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Microhydrodynamics, Brownian Motion, and Complex Fluids [Kietas viršelis]

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(University of Wisconsin, Madison)
  • Formatas: Hardback, 278 pages, aukštis x plotis x storis: 253x178x20 mm, weight: 650 g, Worked examples or Exercises; 57 Line drawings, black and white
  • Serija: Cambridge Texts in Applied Mathematics
  • Išleidimo metai: 13-Sep-2018
  • Leidėjas: Cambridge University Press
  • ISBN-10: 1107024641
  • ISBN-13: 9781107024649
Kitos knygos pagal šią temą:
Microhydrodynamics, Brownian Motion, and Complex FluidsDidesnis paveikslėlis
  • Formatas: Hardback, 278 pages, aukštis x plotis x storis: 253x178x20 mm, weight: 650 g, Worked examples or Exercises; 57 Line drawings, black and white
  • Serija: Cambridge Texts in Applied Mathematics
  • Išleidimo metai: 13-Sep-2018
  • Leidėjas: Cambridge University Press
  • ISBN-10: 1107024641
  • ISBN-13: 9781107024649
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9781107024649.html
Raktažodžiai:
This is an introduction to the dynamics of fluids at small scales, the physical and mathematical underpinnings of Brownian motion, and the application of these subjects to the dynamics and flow of complex fluids such as colloidal suspensions and polymer solutions. It brings together continuum mechanics, statistical mechanics, polymer and colloid science, and various branches of applied mathematics, in a self-contained and integrated treatment that provides a foundation for understanding complex fluids, with a strong emphasis on fluid dynamics. Students and researchers will find that this book is extensively cross-referenced to illustrate connections between different aspects of the field. Its focus on fundamental principles and theoretical approaches provides the necessary groundwork for research in the dynamics of flowing complex fluids.

