Fluid Mechanics and Its Applications

Introduction; Chapter I. General ideas of mass transfer processes in critical regimes; 1. Granulometric characteristics of bulk material; 2. Distribution of different fractions in the process of separation; 3. Fractional separation curves and their properties; Chapter II. Principles of modeling processes in moving media; 1. Correlation between a full-scale process and its model; 2. Mathematical models construction; 3. Similarity criteria determination; Chapter III. System of particles of the same size class in a critical flow.; 1. Dynamics of mass motion of particles in a flow; 2. Definition of a statistical system; 3. Estimation of the state of a statistical system; 4. Principal statistical characteristics of the separation factor; Chapter IV. System of particles of several size classes; 1. Interaction of particles in a flow; 2. Forces caused by interactions of particles of various classes; 3. Two-phase flow entropy in critical flow regimes; 4. Main features of entropy in critical regimes; 5. Mobility factor; 6. Statistical identities; Chapter V. Principal statistical relationships of mass transfer in critical flow; 1. Mass exchange between the zone and the apparatus; 2. Determination of average values; 3. Cell and apparatus, entropy; 4. Separation at low concentrations; 5. General regularities for the zone; Chapter VI. Correlation between the apparatus and the cell.; 1. Coarse particles separation; 2. Fine particles separation; 3. Definition of mass transfer parameters; 4. Cellular model of separation; 5. Physical meaning of separation factors; 6. Extraction from a cell located in the zone; Chapter VII. Structural model of mass transfer in critical regimes of two-phase flows.; 1. Validation of the distribution coefficient; 2. Physical meaning of the distribution coefficient; 3. Analysis of distribution coefficient; 4. Analysis of experimental dependencies from the standpoint of structural models; 5. Check of the structural model adequacy; 6. Correlation between the structural and cellular models of the process; Chapter VIII. Correlation between statistical and empirical results; 1. Approximation of universal separation curve; 2. Principal separation parameters depending on the apparatus height; 3. Equal extractability of various size classes; Chapter IX. Entropy of composition. Optimization criterion.; 1. Entropy and particles stratification; 2. Evaluation of heterogeneity of powder composition; 3. Binary separation; 4. Multi-product separation; 5. Algorithms of optimization of separation into n components; 6. Mathematical model of separation into n components; 7. Optimum conditions for binary separation; 8. Optimum conditions for multi-product separation; Chapter X. Stability and kinetic aspects of mass distribution in critical regimes; 1. Entropy stability; 2. Particles distribution over the channel height; 3. Velocity distribution of particles of a narrow size class; 4. Kinetic aspect of the material distribution; Chapter XI. Critical regimes of two-phase flows in complicated systems; 1. Problem setting; 2. Mathematical model of a duplex cascade; 3. Mathematical model of a cascade process allowing control of the effect of the material feed site on separation results; 4. Cascade model with two or more material inputs into the apparatus; 5. Combined cascade classifiers; 6. Quality criterion for combined cascades; 7. Fractal principle of the construction of schemes of combined classifiers; 8. Some methods of combined schemes optimization; Chapter XII. Stochastic model of critical regimes of two-phase flows; 1. Principal definitions; 2. Statistical description of gravitational separation in turbulent flows; 3. Equations of particles motion taking into account their rotation around the center of mass in a turbulent flow; 4. Description of one-dimensional stationary process of gravitation separation in a turbulent flow; 5. One-dimensional model of a non-stationary process; 6. Statistical equations of random process of gravitational separation; 7. Computation of fractional separation of a narrow class; 8. Approximate computation method; Chapter XIII. Mass transfer in critical regimes of two-phase flows; 1. Mathematical model of a separating cascade; 2. Discrete stationary model of critical regimes of vertical two-phase flows; 3. Optimization of principal parameters of multi-stage separation; Chapter XIV. Universal curves criteria; 1. Substantiation of the curves universality; 2. Generalizing criteria; 3. Universal curves; References