Abstract
In previous chapters, we learned how simultaneous nucleation rate and growth rate of bubbles at instantaneous decompression are determined when temperature, pressure, and concentration of volatiles are obtained. However, to understand the entire image of the vesiculation process and vesicular texture observed in eruptive materials, such instantaneous nucleation rate and growth rate are insufficient. For this purpose, we should understand the history of the vesiculation process, i.e., the temporal development of bubble nucleation and growth processes because the fluid mechanical behavior of vesiculating magma and the vesicular texture of eruptive materials because of the nucleation rate and the growth rate temporally developed in response to temporally changing temperature, pressure, and volatile content in succession and from a mutual influence among each other. In this chapter, based on the assumption that pressure linearly decreases with time, a methodology to understand the temporal development of the vesiculation process will be explained. This helps understand the temporal development of the bubble size distribution function, and the result can be systematically understood using a small number of dimensionless controlling parameters. Moreover, the result will be applied to laboratory experiments to establish an empirical understanding of the vesiculation process.
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Notes
- 1.
The problem of numerical instability is mostly solved using cubic interpolation (CIP).
- 2.
Contribution of changing \(R_\mathrm{C}\) to the number density is ignored.
- 3.
Differentiation is the rate of change of y, or dy, when x is changed infinitesimally in a function \(y=f(x)\), while variation is the rate of change of a function f when f itself changes. In this case, the curve of bubble growth \(R(t^{\prime },t)\) itself changes because of change of nucleation time \(t^{\prime }\).
- 4.
Numerical calculation with systematically changed controlling parameters is called a parametric study.
- 5.
Equations that include exponential function and/or logarithmic function and are algebraically unsolvable.
- 6.
Note that the subject differs from that for the diffusion-limited regime and the viscosity-limited regime discussed in the sections on bubble growth.
- 7.
Note that second nucleation is different from second boiling.
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Toramaru, A. (2022). Temporal Development of Vesiculation. In: Vesiculation and Crystallization of Magma. Advances in Volcanology. Springer, Singapore. https://doi.org/10.1007/978-981-16-4209-8_5
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