This book - a sequel of previous publications 'Flows and Chemical Reactions' and 'Chemical Reactions in Flows and Homogeneous Mixtures' - is devoted to flows with chemical reactions in heterogeneous environments. Heterogeneous media in this volume include interfaces and lines. They may be the site of radiation. Each type of flow is the subject of a chapter in this volume.We consider first, in Chapter 1, the question of the generation of environments biphasic individuals: dusty gas, mist, bubble flow. Chapter 2 is devoted to the study at the mesoscopic scale: particle-fluid exchange of momentum and heat with determination of the respective exchange coefficients. In Chapter 3, we establish simplified equations of macroscopic balance for mass, for the momentum and energy, in the case of particles of one size (monodisperse suspension). Radiative phenomena are presented in Chapter 5.

PREFACE ixLIST OF MAIN SYMBOLS xvCHAPTER 1. GENERATION OF MULTIPHASE FLOWS 11.1. Creation of suspensions of solid particles in a gaseousphase 11.1.1. Creation of a homogeneous suspension of starch particles21.1.2. Soot formation 31.2. Creation of suspensions of bubbles in a liquid 51.2.1. Example of creation of a suspension of bubbles in aliquid 51.2.2. Influence of gravity on suspensions in pipes 71.2.3. Slug flows 81.3. Creation of suspensions of drops in a gas 91.3.1. Destabilization of fluid sheets and layers 101.3.2. Formation of droplets from filaments 221.3.3. Numerical simulation of primary atomization 321.3.4. Secondary atomization 42CHAPTER 2. PROBLEMS AT THE SCALE OF A PARTICLE 472.1. Force exerted by a fluid on a spherical particle 482.1.1. Perfect incompressible fluid 482.1.2. Incompressible viscous fluid 512.2. Heat exchanges 592.3. Combustion of a drop of fuel in an oxidizing environment61CHAPTER 3. SIMPLIFIED MODEL OF A NON-REACTIVE FLOW WITHPARTICLES 653.1. Variables characterizing the flow 663.2. Balance equations 683.2.1. Balances for the particles 693.2.2. Balances for the gaseous phase 713.2.3. Entropy balance and phenomenological relations 713.3. Application to the linearized study of sound propagation ina non-reactive dilute suspension 743.4. Two-phase dilute flows in nozzles 783.4.1. Flow with constant phase shifts 793.4.2. Numerical solutions 82CHAPTER 4. SIMPLIFIED MODEL OF A REACTIVE FLOW WITH PARTICLES854.1. Balance equations for a reactive fog 854.1.1. Balances for the droplets 864.1.2. Balances of the mixture 884.1.3. Gaseous balances 904.1.4. Entropy balance of the spray and phenomenologicalrelations 904.1.5. Equations of the two-phase CEDRE solver 924.1.6. Modified equations to take account of an internaltemperature gradient of the drops: multi-layer model 934.2. Application to a spray flame 984.2.1. Application of a minimum model to the study of thethreshold of appearance of a pulsating flame 984.2.2. Application to the study of the resonant action of anacoustic wave on a spray flame 102CHAPTER 5. RADIATIVE PHENOMENA 1055.1. Basic values and fundamental relations in radiativetransfer 1065.1.1. Definitions 1065.1.2. Radiative Transfer Equation (RTE) 1085.1.3. Radiative flux and power 1105.1.4. Involvement of radiative heat transfer in the equationsof aerothermochemistry 1135.1.5. Turbulence-radiation interaction (TRI) 1185.1.6. Modeling of the radiative properties of gases 1195.1.7. Modeling of the radiative properties of the particles1245.2. Application to the hypersonic flow of atmospheric re-entry1275.2.1. One-dimensional approximation for a re-entering body1285.2.2. 3D calculations for a body experiencing re-entry 1305.3. Application to the boundary layer above a flat plate withsoot formation and radiative transfer 1325.3.1. Recap on a boundary layer with diffusion 1335.3.2. Reminders about the Emmons problem 1365.3.3. Influence of soot and radiative transfer 1425.4. Application to combustion of aluminum-based solidpropellants 144APPENDIX. CONCEPTS SURROUNDING THE HOPF BIFURCATION 149BIBLIOGRAPHY 153INDEX 173