Transport Coefficients of Fluids (Springer Series in Chemical Physics 82)

Until recently the formal statistical mechanical approach offered no practicable method for computing the transport coefficients of liquids, and so most practitioners had to resort to empirical fitting formulas. This has now changed, as demonstrated in this innovative monograph. The author presents and applies new methods based on statistical mechanics for calculating the transport coefficients of simple and complex liquids over wide ranges of density and temperature. These molecular theories enable the transport coefficients to be calculated in terms of equilibrium thermodynamic properties, and the results are shown to account satisfactorily for experimental observations, including even the non-Newtonian behavior of fluids far from equilibrium. Contents......Page 9 1 Introduction......Page 14 References......Page 20 Part I: Transport Coefficients of Dilute Gases......Page 22 2 Boltzmann Equation for Dilute Monatomic Gases......Page 23 2.1 Boltzmann Equation and Boltzmann Entropy......Page 24 2.2 Equilibrium Solution......Page 26 2.3 Linear Transport Processes......Page 28 References......Page 37 3.1 Diffusion Processes......Page 39 3.2 Thermal Conduction......Page 41 3.3 Viscous Phenomena......Page 42 3.4 Nonlinear Transport Processes......Page 43 3.5 Applications of Nonlinear Transport Coefficients......Page 56 References......Page 65 4 Boltzmann Equation for Dilute Polyatomic Gases......Page 67 4.1 Kinetic Equation for Polyatomic Gases......Page 68 4.2 The H Theorem......Page 71 4.3 Generalized Hydrodynamic Equations......Page 73 4.5 Remarks......Page 81 References......Page 82 5.1 Ultrasonic Absorption in Rigid Diatomic Gases......Page 83 5.2 Nonlinear Transport Coefficients and Shock Waves......Page 94 References......Page 101 Part II: Transport Coefficients of Liquids......Page 103 6 Equation of State and Equilibrium Properties of Liquids......Page 104 6.2 Generic van der Waals Equation of State......Page 105 6.3 Free Volume......Page 111 6.4 Temperature and Density Dependence of A and B......Page 112 6.5 Model Canonical Equation of State......Page 115 6.6 Integral Equations for Pair Correlation Functions......Page 123 6.7 Equation for Inverse Correlation Length......Page 140 6.8 Application to Hard Sphere Fluids......Page 141 6.9 Concluding Remarks......Page 156 References......Page 157 7 Generalized Boltzmann Equation......Page 160 7.1 Grand Ensemble and Kinetic Equation......Page 161 7.2 Conservation Laws......Page 166 7.3 Constitutive Equations......Page 169 7.4 Generalized Hydrodynamics......Page 175 7.5 Linear Transport Coefficients......Page 178 7.6 Formal Consideration of the Collision Bracket Integrals......Page 180 7.7 A Monte Carlo Method for the Stress Tensor......Page 183 References......Page 187 8.1 Notational Preliminary......Page 189 8.2 Evolution Equations for Macroscopic Variables......Page 195 8.3 Kinetic Theory of Reacting Fluids......Page 203 8.4 Kinetic Equation for Reacting Fluids......Page 205 8.5 Collision Operators......Page 208 8.6 Density Evolution Equations and Chemical Kinetics......Page 209 8.7 Scattering Theory and Rate Coefficients......Page 217 8.8 The R Matrix Theory of Collision......Page 219 8.9 Collision Complexes and Rate Coefficient......Page 224 8.10 Characterization of Collision Complexes......Page 226 References......Page 229 9.1 Nonequilibrium Ensemble Distribution Function......Page 231 9.2 Dynamic Ornstein–Zernike Equation......Page 233 9.3 Connection with Existing Theory......Page 240 9.4 Local Equilibrium Equation of State......Page 242 References......Page 249 10 Density Fluctuation Theory: Simple Fluids......Page 251 10.1 Excess Normal Stress......Page 252 10.2 Shear Stress......Page 260 10.3 Heat Flux......Page 276 10.4 Concluding Remarks......Page 294 References......Page 295 11 Density Fluctuation Theory: Complex Fluids......Page 297 11.1 Nonequilibrium Ensemble Distribution Function......Page 298 11.2 Excess Normal Stress......Page 299 11.3 Shear Stress......Page 320 11.4 Heat Flux......Page 331 11.5 Concluding Remarks on the Density Fluctuation Theory......Page 348 References......Page 350 12 Free Volume Theory and Transport Coefficients......Page 352 12.1 Modified Free Volume Theory of Diffusion......Page 353 12.2 Comparison with Experiments......Page 358 12.3 Modified Free Volume Theory of Mixtures......Page 365 12.4 Validation of the Mixture Theory......Page 373 12.5 Transport Coefficients of Ordinary Liquids......Page 381 12.6 Conclusion......Page 389 References......Page 392 A.1 Derivation of the Kinetic Equation......Page 394 A.2 Relation Between Collision and Transition Operators......Page 399 B The Constitutive Equation for Velocity......Page 403 References......Page 406 B......Page 407 C......Page 408 E......Page 409 H......Page 410 M......Page 411 R......Page 412 S......Page 413 V......Page 414 W......Page 415 In this monograph, the density?uctuation theory of transport coe?cients of simple and complex liquids is described together with the kinetic theory of liquids, the generic van der Waals equation of state, and the modi?ed free volume theory. The latter two theories are integral parts of the density?- tuation theory, which enables us to calculate the density and temperature dependence of transport coe?cients of liquids from intermolecular forces. The terms nanoscience and bioscience are the catch phrases currently in fashion in science. It seems that much of the fundamentals remaining unsolved or poorly understood in the science of condensed matter has been overshadowed by the frenzy over the more glamorous disciplines of the former, shunned by novices, and are on the verge of being forgotten. The transport coe?cients of liquids and gases and related thermophysical properties of matter appear to be one such area in the science of macroscopic properties of molecular systems and statisticalmechanicsofcondensedmatter. Evennano-andbiomaterials,h- ever, cannot be fully and appropriately understood without?rm grounding and foundations in the macroscopic and molecular theories of transport pr- ertiesandrelatedthermophysicalpropertiesofmatterinthecondensedphase. Oneisstilldealingwithsystemsmadeupofnotafewparticlesbutamultitude of them, often too many to count, to call them few-body problems that can be understoodwithoutthehelpofstatisticalmechanicsandmacroscopicphysics. In the density?uctuation theory of transport coe?cients, the basic approach taken is quite di?erent from the approaches taken in the conventional kinetic theories of gases and liquids. "Until recently the formal statistical mechanical approach offered no practicable method for computing the transport coefficients of liquids, and so most practitioners had to resort to empirical fitting formulas. This has now changed, as demonstrated in this innovative monograph. The author presents and applies new methods based on statistical mechanics for calculating the transport coefficients of simple and complex liquids over wide ranges of density and temperature. These molecular theories enable the transport coefficients to be calculated in terms of equilibrium thermodynamic properties, and the results are shown to account satisfactorily for experimental observations, including even the non-Newtonian behavior of fluids far from equilibrium."--Jacket