Theory and simulation of hard-sphere fluids and related systems / A. Mulero (ed.).

Format:

Book

Contributor:

Mulero, A. (Angel)

Series:

Lecture notes in physics ; 753.

Lecture notes in physics ; 753

Language:

English

Subjects (All):

Fluid mechanics.

Physical Description:

xxvii, 546 pages : illustrations ; 24 cm.

Place of Publication:

Berlin : Springer, [2008]

Summary:

Hard spheres and related objects (hard: disks and mixtures of hard systems) are paradigmatic systems: indeed, they have served as a basis for the theo-retical and numerical development of a number of fields, such as general liquids and fluids, amorphous solids, liquid crystals, colloids and granular matter, to name but a few. The present volume-introduces and reviews some important basics and progress in the study of such systems. Their structure, thermodynamic properties, equations of-state, as well as kinetic and transport properties are considered from different and complementary points of view. This book addresses graduate students, lecturers as well as researchers in statistical mechanics, physics of liquids, physical chemistry and chemical engineering.

Contents:

1 Structure of Hard Spheres and Related Systems / A. Malijevsky, J. Kolafa 1

1.1 Basic Concepts 1

1.2 Low-Density Region 4

1.3 High-Density Region 9

References 24

2 Introduction to the Thermodynamics of Hard Spheres and Related Systems / A. Malijevsky, J. Kolafa 27

2.1 Virial Coefficients of Pure Hard Spheres and Disks 27

2.2 Chemical Potentials of Hard Spheres and Related Systems 31

References 35

3 Equations of State for Hard Spheres and Hard Disks / A. Mulero, C.A. Galan, M.I. Parra, F. Guadros 37

3.1 Introduction 37

3.2 Equations of State for Hard Disks 40

3.3 Equations of State for Hard Spheres 60

3.4 Other Properties of the Hard-Sphere Fluid from Equations of State 96

3.5 Final Remarks 102

References 103

4 Application-of Hard-Sphere and Hard-Disk Equations of State to the Weeks-Chandler-Andersen Reference System / A. Mulero, C.A. Galan, I. Cachadina, F. Cuadros 1ll

4.1 Introduction 111

4.2 Analytical Expressions 113

4.3 Pressure of the Three-Dimensional WCA RS 114

4.4 Potential Energy of the Three-Dimensional WCA RS 120

4.5 Pressure and Potential Energy of the Two-Dimensional WCA RS 121

4.6 Conclusions 128

References 131

5 Binary Mixtures of Additive Hard Spheres. Simulations and Theories / C. Barrio, J.R. Solano 133

5.1 Introduction 133

5.2 Computer Simulations 135

5.3 Consistency Conditions 147

5.4 Virial Coefficients 150

5.5 Contact Values of the Radial Distribution functions, Equation of State, and Consistency 161

5.6 Deriving Density Expansions of the Contact Values of the Radial Distribution Functions from the Approximate Virial Expansion and Consistency Conditions 172

5.7 Rescaling the Density Expansions 176

5.8 Final Remarks 179

References 180

6 Alternative Approaches to the Equilibrium Properties of Hard-Sphere Liquids / M.Lopez de Baro, S.B. Yuste, A. Santos 183

6.1 Introduction 183

6.2 Contact Values and Equations of State for Mixtures 185

6.3 The Rational Function Approximation (RFA) Method for the Structure of Hard-Sphere Fluids 211

6.4 Other Related Systems 224

6.5 Perturbation Theory 235

6.6 Perspectives 240

References 241

7 Density Functional Theories of Hard Particle Systems / P. Tarazona, J. A. Cuesta, Y. Martinez-Raton 247

7.1 Introduction 247

7.2 Brief Tutorial to the Density Functional Formalism 248

7.3 The Exact Density Functional for Hard Rods 254

7.4 The Weighted Density Approximation 255

7.5 The Fundamental Measure Theory 270

7.6 Density Functionals for Hard Sphere Mixtures 290

7.7 Weighted Density Approximation for Mixtures of Hard Spheres 292

7.8 Fundamental Measure Theory for Mixtures of Hard Spheres 295

7.9 Non-Additive Mixtures of Hard Spheres 300

7.10 Density Functional for Anisotropic Bodies 304

7.11 Fundamental Measure Theory for Anisotropic Particles 318

7.12 Summary 334

References 336

8 Ensemble Effects in Small Systems / F.L. Roman, J. A. White, A. Gonzalez, S. Velasco 343

8.1 Velocity Distributions in Hard Particle Systems 345

8.2 Density Fluctuations in Hard-Particle Systems 357

8.3 Density Profiles of Inhomogeneous Systems. Structural Properties 369 References 379

9 Modelling of Transport Properties of Hard Sphere Fluids and Related Systems, and its Applications / C.M. Silva, H. Liu 383

9.1 Introduction 383

9.2 Molecular Dynamics Simulations 387

9.3 Theories of Transport in Hard Sphere and Modified Systems 391

9.4 Diffusion Coefficient 420

9.5 Viscosity 459

9.6 Thermal Conductivity 472

9.7 Conclusions and Final Remarks 485

References 487

10 Kinetic Theory for Binary Granular Mixtures at Low Density / V. Garzo 493

10.1 Introduction 493

10.2 Boltzmann Kinetic Equation for Binary Mixtures of Inelastic Hard Spheres 497

10.3 Homogeneous States 500

10.4 Navier-Stokes Hydrodynamic Equations 503

10.5 Comparison with Monte Carlo Simulations 507

10.6 Einstein Relation in Granular Gases 512

10.7 Onsager's Reciprocal Relations in Granular Gases 514

10.8 Linearized Hydrodynamic Equations and Stability of the Homogeneous Cooling State 516

10.9 Segregation in Granular Binary Mixtures: Thermal Diffusion 521

10.10 Steady States: Uniform Shear Flow 528

10.11 Summary and Concluding Remarks 533

References 537.

Notes:

Includes bibliographical references and index.

ISBN:

9783540787662

3540787666

3540787674

9783540787679

OCLC:

213384279