Keywords:
Porous materials.
;
Electronic books.
Type of Medium:
Online Resource
Pages:
1 online resource (407 pages)
Edition:
1st ed.
ISBN:
9781118762059
URL:
https://ebookcentral.proquest.com/lib/geomar/detail.action?docID=5612952
Language:
English
Note:
Cover -- Half-Title page -- Dedication -- Title Page -- Copyright Page -- Contents -- List of Symbols -- Introduction -- I.1. Introduction -- Upscaling -- I.2. Organization of the text -- I.3. Objectives, contents, and readership -- Intended readership -- Brief guide to the topics of this book -- I.4. Acknowledgments -- 1. Fluids, Porous Media and REV: Basic Concepts -- 1.1. Geologic porous media: basic concepts -- 1.1.1. Porous soils -- 1.1.2. Porous rocks -- 1.1.3. Geologic porous media: examples -- 1.2. Porous media: basic concepts, porosity and specific area -- 1.2.1. Fluid phases -- 1.3. Single-phase flow and Darcy's law: basic concepts -- 1.3.1. Darcy's flux-gradient law -- 1.4. The Darcy-Buckingham law and the Richards equation: basic concepts of unsaturated flow -- 1.4.1. Remarks on unsaturated water flow -- 1.5. Capillarity and two-phase flow systems at different scales: basic concepts -- 1.5.1. Introduction -- 1.5.2. Capillarity pressure jump at different scales -- 1.5.3. Moving from one scale to another: upscaling -- 1.6. A basic approach to pore scale two-phase flow -- 1.7. A basic approach for continuum scale description of two-phase flow in porous media: the Darcy-Muskat model -- 1.7.1. The Buckey-Leverett model -- 1.8. Other issues: capillarity vs. gravity and viscosity, heterogeneity and upscaling -- 1.8.1. Capillarity plus gravity and viscous dissipation -- 1.8.2. Scales and the representative elementary volume -- 1.8.3. Objectives at various scales of analysis -- 1.8.4. Upscaling: first and second upscaling problems -- 2. Two-Phase Physics: Surface Tension, Interfaces, Capillary Liquid/Vapor Equilibria -- 2.1. Summary and objectives -- 2.2. Physics of capillarity and surface tension at equilibrium -- 2.2.1. Observations and practical applications of surface tension, capillary forces and contact angles.
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2.2.2. Interfacial tension: from molecular scale to fluid scale -- 2.2.3. Laplace-Young pressure jump law (capillary pressure) -- 2.2.4. Solid/liquid contact angle θ at equilibrium (Young) -- 2.2.5. Measurements of interfacial tension -- 2.2.6. Immiscibility versus miscibility at fluid interfaces (examples) -- 2.3. Dimensionless groups (characteristic forces, length scales, timescales) -- 2.3.1. Introduction: three forces driving multiphase systems -- 2.3.2. Reynolds and Reynolds-Darcy number, viscous dissipation -- 2.3.3. Capillary forces, surface tension and capillary number Ca -- 2.3.4. Gravitational buoyancy forces and the Bond number Bo -- 2.3.5. Dimensionless contrast ratios (viscosity and density contrasts) -- 2.3.6. Recap of dimensionless groups for a two-phase system -- 2.4. Thermodynamics, Gibbs energy, pressure, suction -- 2.4.1. Interpretation of large suctions, bonding forces and Gibbs energy -- 2.4.2. Thermodynamical systems (isolated or not) -- 2.4.3. Gibbs free energy, heat, work -- 2.5. Kelvin's liquid/vapor relation (suction vs. air humidity) -- 2.5.1. Introduction to Kelvin's law (applications in flow modelin) -- 2.5.2. Qualitative discussion of Kelvin's law (liquid/vapor relations) -- 2.5.3. Thermodynamical variables (pressure, air humidity, etc.) -- 2.5.4. Perfect gases (dry air and water vapor) -- 2.5.5. Kelvin's law: relative air humidity vs. capillary pressure -- 2.5.6. Extended discussion on liquid/vapor thermodynamics (review) -- 3. Capillary Equilibria in Pores, Tubes and Joints -- 3.1. Introduction and summary -- 3.2. Capillary equilibrium in a single tube or planar joint of constant diameter or aperture -- 3.2.1. Introduction: problem formulation and notations -- 3.2.2. Capillary tube: pressure jump (Laplace-Young) -- 3.2.3. Capillary tube: water height (Jurin).
