Dynamics of diffusive bubble growth in magmas: Isothermal case

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Abstract
We have conducted a parametric study and developed a new cell model describing diffusion‐induced growth of closely spaced bubbles in magmatic systems. The model accounts for (1) the effects of advection of melt resulting from bubble growth, and its affect on the local concentration profile; (2) dynamic resistance of the viscous melt during diffusive growth; (3) diffusion of volatiles in response to evolving concentration gradients; (4) mass balance between dissolved volatiles and gas inside the bubble; (5) changes in the equilibrium saturation concentration at the bubble‐melt interface; (6) total pressure within the bubble consisting of ambient, surface tension, and dynamic pressures. The results of this study reveal that bubble growth depends strongly on ambient pressure, volatile oversaturation in the melt, and diffusivity coefficients, but only weakly on bubble separation and initial bubble radius. Increased volatile oversaturation increases growth rate to the point at which it actually reduces time for complete bubble growth. This counterintuitive result is due to significant advective volatile flux toward the bubble interface during growth. Viscosity controls growth dynamics only for cases of high viscosity (>104 Pa s). The documentation of the evolution of gas fraction in the melt and bubble wall thickness as a function of time makes it possible to estimate bubble disruption thresholds which bear on volcanic eruption mechanisms. Model results can be applied to the larger‐scale problem of magmatic degassing in terms of bubble coalescence, flotation and the development of foams in magma chambers and vent systems, and ultimately to the dynamics of eruption mechanisms.