Vesiculation and Crystallization of Magma: Fundamentals of the Volcanic Eruption Process

Preface for English Version
Preface
Contents
Notations
1 Inspired by Nature
	1.1 1986 Izu-Oshima Eruption
		1.1.1 Changes in Eruption Styles
		1.1.2 Bubbles and Crystals
	1.2 Pumice and Plinian Eruption
		1.2.1 Eruption Emitting Pumice or Scoria
		1.2.2 Towada Volcano
		1.2.3 Widespread Volcanic Ash
		1.2.4 Reticulite: The Ultimate Pumice
		1.2.5 Volcanic Eruptions as Global Phenomena
		1.2.6 Variety and Unified Classification of Explosive Eruptions
	1.3 Lava Dome and Pyroclastic Flow
		1.3.1 Eruptions that Do Not Produce Pumice or Scoria: Non-explosive Eruptions
		1.3.2 Heisei Eruption of Unzen Volcano
		1.3.3 Temporal Change of Discharge Rate
		1.3.4 Block-and-Ash Flow
		1.3.5 Interior of Pyroclastic Particles
		1.3.6 Microlite
	1.4 Crystallization and Vesiculation of Magma that Cooled down and Solidified
		1.4.1 Dike as a Place for Cooling Crystallization Experiment in Nature
		1.4.2 Vesiculation in Dikes
		1.4.3 Magma Vesiculation as a Driving Force for Volcanic Explosions
	References
2 Conditions for Magma Vesiculation
	2.1 Significance of Equilibrium Theory
	2.2 Solubility of Gas Components in Liquid and Henry's Law
	2.3 Dissolution Reaction of Water in Silicate Melt
	2.4 Change of Solubility with Pressure: Burnham's Model
	2.5 Solubility When Bubbles and Liquid Have Different Pressure
		2.5.1 General Case Where Bubbles and Liquid Are Not in Mechanical Equilibrium
		2.5.2 Case Where Bubbles and Liquid Are in Dynamic Equilibrium
	2.6 Pressure Dependence of Solubility of Water in the Case of Incomplete Dissociation
	2.7 Change in Solubility by Temperature
	2.8 The Influence of Water on Melting Points of Crystals  and Decompression-Vesiculation Induced Crystallization
	2.9 Concentration of Volatiles and Vesiculation Caused by Cooling Crystallization
	2.10 A System Containing Carbon Dioxide
		2.10.1 Solubility of Carbon Dioxide
		2.10.2 Solubility in a System Containing Water and Carbon Dioxide
		2.10.3 Gas Composition Change with Progress of Vesiculation Relationship Among Total Pressure, Partial Pressure, and Solubility
		2.10.4 Gas Composition and Change of Pressure with Addition of Carbon Dioxide-Rich Fluid
	References
3 Mechanism of Bubble Formation
	3.1 Energetics of Bubble Nucleation
		3.1.1 Thermodynamics of Fluctuations
		3.1.2 Energy of Bubble Generation
	3.2 Homogeneous Nucleation
	3.3 Kinetics of Bubble Nucleation
		3.3.1 Master Equation
		3.3.2 Fokker-Planck Equation for Bubble (Cluster) Size Distribution
		3.3.3 Equilibrium Distribution
		3.3.4 Derivation of the Steady State Nucleation Rate
		3.3.5 Steady State Size Distribution
	3.4 Heterogeneous Nucleation
	3.5 Non-steady State Nucleation Rate
	3.6 Various Kinds of Correction for Classical Nucleation Theory
		3.6.1 Tolman Correction
		3.6.2 Poynting Correction
		3.6.3 Viscosity Correction
	References
4 Growth and Expansion of Bubbles
	4.1 Outline of Calculation of Bubble Growth and Expansion
	4.2 Equilibrium Concentration at the Bubble Surface
		4.2.1 General Expression
		4.2.2 Equilibrium Concentration in the Mechanical Equilibrium
		4.2.3 Expression Using the Critical Radius
	4.3 Steady-State Diffusion-Limited Growth
		4.3.1 Case Not Including the Advection Term
		4.3.2 Case Including the Advection Term
	4.4 Non-steady State Diffusion Growth
	4.5 Bubble Expansion Under Mechanical Equilibrium
		4.5.1 Adiabatic Expansion Versus Isothermal Expansion and the Influence of Latent Heat
		4.5.2 Expansion Rate of Bubbles as a Function of the Bubble Radius
	4.6 An Equation Describing Change in the Bubble Radius in a Viscous Fluid: The Rayleigh-Plesset Equation
	4.7 Time Change of Bubble Expansion: Inertial Expansion
		4.7.1 Bubble Expansion in Inviscid Liquid
