• The Dynamics of Partially Molten Rock
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The Dynamics of Partially Molten Rock

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A valuable synthesis of the physics of magmatism for students and scholarsMagma genesis and segregation have shaped Earth since its formation more than 4.5 billion years ago. Now, for the first tim...
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  • Publication Date: 18 January 2022
  • ISBN: 9780691176567
  • Pages: 368
  • Imprint: Princeton University Press
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A valuable synthesis of the physics of magmatism for students and scholars

Magma genesis and segregation have shaped Earth since its formation more than 4.5 billion years ago. Now, for the first time, the mathematical theory describing the physics of magmatism is presented in a single volume. The Dynamics of Partially Molten Rock offers a detailed overview that emphasizes the fundamental physical insights gained through an analysis of simplified problems. This textbook brings together such topics as fluid dynamics, rock mechanics, thermodynamics and petrology, geochemical transport, plate tectonics, and numerical modeling. End-of-chapter exercises and solutions as well as online Python notebooks provide material for courses at the advanced undergraduate or graduate level.

This book focuses on the partial melting of Earth’s asthenosphere, but the theory presented is also more broadly relevant to natural systems where partial melting occurs, including ice sheets and the deep crust, mantle, and core of Earth and other planetary bodies, as well as to rock-deformation experiments conducted in the laboratory. For students and researchers aiming to understand and advance the cutting edge, the work serves as an entrée into the field and a convenient means to access the research literature. Notes in each chapter reference both classic papers that shaped the field and newer ones that point the way forward.

The Dynamics of Partially Molten Rock requires a working knowledge of fluid mechanics and calculus, and for some chapters, readers will benefit from prior exposure to thermodynamics and igneous petrology.