Daugiau informacijos

Provides a foundation for understanding complex fluids by integrating fluid dynamics, statistical physics, and polymer and colloid science.
Preface xi
1 Kinematics, Balance Equations, and Principles of Stokes Flow
1(25)
1.1 Kinematics of Continua
1(8)
1.1.1 Velocity Fields and the Velocity Gradient
1(5)
1.1.2 Deformation Tensors
6(3)
1.2 Conservation Equations
9(6)
1.2.1 Conservation of Mass
9(1)
1.2.2 Conservation of Momentum
10(4)
1.2.3 Boundary Conditions
14(1)
1.3 General Properties of Stokes Flow
15(11)
1.3.1 Linearity and Reversibility
15(3)
1.3.2 Stress Equilibrium
18(1)
1.3.3 Lorentz Reciprocal Relations
19(1)
1.3.4 Mechanical Energy Balance and the Minimum Dissipation Principle
20(6)
2 Fundamental Solutions of the Stokes Equation and the Point-Particle Approximation
26(29)
2.1 Free-Space Green's Function: The Stokeslet
26(3)
2.2 Point Source and Point Source Dipole
29(2)
2.3 Force Dipole Solutions: Stresslet and Rotlet
31(3)
2.4 Multipole Expansion and Average Stress in a Suspension
34(4)
2.5 Stokes's Law, Hydrodynamic Interactions, and the Mobility of a System of Point Particles
38(4)
2.6 Regularized Stokeslets
42(2)
2.7 Periodic Array of Point Forces
44(6)
2.8 Flow in a Porous Medium and Hydrodynamic Screening
50(5)
3 Beyond Point Particles
55(35)
3.1 General Solution to the Stokes Equation
55(2)
3.2 The Stokeslet Revisited
57(2)
3.3 Spheres in Flow
59(5)
3.3.1 Translating Sphere
59(1)
3.3.2 Rotating Sphere
60(2)
3.3.3 Sphere in a General Linear Row and the Stress in a Dilute Suspension
62(2)
3.4 A Model Microscale Swimmer
64(2)
3.5 Faxen's Laws
66(3)
3.6 Mobility of a System of Spheres
69(1)
3.7 Nonspherical Rigid Particles
69(5)
3.8 Rodlike Particle in a Linear Flow and Jeffery Orbits
74(3)
3.9 Slender Body Theory
77(4)
3.10 Lubrication Theory
81(4)
3.11 Stokesian Dynamics
85(5)
4 Fundamental Solutions for Bounded Geometries
90(14)
4.1 General Reciprocity Result for the Green's Function
90(1)
4.2 Point Force above a Plane Wall
91(3)
4.3 Mobility of Point Particles in a Confined Geometry
94(1)
4.4 Hydrodynamic Migration of Particles in a Confined Geometry
95(2)
4.5 Point Force in Slit and Tube Geometries: Key Features
97(1)
4.6 Integral Representation of Stokes Flow and the Boundary Integral Method
98(6)
5 First Effects of Inertia
104(10)
5.1 Unbounded Uniform Flow around a Sphere at Small but Nonzero Reynolds Number
104(3)
5.2 Flow Near a Moving Wall: Transient Acceleration and Viscous Diffusion
107(2)
5.3 Corrections to Stokes Drag for an Accelerating Sphere
109(1)
5.4 Inertial Migration of a Sphere in Confined Flow
110(1)
5.5 Steady Streaming Due to Oscillatory Boundary Motion
111(3)
6 Thermal Fluctuations and Brownian Motion
114(25)
6.1 Brownian Motion of a Particle in Fluid: The Langevin Equation
114(3)
6.2 Velocity Autocorrelation Function and Properties of the Fluctuating Force
117(3)
6.3 Thermal Fluctuations and the Navier-Stokes Equation
120(4)
6.4 Brownian Motion from Fluctuating Hydrodynamics
124(2)
6.5 Diffusion and Osmotic Stress
126(2)
6.6 Diffusion and the Velocity Autocorrelation: The Taylor-Green-Kubo Formula for Diffusion
128(1)
6.7 Time-Integration of the Inertialess Langevin Equation: "Basic Brownian Dynamics"
129(3)
6.8 Generalized Langevin Equations and Memory
132(1)
6.9 Brownian Fluctuations as a Thermodynamic Driving Force: The Smoluchowski Equation
133(6)
7 Stochastic Differential Equations
139(31)
7.1 The Diffusion Equation and the Wiener Process
139(4)
7.2 Elementary Stochastic Calculus
143(4)
7.3 Time Evolution of the Probability Density for a Stochastic Differential Equation
147(2)
7.4 The Langevin Equation Revisited
149(7)
7.4.1 Inertial Dynamics
149(2)
7.4.2 From Inertial to Inertialess: The High Friction Limit
151(5)
7.5 Coordinate Transformations and Constraints
156(5)
7.5.1 Diffusion on a Plane in Cartesian and Polar Coordinate Systems
156(2)
7.5.2 Stochastic Processes with Constraints: Diffusion on a Circle or Sphere
158(3)
7.6 Rotational Diffusion and the Wormlike Random Walk
161(5)
7.7 Coupled Rotational and Translational Diffusion
166(4)
8 Coarse-Grained Models of Polymers in Dilute Solution
170(31)
8.1 Models of Equilibrium Polymer Structure
170(5)
8.1.1 Wormlike Chain
171(2)
8.1.2 Freely Jointed Chain and Gaussian Chain
173(2)
8.2 Bead-Spring Chain
175(4)
8.3 Diffusivity of a Polymer Chain in Solution
179(4)
8.4 Equilibrium Dynamics of Internal Degrees of Freedom: The Relaxation Spectrum
183(3)
8.5 Polymer Contribution to the Stress Tensor
186(2)
8.6 Bead-Spring Dumbbell Model
188(5)
8.7 Rigid Rod Model
193(8)
9 Rheology and Viscoelastic Flow Phenomena
201(36)
9.1 Fundamentals of Linear Viscoelasticity
201(10)
9.1.1 The Relaxation Modulus and the Weissenberg Number
201(3)
9.1.2 Frequency Response of a Viscoelastic Material
204(7)
9.2 Brownian Motion in a Viscoelastic Fluid: Linear Microrheology
211(5)
9.3 Nonlinear Viscoelasticity: Shear and Extensional Flows
216(11)
9.3.1 Simple Shear Flow: Normal Stress Differences and Cross-stream Migration
216(2)
9.3.2 Flow in a Curved Channel: Hoop Stress and Viscoelastic Flow Instability
218(4)
9.3.3 Uniaxial Extension: Extensional Viscosity and the Trouton Ratio
222(2)
9.3.4 Effects of Finite Extensibility on Shear and Extensional Flows: Scaling Arguments
224(3)
9.4 Material Frame Indifference and Models of Viscoelastic Fluids
227(10)
Appendix Mathematical Background 237(18)
References 255(8)
Index 263
Michael D. Graham is the Vilas Distinguished Achievement Professor and Harvey D. Spangler Professor of Chemical and Biological Engineering at the University ofWisconsin, Madison. His research focuses on theoretical and computational studies of the fluid dynamics of complex fluids. Among his recognitions are a CAREER Award from the National Science Foundation (NSF), the Franēois Frenkiel and Stanley Corrsin Awards from the American Physical Society Division of Fluid Dynamics, and the Kellett Mid-Career Award at the University of Wisconsin, Madison. He has served as associate editor of the Journal of Fluid Mechanics and editor-in-chief of the Journal of Non-Newtonian Fluid Mechanics. He is coauthor of the textbook Modeling and Analysis Principles for Chemical and Biological Engineers (2013).