this study, we report findings from analogue experiments and control-volume based level-set method to investigate the mechanism of mechanical interaction of closely spaced bubbles during their ascent trajectory. Our findings suggest that mutual interaction is responsible for controlling their
deformation, coalescence and post-coalescence break-up processes. The results of numerical simulation show that two consecutive bubbles can suffer contrasting pattern of deformations before their coalescence. We found that the leading bubble gets flattened across the flow direction, while the trailing bubble takes an elongated shape in harmony with the flow direction inside the conduit. Our model emphasizes the relative importance of the two rheological factors: density (ρ*) and viscosity (µ*) ratios with the ambient magma in determining the outcome of the transportation behaviour. We observed that upward velocity of the bubbles is more sensitive to ρ* when compared with µ*. Importantly, from our results it is possible to
estimate the optimum spacing between two in-axis bubbles required for initiating any hydrodynamic interaction. We found that a threshold separation of ~ 1.5 (non-dimensionalized with the bubble size) is necessary for bubble coalescence. Extension of this analysis also allows us to predict that a ~50% bubble volume of the total magmatic system is essential for generating large bubbles, that can perhaps be considered as onset of slug flow inside a conduit. Furthermore, time series analysis of these models suggest that such larger bubbles will eventually get fragmented to produce smaller bubbles.