Analytical models for bubble growth during decompression of high viscosity magmas

Analytical models for decompressional bubble growth in a viscous magma are developed to establish the influence of high magma viscosity on vesiculation and to assess the time-scales on which bubbles respond to decompression. Instantaneous decompression of individual bubbles, analogous to a sudden release of pressure (e.g. sector collapse), is considered for two end-member cases. The infinite melt model considers the growth of an isolated bubble before significant bubble interaction occurs. The shell model considers the growth of a bubble surrounded by a thin shell and is analogous to bubble growth in a highly vesicular magmatic foam. Results from the shell model show that magmas less viscous than 10⁹ Pa s can freely expand without developing strong overpressures. The timescales for pressure re-equilibration are shortened by increased ratios of bubble radius to shell thickness and by larger decompression. Time-scales for isolated bubbles in rhyolitic melts (infinite melt model) are significantly longer, implying that such bubbles could experience internal pressures greater than the ambient pressure for at least a few hours following a sudden release of pressure. The shell model is developed to assess bubble growth during the linear decompression of a magma body of constant viscosity. For the range of decompression rates and viscosities associated with actual volcanic eruptions, bubble growth continues at approximately the equilibrium rate, with no attendant excess of internal pressure. The results imply that viscosity does not have any significant role in preventing the explosive expansion of high viscosity foams. However, for viscosities of >10⁹ Pa s there is the potential for a viscosity quench under the extreme decompression rates of an explosive eruption. It is proposed that the typical vesicularities of pumice of 0.7–0.8 are a consequence of the viscosity of the degassing magmas becoming sufficiently high to inhibit bubble expansion over the characteristic time-scale of eruption. For fully degassed silicic lavas with viscosities in the range 10¹⁰ to 10¹² Pa s time-scales for decompression of isolated bubbles can be hours to many months.