NOTES AND EXAMPLES IN MECHANICS
CONTENTS BASIC PRINCIPLES OF THE KINETIC THEORY INTRODUCTION MOLECULAR STRUCTURE OF A GAS BASIC PRINCIPLES THE MAXWELLIAN DISTRIBUTION FUNCTION DETERMINATION OF THE CHARACTERISTIC VELOCITIES MOLECULAR FLUX ELEMENTARY THEORY OF TRANSPORT PROCESSES CHARACTERISTIC DIMENSIONS POTENTIALS OF MOLECULAR INTERACTIONS BROWNIAN MOTION DYNAMICS OF A BINARY COLLISION CONSERVATION LAWS ASYMPTOTIC POST-COLLISIONAL VELOCITIES ASYMPTOTIC VELOCITIES FOR GAS MIXTURES SCATTERING ANGLE ? DI?ERENTIAL CROSS SECTION APPENDIX THE BOLTZMANN EQUATION THE BBGKY HIERARCHY THE LIOUVILLE THEOREM EQUATIONS OF THE BBGKY HIERARCHY THE TRANSFER EQUATION SUMMATIONAL INVARIANTS MACROSCOPIC DESCRIPTION MOMENTS OF THE DISTRIBUTION FUNCTION BALANCE EQUATIONS FOR THE MOMENTS THE DE?NITION OF EQUILIBRIUM EQUILIBRIUM STATES ENTROPY AND ENTROPY FLUX THE H-THEOREM INTERACTIONS OF GAS MOLECULES WITH SOLID SURFACES SCATTERING KERNELS THE PARADOXES OF LOSCHMIDT AND ZERMELO THE MANY FACES OF ENTROPY 2 10 APPENDIX THE CHAPMAN–ENSKOG METHOD THERMODYNAMICS OF A SINGLE FLUID SIMPLI?ED VERSION OF THE CHAPMAN–ENSKOG METHOD THE INTEGRAL EQUATION SOLUTION OF THE INTEGRAL EQUATION CONSTITUTIVE EQUATIONS AND TRANSPORT COE?CIENTS FORMAL VERSION OF THE CHAPMAN–ENSKOG METHOD THE DIMENSIONLESS BOLTZMANN EQUATION THE INTEGRAL EQUATIONS THE SECOND APPROXIMATION EXPANSION OF THE SCALAR COE?CIENTS A AND B TRANSPORT COE?CIENTS THE BGK MODEL MOMENT METHODS GRAD’S MOMENT METHOD BALANCE EQUATIONS GRAD’S DISTRIBUTION FUNCTION GRAD’S DISTRIBUTION FROM ENTROPY MAXIMIZATION DETERMINATION OF THE NON-CONVECTIVE FLUXES, PRODUCTION TERMS, ENTROPY DENSITY AND ENTROPY FLUX FIELD EQUATIONS THE METHOD OF MAXWELL AND IKENBERRY–TRUESDELL CALCULATION OF THE PRODUCTION TERMS THE MAXWELLIAN ITERATION THE CHAPMAN–ENSKOG–GRAD COMBINED METHOD NON-INERTIAL REFERENCE FRAMES OBJECTIVE TENSORS THE BOLTZMANN EQUATION IN NON-INERTIAL REFERENCE FRAMES FRAME DEPENDENCE OF THE HEAT FLUX VECTOR POLYATOMIC GASES SOME PROPERTIES OF POLYATOMIC GASES SEMI-CLASSICAL MODEL BOLTZMANN AND TRANSFER EQUATIONS THE EQUILIBRIUM DISTRIBUTION FUNCTION THE NON-EQUILIBRIUM DISTRIBUTION FUNCTION THE LAWS OF NAVIER–STOKES AND FOURIER A LIMITING CASE CLASSICAL MODEL BASIC FIELDS ROUGH SPHERICAL MOLECULES DENSE GASES THE THERMAL EQUATION OF STATE THE VAN DER WAALS EQUATION THE VIRIAL EQUATION OF STATE ENSKOG’S DENSE GAS THE ENSKOG’S EQUATION DETERMINATION OF THE POTENTIAL CONTRIBUTIONS EQUILIBRIUM CONSTITUTIVE EQUATIONS DETERMINATION OF THE KINETIC CONTRIBUTIONS THE MODI?ED ENSKOG EQUATION GRANULAR GASES MACROSCOPIC DESCRIPTION OF A GRANULAR GAS INTEGRAL EQUATIONS FIRST APPROXIMATION F(0) SECOND APPROXIMATION F (1) CONSTITUTIVE EQUATIONS FOR THE PRESSURE TENSOR AND THE HEAT FLUX VECTOR GRANULAR GASES OF ROUGH SPHERICAL MOLECULES MIXTURES OF MONATOMIC GASES THERMODYNAMICS OF FLUID MIXTURES THE COMBINED CHAPMAN–ENSKOG–GRAD METHOD THE NAVIER–STOKES LAW THE LAWS OF FICK AND FOURIER 8 10 MATRICES AS FUNCTIONS OF THE COLLISION INTEGRALS 8 11 BINARY MIXTURES 8 11 1 COE?CIENTS OF SHEAR VISCOSITY AND THERMAL CONDUCTIVITY 8 11 2 COE?CIENTS OF DI?USION AND THERMAL–DI?USION RATIO 8 11 3 COE?CIENTS FOR SOME INTERMOLECULAR POTENTIALS 8 12 APPENDIX CHEMICALLY REACTING GAS MIXTURES THERMODYNAMICS OF CHEMICALLY REACTING SYSTEMS EXTENT OF REACTION AND A?NITY CHEMICAL POTENTIALS THE LAW OF MASS ACTION THE ARRHENIUS EQUATION BOLTZMANN EQUATIONS TRANSFER AND BALANCE EQUATIONS MODELS FOR DI?ERENTIAL CROSS SECTIONS EQUILIBRIUM DISTRIBUTION FUNCTION TRANSPORT COE?CIENTS FOR H2 + CL ?HCL + H CHAPMAN–ENSKOG METHOD QUATERNARY MIXTURE H2, CL, HCL, H REMARKS ON THE REACTIVE CONTRIBUTIONS TO THE TRANSPORT COE?CIENTS TREND TO EQUILIBRIUM OF H2 + CL ?HCL + H DETERMINATION OF THE PRODUCTION TERMS CONSTITUENTS AT SAME TEMPERATURE THE H-THEOREM AND THE TENDENCY TO EQUILIBRIUM SYMMETRIC REACTIONS THE IN?UENCE OF THE HEAT OF REACTION ON SLOW REACTIONS CHEMICAL REACTIONS WITHOUT ACTIVATION ENERGY REMARKS ON THE GEOMETRY OF THE COLLISIONS REMARKS ON INELASTIC REACTIVE COLLISIONS REFERENCES