		4.7.2 The Case Where the Pressure in Bubbles is Constant: Simple Inertial Expansion
	4.8 The Influence of Viscosity on Bubble Expansion: Viscosity-Limited Expansion
		4.8.1 The Case Where Pressure in Bubbles and Overpressure in Bubbles  are Constant
		4.8.2 Expansion Under Constant Amount of Decompression
		4.8.3 The Case of Decompression at a Constant Rate
		4.8.4 Bubble Growth Calculation with a Combination of Diffusion and Viscosity
	4.9 Outline of Bubble Growth and Experimental Results
		4.9.1 Characteristic Timescale in Bubble Growth
		4.9.2 Dimensionless Parameters Controlling Bubble Growth
		4.9.3 Comparison with Experiments
	4.10 Extension of the Rayleigh-Plesset Equation
		4.10.1 Extension to Viscoelastic Liquid
		4.10.2 Extension to Multi-bubbles: A Cell Model
	References
5 Temporal Development of Vesiculation
	5.1 Overall Scheme
	5.2 Temporal Development of Vesiculation Using the Eulerian Approach
		5.2.1 Partial Differential Equation Representing the Conservation of the Number  of Bubbles
		5.2.2 Derivation of a Moment Equation
	5.3 Temporal Development of Vesiculation Using the Lagrangian Approach
	5.4 Controlling Parameters in Decompression-Induced Vesiculation
	5.5 Temporal Development of Vesiculation Under the Condition of Constant Decompression Rate
		5.5.1 Decompression Rate
		5.5.2 Solution by Moment Equations Based on Eulerian Description
		5.5.3 Solution by Lagrangian Description
		5.5.4 Bubble Growth as a Factor Determining BND
	5.6 Temporal Development of Vesiculation Process Under the Condition  of a Constant Amount of Decompression
		5.6.1 Outline of Nucleation and Growth
		5.6.2 Maximum Nucleation Rate
		5.6.3 Bubble Number Density
		5.6.4 The Rate of Decrease in Water Concentration in Melt
	5.7 Vesiculation Experiments
		5.7.1 Experiment Under Constant Decompression Rates
		5.7.2 Experiment Under Constant Amount of Decompression
	5.8 The Limits of Homogeneous Nucleation
	5.9 Second Nucleation
	References
6 Other Bubble-Related Processes
	6.1 Secondary Growth of Bubbles: Ostwald Ripening
		6.1.1 Mechanism of Secondary Growth
		6.1.2 Solution of the Size Distribution by Lifshitz and Slyozov (The LS Theory)
		6.1.3 Qualitative Understanding of the Growth Law
		6.1.4 Comparison with Experiments
	6.2 Deformation of Bubbles
		6.2.1 Theoretical Study
		6.2.2 Experimental Study
	6.3 Coalescence of Bubbles
		6.3.1 Coalescence Frequency
		6.3.2 Shortening Process of Interbubble Distance: An Elemental Process  of Coalescence
		6.3.3 Shape Relaxation of Bubbles
		6.3.4 Temporal Development of Size Distribution in the Case Where the Initial Size Distribution Is Monodisperse
		6.3.5 Analysis by Continuous Size Distribution
		6.3.6 Comparison with Experiments
	6.4 Development of Gas Permeability
		6.4.1 Importance of Gas Permeability
		6.4.2 Bubble Connection in an Isotropic Field Without Flow
		6.4.3 Bubble Connection in Shear Flow
	6.5 Detachment and Ascending of Bubbles
		6.5.1 Detachment of Bubbles
		6.5.2 Bubble Ascent
		6.5.3 Bubble Ascent and Advective Overpressure
	6.6 Bubble Shrinkage
		6.6.1 Rayleigh Collapse
		6.6.2 The Influence of Gas in Bubbles on Bubble Shrinkage
	6.7 Bubble Oscillation
		6.7.1 The Case Where the Amount of Gas in a Bubble Is Constant
		6.7.2 Linear Analysis of the Rayleigh-Plesset Equation
	6.8 Influence of Viscoelasticity of Liquid on Collapse and Oscillation  of Bubbles
	References
7 Cooling Crystallization of Magma
	7.1 Thermodynamics of Cooling Crystallization
		7.1.1 Melting Points of Crystals and Equilibrium Phase Diagrams
		7.1.2 Thermodynamic Discussion of Crystal Nuclei and Gibbs-Thomson Relation
	7.2 Classical Understanding of Igneous Rock Texture Using Nucleation Rate  and Growth Rate
	7.3 Nucleation of Crystals
		7.3.1 Basic Characteristics of Homogeneous Nucleation
