A theoretical model for fragmentation of viscous bubbly magmas in shock tubes
A theoretical model for fragmentation of viscous bubbly magmas in shock tubes
复制标题
DOI：
10.1029/2004jb003513
复制
发表时间：
2005-10-07
影响因子：
3.9
通讯作者：
Mitani, NK
中科院分区：
文献类型：
--
作者：
Koyaguchi, T;Mitani, NK
为了研究激波管内粘性气泡岩浆的破碎机制，建立了一维时变可压缩流动与气泡膨胀的耦合模型。最初，高压下的气泡岩浆在大气压力下通过隔膜与空气分离。当隔膜破裂时，冲击波传播到空气中，稀薄波传播到气泡岩浆中。结果，气泡岩浆被减压并膨胀。应用胞体模型计算了膨胀气泡周围的气体超压和环向应力。假设当环向应力或气体体积分数达到一定阈值时，岩浆碎片和岩浆流动由气泡流动转变为气体-火山碎屑弥散。可识别出两种破碎机制：(1)高粘度岩浆在环向应力达到熔体抗拉强度时破碎（应力破碎）；(2)低粘度岩浆环向应力不增大，气泡膨胀后，气体体积分数达到一定阈值时发生破碎（膨胀破碎）。在应力破碎过程中，在破碎面后面形成一个陡峭的压力梯度带，并与破碎面一起传播到岩浆中。分析认为，自持续应力破碎过程可以用气泡流区行波型解和气-火山碎屑流区自相似解的组合来描述。在这些解的基础上，导出了一些预测破碎速度（破碎面向下传播的速度）的简单公式。该公式应用于激波管技术的最新实验结果以及自然界中的火山爆炸。
[1] A coupled model for one-dimensional time-dependent compressible flow and bubble expansion is developed to investigate fragmentation mechanisms of viscous bubbly magmas in shock tubes. Initially a bubbly magma at a high pressure is separated from air at the atmospheric pressure by a diaphragm. As the diaphragm is ruptured, a shock wave propagates into the air, and a rarefaction wave propagates into the bubbly magma. As a result, the bubbly magma is decompressed and expands. Gas overpressure and hoop stress around expanding bubbles are calculated by applying the cell model. It is assumed that the magma fragments and the flow changes from bubbly flow to gas-pyroclast dispersion when the hoop stress or the gas volume fraction reaches a given threshold. Two types of fragmentation mechanisms are recognized: ( 1) high-viscosity magma fragments as the hoop stress reaches the tensile strength of the melt ( stress fragmentation) and ( 2) the hoop stress does not grow in low-viscosity magma so that fragmentation occurs after bubble expansion when the gas volume fraction reaches a threshold ( expansion fragmentation). During stress fragmentation a zone of steep pressure gradient forms just behind the fragmentation surface, which propagates into the magma together with the fragmentation surface. Analytical considerations suggest that the self-sustained stress fragmentation process can be described by a combination of a traveling- wave-type solution in the bubbly flow region and a self-similar solution in the gas-pyroclast flow region. Some simple formulae to predict the fragmentation speed ( downward propagation velocity of the fragmentation surface) are derived on the basis of these solutions. The formulae are applied to recent experimental results using shock tube techniques as well as Vulcanian explosions in nature.