  • The first book to bring together in a unified way the theory for partially molten rocks
  • End-of-chapter exercises with solutions and an online supplement of Jupyter notebooks
  • Coverage of the mechanics, thermodynamics, and chemistry of magmatism, and their coupling in the context of plate tectonics and mantle convection
  • Notes at the end of each chapter highlight key papers for further reading
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Price: $99.95
Pages: 368
Publisher: Princeton University Press
Imprint: Princeton University Press
Publication Date: 18 January 2022
ISBN: 9780691176567
Format: Hardcover
Richard F. Katz is professor of geodynamics at the University of Oxford.
  • Preface
  • List of Symbols
  • CHAPTER 1 Introduction
    • 1.1 Motivation
    • 1.2 Basic Physical Considerations
    • 1.3 Research Questions and Applications
    • 1.4 About This Book
      • 1.4.1 Overview of the Organization and Content
      • 1.4.2 References to the Literature
      • 1.4.3 Mathematical Notation
    • 1.5 The Way Forward?
  • CHAPTER 2 A Condensed History of Magma/Mantle Dynamics
    • 2.1 Foundation
    • 2.2 Axial Age
    • 2.3 Exploration
    • 2.4 Generalization, Extension, and Future History
  • CHAPTER 3 A Review of One-Phase Mantle Dynamics
    • 3.1 Governing Equations
    • 3.2 Mantle Convection
    • 3.3 Kinematic Solutions for Corner Flow
    • 3.4 Literature Notes
    • 3.5 Exercises
  • CHAPTER 4 Conservation of Mass and Momentum
    • 4.1 The Representative Volume Element and Phase-Averaged Quantities
    • 4.2 Conservation of Mass
    • 4.3 Conservation of Momentum
      • 4.3.1 Stress and Pressure
      • 4.3.2 The Interphase Force
      • 4.3.3 Constitutive Equations in the Magma–Mantle Limit
    • 4.4 A Note about Disaggregation
    • 4.5 The Full Mechanical System, Assembled
    • 4.6 Special, Limiting Cases
      • 4.6.1 No Porosity, No Melting
      • 4.6.2 Partially Molten, Rigid Medium
      • 4.6.3 Constant, Uniform Solid Viscosity
    • 4.7 Literature Notes
    • 4.8 Exercises
  • CHAPTER 5 Material Properties
    • 5.1 Microstructure
      • 5.1.1 Grain-Size Change
      • 5.1.2 Textural Equilibration
    • 5.2 Permeability
    • 5.3 Viscosity
      • 5.3.1 Shear Viscosity of the Aggregate
      • 5.3.2 Compaction Viscosity of the Aggregate
      • 5.3.3 Shear Viscosity of the Liquid
    • 5.4 Thermodynamic Properties
      • 5.4.1 Density
      • 5.4.2 Solid–Liquid Phase Change
    • 5.5 Literature Notes
    • 5.6 Exercises
  • CHAPTER 6 Compaction and Its Inherent Length Scale
    • 6.1 The Compaction-Press Problem
    • 6.2 The Permeability-Step Problem
    • 6.3 Propagation of Small Porosity Disturbances
    • 6.4 Magmatic Solitary Waves
    • 6.5 Solitary-Wave Trains
    • 6.6 The Compaction Length in the Asthenosphere
    • 6.7 Literature Notes
    • 6.8 Exercises
  • CHAPTER 7 Porosity-Band Emergence under Deformation
    • 7.1 Governing Equations
    • 7.2 Linearized Governing Equations
    • 7.3 Viscosity
    • 7.4 The (In)Stability of Perturbations
      • 7.4.1 Pure Shear
      • 7.4.2 Simple Shear
    • 7.5 Wavelength Selection by Surface Tension
    • 7.6 Literature Notes
    • 7.7 Exercises
  • CHAPTER 8 Conservation of Energy
    • 8.1 The Internal-Energy Equation
    • 8.2 The Enthalpy Equation
    • 8.3 The Temperature Equation
    • 8.4 The Entropy Equation
    • 8.5 Boussinesq and Lithostatic Approximations
    • 8.6 Dissipation-Driven Melting and Compaction
    • 8.7 Decompression Melting
    • 8.8 Literature Notes
    • 8.9 Exercises
  • CHAPTER 9 Conservation of Chemical-Species Mass
    • 9.1 Thermodynamic Components
      • 9.1.1 Congruent Melting
      • 9.1.2 Incongruent Melting
    • 9.2 Trace Elements
      • 9.2.1 Equilibrium Transport Model
      • 9.2.2 Disequilibrium Transport Model
    • 9.3 Radiogenic Trace Elements and Their Decay Chains
    • 9.4 Closed-System Evolution of a Decay Chain
      • 9.4.1 Evolution with Melting Only
      • 9.4.2 Evolution due to Ingrowth Only
      • 9.4.3 Evolution by Both Melting and Ingrowth
    • 9.5 Literature Notes
    • 9.6 Exercises
  • CHAPTER 10 Petrological Thermodynamics of Liquid and Solid Phases
    • 10.1 The Equilibrium State
      • 10.1.1 Partition Coefficients from Ideal Solution Theory
      • 10.1.2 Computing the Equilibrium State
      • 10.1.3 Application to a Two-Pseudo-Component System
      • 10.1.4 Application to a Three-Pseudo-Component System
      • 10.1.5 Approaching the Eutectic Phase Diagram
      • 10.1.6 Linearizing the Two-Component Phase Diagram
      • 10.1.7 Degree of Melting
    • 10.2 Thermochemical Disequilibrium and the Rate of Interphase Mass Transfer
      • 10.2.1 Affinity as the Thermodynamic Force for Linear Kinetics
      • 10.2.2 Linearized Melting Rates
    • 10.3 Computing the Melting Rate at Equilibrium
    • 10.4 Remarks about Mantle Thermochemistry
    • 10.5 Literature Notes
    • 10.6 Exercises
  • CHAPTER 11 Melting Column Models
    • 11.1 Fluid Mechanics
    • 11.2 Melting-Rate Closures
      • 11.2.1 Prescribed Melting Rate
      • 11.2.2 Thermodynamically Consistent Melting Rate
    • 11.3 The Visco-Gravitational Boundary Layer
    • 11.4 The Decompaction Boundary Layer
    • 11.5 Isotopic Decay-Chain Disequilibria in a Melting Column
      • 11.5.1 Constant Transport Rates
      • 11.5.2 Variable Transport Rates
    • 11.6 Literature Notes
    • 11.7 Exercises
  • CHAPTER 12 Reactive Flow and the Emergence of Melt Channels
    • 12.1 Governing Equations
    • 12.2 The Melting-Rate Closure
    • 12.3 Problem Specification
    • 12.4 Scaling and Simplification
    • 12.5 Linearized Stability Analysis
      • 12.5.1 The Base State
      • 12.5.2 The Growth Rate of Perturbations
      • 12.5.3 The Large-Damköhler Number Limit
      • 12.5.4 A Modified Problem and Its Analytical Solution
    • 12.6 Physical Mechanisms
    • 12.7 Application to the Mantle
    • 12.8 Literature Notes
    • 12.9 Exercises
  • CHAPTER 13 Tectonic-Scale Models and Modeling Tools
    • 13.1 Governing Equations in the Small-Porosity Approximation
    • 13.2 Corner-Flow with Magmatic Segregation
    • 13.3 Melt Focusing through a Sublithospheric Channel
      • 13.3.1 Lateral Transport in Semi-Infinite Half-Space
      • 13.3.2 Lateral Transport to a Mid-Ocean Ridge
    • 13.4 Coupled Dynamics and Thermochemistry with the Enthalpy Method
    • 13.5 Literature Notes
    • 13.6 Exercises
  • CHAPTER 14 Numerical Modeling of Two-Phase Flow
    • 14.1 The One-Dimensional Solitary Wave (Instantaneous)
      • 14.1.1 Finite Difference Discretization
      • 14.1.2 Finite Element Discretization
    • 14.2 The One-Dimensional Solitary Wave (Time-Dependent)
    • 14.3 A Two-Dimensional Manufactured Solution (Instantaneous)
    • 14.4 Magmatic Solitary Waves as a Benchmark for Numerical Solutions
    • 14.5 Porosity Bands as a Benchmark for Numerical Solutions
    • 14.6 Literature Notes
    • 14.7 Exercises
  • CHAPTER 15 Solutions to Exercises
    • 15.1 Exercises from Chapter 3: One-Phase Mantle Dynamics
    • 15.2 Exercises from Chapter 4: Conservation of Mass and Momentum
    • 15.3 Exercises from Chapter 5: Material Properties
    • 15.4 Exercises from Chapter 6: Compaction and Its Inherent Length Scale
    • 15.5 Exercises from Chapter 7: Porosity-Band Emergence under Deformation
    • 15.6 Exercises from Chapter 8: Conservation of Energy
    • 15.7 Exercises from Chapter 9: Conservation of Chemical-Species Mass
    • 15.8 Exercises from Chapter 10: Petrological Thermodynamics of Liquid and Solid Phases
    • 15.9 Exercises from Chapter 11: Melting Column Models
    • 15.10 Exercises from Chapter 12: Reactive Flow and the Emergence of Melt Channels
    • 15.11 Exercises from Chapter 13: Tectonic-Scale Models
    • 15.12 Exercises from Chapter 14: Numerical Modeling of Two-Phase Flow
  • Bibliography
  • Index