		7.3.2 Comparison with Nucleation Experiments
	7.4 Diffusion-Limited Growth
		7.4.1 Steady-State Diffusion Growth of Spherical Crystals
		7.4.2 Non-steady State Diffusion Growth on the Plane Crystal Face
	7.5 Reaction-Limited Growth
		7.5.1 Theoretical Consideration
		7.5.2 Comparison with Experiments
		7.5.3 Balanced Growth Between Diffusion and Reaction
	7.6 Temporal Development of the Crystallization Process: Crystallization  of a Binary Eutectic System
		7.6.1 Scaling and Controlling Parameters
		7.6.2 Basic Behavior of the Crystallization Process Under Constant Heat Loss
		7.6.3 Crystallization Parameters Characterizing Crystallization Process
		7.6.4 Relationship Between the Cooling Rate Dependence of the Crystal Number Density and the Crystal Growth Law
		7.6.5 Comparison with Laboratory Experiments
		7.6.6 Experiments in Nature
		7.6.7 Summary of Factors Controlling the Crystal Number Density
	7.7 Chemical Composition of Crystals
		7.7.1 The Solid-Liquid Equilibrium and Disequilibrium in Binary Solid Solution  and Chemical Composition of Crystals
		7.7.2 Relationship Between the Growth Law and Zoning Structure
		7.7.3 Diffusion Profile Taking the Moving Interface into Consideration  and Chemical Composition of Crystals
	References
8 Crystallization Induced by Vesiculation
	8.1 Similarity and Difference Between Decompression-Induced Crystallization and Cooling Crystallization
		8.1.1 Phase Equilibrium Relation
		8.1.2 The Degree of Supercooling in Decompression-Induced Crystallization
	8.2 Crystallization in the Equilibrium Vesiculation Regime
		8.2.1 Thermodynamic Factors in the Equilibrium Vesiculation Regime
		8.2.2 Crystal Number Density in Equilibrium Vesiculation Regime
		8.2.3 MND Water Exsolution Rate Meter and Decompression Rate Meter
	8.3 Crystallization in the Disequilibrium Vesiculation Regime
		8.3.1 Thermodynamic Factor in the Disequilibrium Vesiculation Regime
		8.3.2 Water Exsolution Rate in the Disequilibrium Vesiculation Regime
		8.3.3 The Crystal Number Density in the Disequilibrium Vesiculation Regime
	8.4 Calculation Combining the Vesiculation Process and the Crystallization Process
		8.4.1 Problems of the Simplified Model
		8.4.2 The Case Where Homogeneous Nucleation of Bubbles and Crystals Occurs
		8.4.3 The Case Where Heterogeneous Nucleation of Bubbles and Crystals Occurs
	8.5 Comparison with Decompression-Induced Crystallization Experiments
		8.5.1 Brief Summary of Experimental Studies
		8.5.2 SDE
		8.5.3 MDE and CDE
	8.6 Complexity of Crystal Growth
	References
9 CSD (Crystal Size Distribution)
	9.1 The Background of CSD Introduction in Rock Texture and the Current State of Research
		9.1.1 Background of CSD Introduction
		9.1.2 Attaching Physical Significance to Exponential CSD
		9.1.3 Perographic Studies of CSD
		9.1.4 Problems in CSD Studies and Establishment of Calculation Methods of CSD
	9.2 Analytical Solution of CSD Based on an Eulerian Description
		9.2.1 Solution by Separation of Variables: A General Solution and Examples  of Formation of Exponential Distribution
		9.2.2 A General Solution in the Case Where the Growth Rate Depends only on Time
		9.2.3 A General Solution in the Case Where Growth Rate Depends only on the Size
	9.3 Analytic Solution of CSD Based on a Lagrangian Description
		9.3.1 Method
		9.3.2 Case 1: J=J0 exp( t/tJ) and G=G1= Constant; Exponential Distribution
		9.3.3 Case 2: J=J0 exp(t/ tJ) and Diffusion Growth
		9.3.4 Case 3: J=J0 exp(t/tJ) and G=G0 exp(t/tG)
		9.3.5 Case 4: The Nucleation Rate and the Crystallization Rate Are Constant; Exponential Distribution
	9.4 Comparison with Experiments
		9.4.1 Experimental Studies on CSD
		9.4.2 Application of a Closed-System CSD to Experiments
	9.5 Open-System CSD
