Numerical study of nucleation and growth of bubbles in viscous magmas

The nucleation and growth processes of bubbles in viscous magmas with a constant decompression rate have been numerically investigated based on a formulation which accounts for effects of viscosity, as well as diffusivity, interfacial tension, and decompression rate. The numerical solutions show two regimes in the nucleation and growth process, a diffusion‐controlled regime and a viscosity‐controlled regime, mainly depending on the decompression rate, initial saturation pressure and viscosity. The basic mechanism common to both regimes is that growth governs nucleation through depletion of degassing components. In the diffusion‐controlled regime, bubble growth is limited by the diffusion of degassing components, and the total number density of bubbles, N , is proportional to (decompression rate / diffusivity) 3/2 . In the viscosity‐controlled regime the bubble growth is limited by the expansion of gas bubbles, and In(const× N ) is approximately proportional to a dimensionless parameter, , where μ is viscosity, is the decompression rate, and P 0 is the initial saturation pressure. The transition between the two regimes dramatically occurs when the value of the above parameter decreases below about 2×l0 3 . In the viscosity‐controlled regime abundant tiny bubbles (exceeding 10 14 (m −3 )) form with a relatively high internal pressure. Such a highly stressed melt is easily fragmented into fine ash by an external shock or other disturbance. In basaltic eruptions the vesiculation is essentially controlled by diffusion, and the viscosity‐controlled regime is limited to very high decompression rate and very small water content. When andesitic magma saturated by water at 10 MPa is decompressed through the propagation of rarefaction wave induced by a landslide, as took place in the Mount St. Helens 1980 eruption, the vesiculation is controlled by the viscosity up to 100 m depth. On the other hand, in a rhyolitic magma for the same situation, vesiculation is controlled by the viscosity over the whole depth of the magma column. In the viscosity‐controlled regime, the vesicularity may be 90% or less as seen in silicic pumice, whereas in the diffusion‐controlled regime the vesicularity equals or exceeds 98% such as in reticulite in Hawaiian basalt. An observed variation of the number density of bubbles by several orders of magnitude in plinian eruptions and the correlation with the SiO 2 content can be attributed approximately to the dependence of diifusivity or viscosity on SiO 2 content and temperature, assuming the apparent correlation between SiO 2 content and temperature of magma.