Transport equations Basic Approach Mass Balances Momentum Balances Energy Balances entropy Balance Mixture equations Multicomponent Multiphase Flow One dimensional steady gas solid flow Dimensional, Steady Mixture Momentum Balance One-Dimensional, Steady Gas Momentum Balance: Pressure Drop in Both Phases - Model A Fluid Particle Drag Buoyancy Drag for Models B and C Entrance Length in Pneumatic Transport Pressure DroP Pressure Drop Correlation in a Dilute Lift Line Drift flux Hold-Up in Homogeneous and Slip Flow Single Particle Analysis Ergun euation Prediction Two Regimes in a Bubble Column Other Applications Critical granular One-Dimensional Granular Flow Momentum Balance One Dimensional Statics: Jamssen euation Incompressible, Frictionless Flow and Discharge Thermodynamics of Powders: Compressibility Critical Flow Theory for granular Materials Example of Critical GranrlaFlow Sound Speed" from Kinetic theory Fluidization Regimes Minimum Fluidization Velocity Geldart's Classification of powders Kinetic Energy Dissipation Analysis On the origin of bubbles Propagation in Incompressible Fluids Shocks and Dispersion with No Solids Stress Bubbling Criterion for Small Particles Inviscid multiphase flows bubbling bed Compressible granular Flow Well posedness of Two-Phase Models Flow and Pressure Propagation Solid vorticity and Void Propagation lMm Bubble Model Computer fluidization Models Comparison of Computations to observations Viscous flow and circulating fluidized beds Multiphase Navier*Stokes equation Model Dimensional Analysis: Scale Factors CFB or Riser Flow; Experimental Need for Clusters in One-D Modeling Computation of Cluster Flow Computation of Core-Annular Regime Radial Profiles and Turbulence Kinetic theory approach Distribution for Particles Properties of the Maxwellian State Dynamics of an Encounter between Two Particles 2M The Frequency of collisions Mean Free Path Elementary Treatment of Transpon Coefficients Boltzmann Integral-Differential Ęuation Maxwell's Transport Equation Conservation Laws with No Collisions Second Approximation to the Frequency Distribution lnteral equation solver strategy Viscous Kinetic Stress Tensor Dense Transport Theorem Particulate Momentum Equation Fluctuating Kinetic Energy Ęguation Viscosity - Collisional Momentum Transfer Granular Conductivity Applications of kinetic theory Granular Shear Flow Flow down a Chute Bubbling Bed: Flow Pattems Liquid-Solid Fluidization Circulating Fluidized Bed Loop Simulation 3U Maximum Solids Circulation in a CFB Kinetic theory of granular mixtures Empirical input restitution coefficuents Restitution Coefficients Boltzmann equations for a Mixture Dense Transport Theorem GranularTemperatures and Applications Particle_to_Particle Drag Exercises for Kinetic Theory Sedimentation and consolidation Conservation of Particles Settling in a Sedimentation Column: Introduction Free Settling Compression Settling Consolidation: Relation to Osmotic Pressure Electrokinetic Phenomónon: Zeta Potential Effect of Zeta Potential on Sedimentation Overall (Macroscopic Balances) Eulerian Approach: One-D Energy Balance Leibniz Formula and Relation to Transport D: Lagrangian Approach: One-D Conservation of Species and Population Balance Reynolds Transport Theorem Appendix F: First order Partial Differential equation Solution of a Hyperbolic System of First Order Partial Differential equations