		9.5.1 Exponential Distribution as a Steady-State Solution: In the Case Where the Extraction Rate Is Constant
		9.5.2 Non-steady State Solution
	9.6 Avrami Model and Size Distribution
	References
10 Exploring Eruptive Phenomena from  Vesiculation and Crystallization
	10.1 Mode of Occurrence of Eruptive Products and Rock Texture
		10.1.1 Geological Occurrence
		10.1.2 Convenient Classification of Bubbles and Crystals
	10.2 Pumice and Scoria (Highly Vesicular Volcanic Rock) Erupted from Plinian Eruptions
		10.2.1 Characteristics of Bubble Texture
		10.2.2 Matrix-Bubble
		10.2.3 Pheno-Bubble
		10.2.4 Vesicularity
	10.3 Microlite Crystalline Texture of Plinian or Subplinian Eruptions
		10.3.1 Characteristics of Crystalline Texture
		10.3.2 Crystal Number Density, Water Exsolution Rate, Decompression Rate, and Ascent Velocity: Application of MND Water Exsolution Rate Meter
		10.3.3 Relationship with Shift of Eruption Style
		10.3.4 Relationship Between the Crystal Number Density and the Crystallinity
		10.3.5 Chemical Composition of Microlite Emitted from the 2011 Subplinian Eruption of Shinmoedake
	10.4 Volcanic Ash Emitted from Vulcanian Eruptions
		10.4.1 Characteristics of Vulcanian Eruptions
		10.4.2 Vulcanian Eruptions at Sakurajima Volcano and Characteristics of Its Volcanic Ash
		10.4.3 Relationship Between Crystal Texture and Surface Phenomena
	10.5 Microlite Texture in Lava Domes
		10.5.1 A Lava Dome of the Heisei Eruption of Unzen
		10.5.2 Controlling Factors Dividing Explosive Eruptions and Nonexplosive Eruptions
	10.6 Bubbles and Crystalline Texture in Rhyolite Lava
		10.6.1 Rhyolite Lava
		10.6.2 Deformation Index of Bubbles
		10.6.3 Crystalline Texture of Rhyolite Lava
	10.7 Phenocryst Texture of Lava Flow
		10.7.1 Porphyritic Texture: Phenocrysts and Groundmass
		10.7.2 Lava of Sakurajima Volcano in Historical Times
		10.7.3 CSD of Phenocrysts
		10.7.4 Interpretation of Phenocryst CSD
		10.7.5 Growth Rate and Magma Supply Rate in Open-System CSD
		10.7.6 Possibility of Long-Term Prediction Using Phenocryst CSD
	10.8 Rock Texture of Intrusions
		10.8.1 Difference in Characteristics of Structure and Texture Based on the Size  of Intrusive Body
		10.8.2 Spatial Change in the Crystal Number Density of Groundmass in Narrow Dikes
		10.8.3 Spatial Variation of Groundmass Textures, Focusing on the Mutual Relationship Between Plagioclase and Pyroxene
	References
11 Appendix
	11.1 Thermodynamic Potential
	11.2 Summary of an Equilibrium Phase Diagram of a Water-Bearing System
	11.3 Derivation of the Fokker-Planck Equation
		11.3.1 Derivation of an Equation in Terms of the Number of Molecules as Size, l
		11.3.2 Transformation from N(l,t) to F(R,t)
	11.4 FE0  of Equilibrium Size Distribution
	11.5 Integration to Obtain Steady-State Nucleation Rate
	11.6 Physical Properties of Silicate Melt
		11.6.1 Surface Tension
		11.6.2 Diffusivity of Water in Silicate Melts
		11.6.3 Newtonian Viscosity
	11.7 A Constitutive Equation of a Viscoelastic Body
	11.8 Cooling of Dikes, Sills, and Lava
		11.8.1 The Case Where Latent Heat of Crystallization is Not Taken into Consideration
		11.8.2 The Case Where Latent Heat of Crystallization is Considered (Stefan Problem)
		11.8.3 Comparison of the Relationship Between the Cooling Rate and the Distance
	11.9 The Basis of a 2D Textural Analysis
		11.9.1 Introduction
		11.9.2 Basic Measured Quantities
		11.9.3 Determination of the Bubble/Crystal Number Density
		11.9.4 Determination of langleRArangle
	References
488871_1_En_1_PartFrontmatter_OnlinePDF.pdf
	Part I Introduction
488871_1_En_2_PartFrontmatter_OnlinePDF.pdf
	Part II Vesiculation of Magma
488871_1_En_3_PartFrontmatter_OnlinePDF.pdf
	Part III Crystallization of Magma
488871_1_En_4_PartFrontmatter_OnlinePDF.pdf
	Part IV Application
488871_1_En_BookBackmatter_OnlinePDF.pdf
	Index
	Index