Meso-Scale Modeling: The EMMS Model for Gas-Solid Systems

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


This chapter introduces the EMMS model for gas-solid two-phase flow and the motive for this series of work. The EMMS model focuses on the meso-scale phenomenon of particle clustering, correlating it to the micro-scale of single particles and the macro-scale of the vessel operating conditions, material properties, and boundary conditions by analyzing the compromise between dominant mechanisms to define the meso-scale stability condition. The EMMS model can be solved for the eight parameters that describe the meso-scale structure and capture the so-called choking and drag-reduction phenomena in gas-solid fluidization systems, and further enables the intrinsic regime, operation diagram and overall fluid dynamics of systems to be determined. This chapter provides a solid basis to integrate the EMMS model with computational fluid dynamics (CFD) simulations and develop the EMMS paradigm.


Choking Cluster Compromise Drag EMMS Fluidization Hydrodynamics Meso-scale structure Multiscale Stability condition 



Acceleration, m/s2


Coefficient of added mass force, -


Drag coefficient for particles, -


Drag coefficient for a single particle, -


Diameter, m


Gas-solid interaction, N


Volume fraction (of dense phase), -


Conservation equation, -


Gravity acceleration, m/s2


Solids flow rate, kg/(m2·s)


Solids bed height, m


Solids inventory, kg


Proportional factor, -


Saturation carrying capacity, kg/(m2·s)


Particle or cluster number in unit volume, m-3


Rate of energy dissipation per unit mass of solids, m2/s3


Pressure, kPa


Volume flow rate, m3/s


Radial coordinate, m


Radius, m


Reynolds number, -


Time, s


Superficial velocity, m/s


Velocity, m/s


Energy consumption with respect to unit volume, J/m3 s


Axial coordinate, m


Bubble holdup, -


Kinematic viscosity, m2/s


Density, kg/m3


Variation of local solids concentration fluctuation, -


Voidage, -


Viscosity, Pa·s



Top dilute region


Bottom dense region




Dense phase








Dilute phase, fluid






Imposed pressure




Minimum bubbling


Minimum fluidization






Value for choking point


Suspension, slip




Transport, terminal




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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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