THE DYNAMICAL THEORY OF GASES
CONTENTS MOLECULAR DESCRIPTION MECHANICS OF CONTINUOUS MEDIA AND ITS RESTRICTION MACROSCOPIC STATE VARIABLES DILUTE GAS INTERMOLECULAR POTENTIAL DE?NITION OF POTENTIAL HARD SPHERE POTENTIAL LENNARD-JONES POTENTIAL AB INITIO POTENTIAL DE?ECTION ANGLE DI?ERENTIAL CROSS SECTION TOTAL CROSS SECTION EQUIVALENT FREE PATH RAREFACTION PARAMETER AND KNUDSEN NUMBER VELOCITY DISTRIBUTION FUNCTION DE?NITION OF DISTRIBUTION FUNCTION MOMENTS OF DISTRIBUTION FUNCTION ENTROPY AND ITS FLOW VECTOR GLOBAL MAXWELLIAN LOCAL MAXWELLIAN BOLTZMANN EQUATION ASSUMPTIONS TO DERIVE THE BOLTZMANN EQUATION GENERAL FORM OF THE BOLTZMANN EQUATION CONSERVATION LAWS ENTROPY PRODUCTION DUE TO INTERMOLECULAR COLLISIONS INTERMOLECULAR COLLISIONS FREQUENCY GAS–SURFACE INTERACTION GENERAL FORM OF BOUNDARY CONDITION FOR IMPERMEABLE SURFACE DI?USE–SPECULAR KERNEL CERCIGNANI–LAMPIS KERNEL ACCOMMODATION COE?CIENTS GENERAL FORM OF BOUNDARY CONDITION FOR PERMEABLE SURFACE ENTROPY PRODUCTION DUE TO GAS–SURFACE INTERACTION LINEAR THEORY SMALL PERTURBATION OF EQUILIBRIUM LINEARIZATION NEAR GLOBAL MAXWELLIAN LINEARIZATION NEAR LOCAL MAXWELLIAN PROPERTIES OF THE LINEARIZED COLLISION OPERATOR LINEARIZATION OF BOUNDARY CONDITION IMPERMEABLE SURFACE BEING AT REST IMPERMEABLE MOVING SURFACE PERMEABLE SURFACE LINEARIZATION NEAR REFERENCE MAXWELLIAN PROPERTIES OF SCATTERING OPERATOR DI?USE SCATTERING SERIES EXPANSION RECIPROCAL RELATIONS GENERAL DE?NITIONS KINETIC COE?CIENTS TRANSPORT COE?CIENTS CONSTITUTIVE EQUATIONS VISCOSITY THERMAL CONDUCTIVITY NUMERICAL RESULTS MODEL EQUATIONS BGK EQUATION S-MODEL ELLIPSOIDAL MODEL DIMENSIONLESS FORM OF MODEL EQUATIONS DIRECT SIMULATION MONTE CARLO METHOD MAIN IDEAS GENERATION OF SPECI?C DISTRIBUTION FUNCTION SIMULATION OF GAS–SURFACE INTERACTION KERNEL DECOMPOSITION CERCIGNANI–LAMPIS SCATTERING INTERMOLECULAR INTERACTION CALCULATION OF POST-COLLISION VELOCITIES CALCULATION OF MACROSCOPIC QUANTITIES STATISTICAL SCATTER DISCRETE VELOCITY METHOD VELOCITY DISCRETIZATION ONEFOLD INTEGRAL TWOFOLD INTEGRAL ITERATIVE PROCEDURE FINITE DI?ERENCE SCHEMES MAIN PRINCIPLES ONE-DIMENSIONAL PLANAR FLOWS TWO-DIMENSIONAL PLANAR FLOWS ONE-DIMENSIONAL AXISYMMETRIC FLOWS FULL KINETIC EQUATION VELOCITY SLIP AND TEMPERATURE JUMP PHENOMENA GENERAL REMARKS VISCOUS VELOCITY SLIP DE?NITION AND INPUT EQUATION VELOCITY AND HEAT FLOW PRO?LES NUMERICAL AND EXPERIMENTAL DATA THERMAL VELOCITY SLIP RECIPROCAL RELATION TEMPERATURE JUMP TEMPERATURE PRO?LE NUMERICAL DATA PLANAR COUETTE FLOW DE?NITIONS FREE-MOLECULAR REGIME VELOCITY SLIP REGIME KINETIC EQUATION NUMERICAL SCHEME PLANAR HEAT TRANSFER TEMPERATURE JUMP REGIME PLANAR POISEUILLE AND THERMAL CREEP FLOWS SLIP SOLUTION SPLITTING SCHEME FREE-MOLECULAR LIMIT ONE-DIMENSIONAL AXISYMMETRICAL FLOWS CYLINDRICAL COUETTE FLOW SLIP FLOW REGIME RESULTS HEAT TRANSFER BETWEEN TWO CYLINDERS TEMPERATURE JUMP SOLUTION CYLINDRICAL POISEUILLE AND THERMAL CREEP FLOWS FLOWS THROUGH A LONG RECTANGULAR CHANNEL FLOWS THROUGH SLITS AND SHORT CHANNELS FORMULATION OF THE PROBLEM SMALL PRESSURE AND TEMPERATURE DROPS HYDRODYNAMIC SOLUTION ARBITRARY PRESSURE DROP DE?NITION END CORRECTION FOR CHANNEL TWO-DIMENSIONAL AXISYMMETRICAL FLOWS FLOWS THROUGH ORI?CES AND SHORT TUBES FREE-MOLECULAR FLOW SMALL PRESSURE DROP KINETIC EQUATIONS END CORRECTION FOR TUBE TRANSIENT FLOW THROUGH A TUBE FLOWS THROUGH LONG PIPES UNDER ARBITRARY PRESSURE AND TEMPERATURE DROPS STATIONARY FLOWS MAIN EQUATIONS ISOTHERMAL FLOWS NONISOTHERMAL FLOWS PIPES WITH VARIABLE CROSS SECTION TRANSIENT FLOWS APPROACHING TO EQUILIBRIUM ACOUSTICS IN RARE?ED GASES DESCRIPTION OF WAVES IN CONTINUOUS MEDIUM COMPLEX PERTURBATION FUNCTION ONE-DIMENSIONAL FLOWS OSCILLATORY COUETTE FLOW SLIP REGIME LONGITUDINAL WAVES HYDRODYNAMIC REGIME HIGH-FREQUENCY REGIME