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Entropic Invariants of Two-Phase Flows - 1st Edition - ISBN: 9780128014585, 9780128016435

Entropic Invariants of Two-Phase Flows

1st Edition

Author: Eugene Barsky
eBook ISBN: 9780128016435
Paperback ISBN: 9780128103128
Hardcover ISBN: 9780128014585
Imprint: Elsevier Science
Published Date: 14th August 2014
Page Count: 266
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In this book, a new approach to the theory and practice of two-phase systems based on a global invariant – entropy, – and other invariants is formulated and experimentally confirmed.

Key Features

  • Offers a novel approach to the study of the two-phase flows systems based on statistical mechanics and probability theory
  • Provides the tools for computing and modelling two-phase systems, predicts mass transfer and enables system optimization
  • Provides a plethora of examples in among others, separation processes, dust production, pneumatic transport, and boiling bed


Students, scientists, engineers engaged in the design and operation of the respective equipment, companies engaged in the production and operation of the respective equipment, mineral technologists, and mining engineers

Table of Contents

  • Introduction
  • Chapter 1. Modern Conceptions of Thermodynamic Entropy
    • 1. Entropy substantiation
    • 2. Entropy, ensemble of states, probability
    • 3. Problematic aspects of entropy
  • Chapter 2. Invariants for Continuous Flows
    • 1. Substantiation of the necessity to model technological processes
    • 2. Certain aspects of continuous flows modeling
    • 3. Invariants for continuous flows
    • 4. Analysis of flow parameters using similarity criteria
  • Chapter 3. Modern Notions of Two-Phase Flows
    • 1. Peculiarities of unit particles settling
    • 2. Final settling velocities
    • 3. Particle interaction with a moving medium
    • 4. Features of two-phase flow generation
    • 5. Mass suspension of particles in a flow
    • 6. Carrying capacity of two-phase flows
  • Chapter 4. Empirical Invariants for Two-Phase Flows
    • 1. Fractional extraction
    • 2. Affinization of fractional extraction curves
    • 3. Unified separation curves
    • 4. Generalizing empirical invariant
  • Chapter 5. Entropy of Mixture Composition
    • 1. Invariants for granulometric composition
    • 2. Uncertainty of mixture composition
  • Chapter 6. Two-Phase Flow as a Statistical System
    • 1. Substantiation of physical analogy
    • 2. Model of particle collisions in a two-phase flow
    • 3. External interaction model in a two-phase flow
    • 4. Statistical model substantiation
  • Chapter 7. Main Statistical Parameters of a Two-phase Flow
    • 1. Substantiation of a statistical system for solid particles continuum
    • 2. Generalising parameter for a two-phase flow
    • 3. Generalising invariant for two-phase flows
    • 4. Definition of chaotising factor for two-phase flows
  • Chapter 8. Substantiation of Statistical Parameters of Mass Transfer in Two-Phase Flows
    • 1. Multidimensional model of a two-phase system
    • 2. Two-phase flow mobility in separation regimes
    • 3. Generalising invariants for parameters characterising two-phase flows
    • 4. Substantiation of entropy of two-phase flows with a polyfractional solid phase
    • 5. Equilibrium state as a condition of maximal entropy
  • Chapter 9. Specific Properties of Entropy of Two-Phase Flows
    • 1. Composition entropy as a criterion of solid-phase separation quality
    • 2. Statistical equilibrium for particle distribution in a flow
    • 3. Stability of entropy and the entire mass distribution process in a two-phase flow
  • Chapter 10. Invariants for Separation Curves
    • 1. Regimes of solid-phase particle motion in flows
    • 2. Particle extraction in two-phase flow separation regimes
  • Chapter 11. Basic Physics of Cascade Separation
    • 1. Main principles of cascade mass-exchange processes
    • 2. Discrete model
    • 3. Analysis of a mathematical model of a regular cascade
    • 4. Separation at cyclic feed of initial material into cascade apparatus
    • 5. Absorbing Markov chain in cascade classification of bulk materials
    • 6. Mathematical model of cascade separation with arbitrary distribution coefficients
    • 7. Discrete model of critical regimes of vertical two-phase flows
    • 8. Optimisation of principal parameters of multi-stage separation
  • Chapter 12. Application of the Obtained Results
    • 1. Invariants for estimating the perfection of the design of separation apparatuses
    • 2. Method of theoretical estimation of vertical cascade separators
    • 3. Experimental check of the adequacy of the method of cascade separators computation
    • 4. Computation method of multirow combined separation cascade
    • 5. Optimization of multirow classifier operation
    • 6. Separator efficiency rank
    • 7. Flow velocity ensuring optimal separation
  • Annotation
  • Bibliography
  • Index


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© Elsevier Science 2014
14th August 2014
Elsevier Science
eBook ISBN:
Paperback ISBN:
Hardcover ISBN:

About the Author

Eugene Barsky

The author, Dr. Eugene Barsky, has been engaged in this subject for 18 years, since 1993. His M.Sc. thesis completed in 1998 was devoted to the development of models of cascade separation of solid materials in flows. His PhD thesis completed in 2001 was devoted to the development of entropy criterion of separation processes optimization. Among dozens of criteria applied, the entropy criterion has proved to be the most unbiased one. Since that time, the author has been developing these topics in depth. He created a number of industrial cascade apparatuses for powders separation and dust collection, wrote about 20 articles, published two books, participated in many scientific congresses and conferences. The material accumulated during 6 recent years is presented in the proposed book.

Affiliations and Expertise

Department of Industrial Engineering, Azrieli College of Engineering, Jerusalem, Israel

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