Footprint and Philosophy

  • Jinghai Li
  • Wei Ge
  • Wei Wang
  • Ning Yang
  • Xinhua Liu
  • Limin Wang
  • Xianfeng He
  • Xiaowei Wang
  • Junwu Wang
  • Mooson Kwauk


This chapter summarizes the footprint, philosophy and strategy of this book. The historical evolution of the energy minimization multiscale (EMMS) model is briefly introduced; the structure of the book is also outlined. To introduce the philosophy of this book, the spectrum of science and technology and the common multiscale nature of different disciplines are discussed. As meso-scales are identified as the critical issue in understanding complex systems, three such levels (material, reactor and system) in process engineering are analyzed in detail, emphasizing the importance of compromise between dominant mechanisms in generating meso-scale phenomena. Finally, the footprint of the EMMS model from a simple idea to a computational paradigm (the EMMS paradigm), and further to meso-science, is outlined to complete the overview of this book.


Chemical engineering Competition Complexity Complex systems Compromise Coordination EMMS model EMMS paradigm Fluid dynamics Multi-phase flow Mesoscale Meso-scale Mesoscience Meso-science Multiphase Multiscale Multi-scale Stability condition Supercomputing Variational Virtual process engineering 


\( C_{\text{d}} \)

Drag coefficient, dimensionless


Cluster diameter, m


Particle diameter, m

\( E_{\text{j}} \left( {\mathbf{x}} \right) \)

Objective function with respect to dominant mechanism j

\( E_{\text{OH}} \)

Hydrophilic potential in unit volume, m2/s3

\( E_{\text{WT}} \)

Lipophilic potential in unit volume, m2/s3

\( E_{\text{s}} \)

Surface energy in unit area, m2/s3

\( E_{{{\upmu}}} \)

Viscous dissipation rate in unit volume, m2/s3


Constraints condition i


Volume fraction of dense phase, dimensionless

\( g \)

Gravitational acceleration, m/s2

\( H \)

The height of the bed, m

\( H_{\text{a}} \)

Potential a in unit volume, m2/s3

\( H_{\text{b}} \)

Potential b in unit volume, m2/s3

\( L \)

Characteristic length of flow, m

\( N_{\text{surf}} \)

Rate of energy dissipation due to bubble breakage and coalescence per unit mass, W/kg

\( N_{\text{st}} \)

Rate of energy dissipation for transporting and suspending particles per unit mass, W/kg

\( N_{\text{turb}} \)

Rate of energy dissipation in turbulent liquid phase per unit mass, W/kg

\( R \)

Pipe radius, m

\( Re \)

Reynolds number, dimensionless

\( r \)

Radial coordinate, m


Gas in the dense phase superficial velocity, m/s


Gas in the dilute phase superficial velocity, m/s


Solid in the dense phase superficial velocity, m/s


Solid in the dilute phase superficial velocity, m/s

\( W_{\text{st}} \)

Energy consumption for transporting and suspending particles in unit volume, W/m3

\( \bar{W}_{\rm v} \)

Viscous shear dissipation rate in unit volume, W/m3

\( \bar{W}_{\text{te}} \)

Turbulent dissipation rate in unit volume, W/m3


State parameter

\( S \)

Surface energy in unit volume, m2/s3

\( Sh \)

Sherwood number, dimensionless

Greek Letters

\( \varepsilon \)

Local average voidage, dimensionless


Voidage in dense phase, dimensionless


Voidage in dilute phase, dimensionless

\( \varphi_{\rm r} \)

Dissipation rate of unit amount of kinetic energy across unit length, m2/s3

\( \eta \)

Kolmogorov microscales, m

\( \rho \)

Density, kg/m3



Index of particle a


Index of particle b


Dense phase


Dilute phase or fluid




Minimum bubble


Minimum fluidization







Circulating fluidized bed


Computational fluid dynamics


Central processing unit


Compute unified device architecture


Energy-minimization multiscale




Graphics processing unit


Multi-objective variational




Particle-fluid compromising


Two-fluid model


Virtual process engineering


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jinghai Li
    • 1
  • Wei Ge
    • 1
  • Wei Wang
    • 1
  • Ning Yang
    • 1
  • Xinhua Liu
    • 1
  • Limin Wang
    • 1
  • Xianfeng He
    • 1
  • Xiaowei Wang
    • 1
  • Junwu Wang
    • 1
  • Mooson Kwauk
    • 1
  1. 1.Institute of Process EngineeringChinese Academy of SciencesBeijingPeople’s Republic of China

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