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, P02/(4μ|P˙|) , where μ is viscosity, |trueP˙| is the decompression rate, and P0 is the initial saturation pressure. The transition between the two regimes dramatically occurs when the value of the above parameter decreases below about 2×l03. In the viscosity‐controlled regime abundant tiny bubbles (exceeding 1014 (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 SiO2 content can be attributed approximately to the dependence of diifusivity or viscosity on SiO2 content and temperature, assuming the apparent correlation between SiO2 content and temperature of magma.

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The vesiculation of magmas is the most important process which controls eruption style on terrestrial planets and physical and geological characteristics of volcanoes. This paper, focusing on the evolution of bubble size distribution, investigates the vesiculation behavior in ascending magmas with constant velocities. Taking into account homogeneous nucleation, growth by diffusion of volatile components, expansion by depressurization, and depletion of volatile components in a silicate melt by progressive vesiculation, the governing equations describing the vesiculation of magma and the evolution of bubble size distribution are formulated. The behavior of solution is controlled by three nondimensional parameters which represent the nucleation facility (related to the gas/silicate melt interfacial tension), the effective diffusivity (diffusivity divided by ascent velocity) of volatile components in a magma, and the initial saturation pressure. The governing equations are numerically solved for the limited range of variable parameters. Consequently, the bubble size distribution, the nucleation rate, and the volatile concentration in magma are obtained as functions of time (depth). The result provides the following qualitative understanding of the vesiculation process. The nucleation takes place localized in a narrow depth interval. The nucleation depth (pressure) where the nucleation rate reaches a maximum value increases with the nucleation facility and the effective diffusivity and almost linearly increases with the initial saturation pressure. The nucleation interval, the maximum nucleation rate, and the total number of bubbles nucleated decrease with the effective diffusivity. The volatile concentration in magma monotonically decreases with the progressive vesiculation, not by the nucleation of bubbles but by the growth of bubbles nucleated. The depletion factor (the ratio of the volatile concentration in magma at surface to the initial saturation) decreases with the nucleation facility and the effective diffusivity. The quantitative understanding is made by describing moments of the bubble size distribution function, the nucleation depth and interval, the maximum nucleation rate, and the depletion factor as functions of parameters representing an eruption. The results of numerical solutions are simply interpreted as the single nucleation event and the subsequent growth process using two independent quantities: the total number of bubbles per unit volume and the mean bubble radius. The results are also extrapolated to realistic values of parameters corresponding to the Plinian and sub‐Plinian eruptions. Under the condition of a constant depressurization and no interaction among bubbles, the total number of bubbles per unit volume is strongly reduced with increasing effective diffusivity, and bubbles grow according to the law in which the mean bubble radius is proportional to τ2/3, where τ represents the effective time of diffusion. These results suggest, through the silica content dependence of the diffusivity o...

[1] An analogue experiment using a starch-water mixture has been carried out in order to understand the effect of cooling rate on the morphological characteristics of a basalt columnar joint. If the contraction of material is essential for the formation of columnar joint structure, the water loss rate by desiccation (hereafter referred to as desiccation rate) in the experiment is analogous to the cooling rate in solidifying basalt. In the experiment the desiccation rate is controlled by varying the distance between the starch-water mixture and a lamp used as the heat source. We find that there are three regimes in the relation between joint formation and desiccation rate: (1) At desiccation rates higher than $1.4 Â 10 À2 (g cm À2 h À1 ) (normal columnar joint regime), the average crosssectional area S of a column is inversely proportional to the average desiccation rate, h. (2) Between that desiccation rate and a critical desiccation rate, 0.8 Â 10 À2 (g/cm 2 h), S approaches infinity as h _ M i decreases close to a critical desiccation rate (i.e., exponent d monotonically increases from unity to infinity) (critical regime). (3) Below the critical desiccation rate, no columnar structure forms (no columnar joint regime forms). Applying the present experimental result to the formation of basalt column, the basalt columnar cross-sectional area is inversely proportional to the cooling rate with factors including elasticity, crack growth coefficient, thermal expansion, glass transition temperature, and crack density ratio at stress maximum. Also, it can be predicted that there exists a critical cooling rate below which the columnar joint does not form; the presence of a critical regime between the normal columnar jointing and no columnar jointing during a certain cooling rate range can also be predicted. We find that at higher cooling rate the preferred column shape is a pentagon, whereas at lower cooling rate it is a hexagon.

The morphological stability criteria of melts in edge and corner regions in a partially molten system containing several solid phases (three) under textural equilibrium are proposed in terms of dihedral angles. Owing to the variety of edge and corner regions due to combination of the crystalline phases in the multi‐solid phase system, melts are morphologically stable in some types of edges and corners, and unstable in others. In order to apply the stability criteria to the partially molten regions in the upper mantle we conducted a partial melting experiment with a peridotite mainly composed of olivine (OL), orthopyroxene (OPX), and clinopyroxene (CPX) crystals at 1300°C, 1 GPa and for 300 hours. Various types of dihedral angles were measured on the run product which contained about 7% melt. The melt versus OL/OL dihedral angle was significantly smaller than other types of melt versus solid/solid dihedral angles. Applying the stability criteria to these experimental results, we predict that in the partially molten peridotite the melts are morphologically stable only in OL‐OL‐OL edge regions and in OL‐OL‐OL‐OL and OL‐OL‐OL‐OPX corner regions. The connectivity of the melt phase is determined by the melt distribution in the stable edge and corner regions at melt fractions less than 29%. The melt distribution can be modeled by the bond distribution in a lattice, that is, bond percolation. The connectivity of the melt phase is estimated as a function of the modal composition and grain size distribution of the matrix and is graphically presented as a connectivity diagram (OL‐OPX‐CPX modal composition diagram). The trajectory of modal composition of the solid matrix in the connectivity diagram determines the connectivity history of a rock during progressive partial melting in the upper mantle. Three different cases of connectivity history are discerned depending upon the modal composition before melting and are characterized by the critical melt fractions ϕmc, at which the melt phase suddenly becomes connecting, such as ϕmc = 0, 0 < ϕmc < 0.29, and ϕmc ≒ 0.29. In a peridotite the modal portion of olivine but also the relative grain size are the most important determinant of the connectivity behavior in the upper mantle.