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3.2.4. Capillary tube: extensions and examples (other fluids, etc.) -- 3.2.5. Example of water/air equilibrium in a capillary tube: calculation of water height for a tube of diameter 100 μm -- 3.2.6. Planar joint: introduction - planar geometry of the meniscus -- 3.2.7. Planar joint: pressure jump across the water/air meniscus -- 3.2.8. Planar joint: equilibrium height of meniscus (capillary rise) -- 3.2.9. Example: parameter values for water and "light oil" in a joint -- 3.3. Capillary equilibria in variable tubes and joints (a(x)) -- 3.3.1. Introduction, description of the problem, and hypotheses -- 3.3.2. Non-existence of two-phase equilibria, depending on initial state -- 3.3.3. Geometric correction for variable tubes/joints: wetting angle θ + ϕ(x) in a fixed frame -- 3.4. Capillary equilibrium in a random set of tubes: calculation of water retention curve θ(ψ) -- 3.4.1. Introduction and summary -- 3.4.2. Capillary water/air equilibrium in a random set of "pores" -- moisture retention curve θ(pC) for uniformly distributed radii -- 3.4.3. Capillary water/air equilibrium and moisture retention curve θ(pc) for Pareto distributed radii with exponent ω = 2 -- 3.4.4. Limitations of the Boolean model of random tubes -- 3.4.5. Soil water retention curves in hydro-agriculture (overview) -- 3.5. Capillary equilibrium of soap films: minimal area surfaces and Euler-Lagrange equations -- 3.5.1. Introduction and summary -- 3.5.2. Soap film surface (preliminary formulation) -- 3.5.3. Euler-Lagrange equations for minimizing integrals -- 3.5.4. Euler-Lagrange equation minimizing the area -- 3.6. Case study of soap film equilibrium between two circular rings: minimal area surface (catenoid) -- 3.6.1. Presentation of the case study: soap film between two rings -- 3.6.2. Formulation: minimal area surface between two coaxial circles.
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3.6.3. Expressing Euler-Lagrange for the generating curve Y(x) -- 3.6.4. Solution of Euler-Lagrange equations: catenoid surface between two coaxial circles of different diameters -- 3.6.5. A special solution of the Euler-Lagrange equations: the catenoid surface between two identical coaxial rings -- 3.6.6. Parametric study and conclusions (existence/unicity of the soap film depending on ring geometry) -- 3.7. Additional topic: the equilibrium depth of a bubble -- 4. Pore-Scale Capillary Flows (Tubes, Joints) -- 4.1. Introduction and summary: pore-scale flow in capillary tubes and planar joints (steady and transient) -- 4.1.1. Introduction and summary -- 4.1.2. Case of steady flow systems (single phase and two phase) -- 4.1.3. Remark on the quasi-static nature of the water retention curve -- 4.1.4. Case of transient flow problems -- 4.1.5. Numerical experiment (2D visco-capillary invasion) -- 4.2. Single-phase steady flow in tubes: Poiseuille, Darcy, Kozeny-Carman permeability -- 4.2.1. Overview: Stokes, Poiseuille, Specific Area, Darcy, Kozeny permeability -- 4.2.2. Specific area concept -- 4.2.3. Poiseuille flow in a cylindrical tube or a planar joint -- 4.2.4. Kozeny-Carman permeability for single-phase flow (from Poiseuille to Darcy) -- 4.3. Unsaturated and two-phase steady flow in sets of planar joints: equivalent mesoscale quantities (porosity φ, permeability k, capillary length λcap) -- 4.3.1. Summary and overview -- 4.3.2. Upscaling unsaturated flow through a set of joints (equivalent permeability, porosity, and capillary length) -- 4.3.3. Upscaling two-phase flow in smooth or rough statistical joints: water retention θ(pc) -- conductivity curves {KW(pc), KNW(pc)} -- 4.3.4. Unsaturated or two-phase constitutive curves from statistical pore-scale models (discussion, review).
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4.4. Transient two-phase visco-capillary dynamics: interface motion X(t) in axially uniform or variable tubes/joints -- 4.4.1. Introduction, objectives, and literature review -- 4.4.2. Eulerian/Lagrangian equations for transient two-phase flow: axial interface displacement in tubes and joints -- 4.4.3. Quasi-analytical results on transient dynamics of immiscible fluids: axial displacement in variably constricted tubes and joints -- 4.4.4. Geometrical correction on interface dynamics X(t) in the case of very rough, highly variable tubes or joints (remarks) -- 4.4.5. Interface dynamics X(t) in tubes, pores, joints (prospects) -- 4.5. Two-dimensional two-phase dynamics: transient drainage in a planar joint with randomly variable aperture field a(x,y) -- 4.5.1. Introduction and summary -- 4.5.2. The 2D "rough fracture" and its random aperture field a(x,y) -- 4.5.3. The 2D synthetic drainage experiment (two-phase flow) -- 4.6. Other transient capillary phenomena in fluid dynamics: waves, bubbles, etc. (brief indications) -- 4.6.1. Capillary waves -- 4.6.2. Rayleigh-Plateau instability -- 4.6.3. Bubble dynamics and cavitation -- 4.6.4. Liquid/vapor phase changes, boiling, bubbles in porous media -- 5. Darcy-Scale Capillary Flows in Heterogeneous or Statistical Continua (Richards and Muskat) -- 5.1. Introduction, objectives and applications -- 5.1.1. Introduction and summary -- 5.1.2. Flow regimes and potential applications -- 5.1.3. Hierarchy of scales and related issues (discontinuities) -- 5.1.4. Material discontinuities in Darcy-scale flows -- 5.2. Concepts: porous media, Darcy scale and REV (revisited) -- 5.3. Single-phase Darcy-scale continuum flow equations (Navier-Stokes, Poiseuille, Darcy) -- 5.3.1. Introduction and summary -- 5.3.2. Darcy's law: from Navier-Stokes to Darcy in a nutshell.
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5.3.3. Darcy's law for isotropic media (scalar permeability, single phase flow).
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