  This is a summary of the article with the same title, accepted for
publication in Advances in Chemical Engineering, 47: 193-277 (2015). Gas-solid
fluidization is a typical nonlinear nonequilibrium system with multiscale
structure. In particular, the mesoscale structure in terms of bubbles or
clusters, which can be characterized by nonequilibrium features in terms of
bimodal velocity distribution, energy non equipartition, and correlated density
fluctuations, is the critical factor. Traditional two-fluid model (TFM) and
relevant closures depend on local equilibrium and homogeneous distribution
assumptions, and fail to predict the dynamic, nonequilibrium phenomena in
circulating fluidized beds even with fine-grid resolution. In contrast, the
mesoscale modeling, as exemplified by the energy-minimization multiscale (EMMS)
model, is consistent with the nonequilibrium features in multiphase flows.
Thus, the structure-dependent multi-fluid model conservation equations with the
EMMS-based mesoscale modeling greatly improve the prediction accuracy in terms
of flow, mass transfer, and reactions as well as the understanding of flow
regime transitions. Such discrepancies raise the question of the applicability
of the local equilibrium assumption underlying the TFM and further shed light
to the necessity of mesoscale modeling.
