Dynamic viscoplastic granular flows: A persistent challenge in gas-solid fluidization

Abstract Fluidization is a prime example of complex granular flows driven by fluid-solid interactions. The interplay of gravity, particle-particle and fluid-particle forces leads to a rich spectrum of hydrodynamic behavior. A number of complex mathematical formulations exist to describe granular flows. At a macroscopic scale, Eulerian models based on the Kinetic Theory of Granular Flow (KTGF) have been successfully employed to simulate dilute and moderately dense systems, such as circulating fluidized bed reactors. However, their applications to dense flows are challenging, because sustained particle contacts are important. As solid fraction rises, the behavior of granular media responds dramatically to particle properties and changes in concentration. Lacking a coherent transition between formulations of dilute, dense and quasi-static flow behavior, kinetic models are incapable of describing how microstructure emerges and affects the rheology. The behavior of transitional granular flows, such as pulsed fluidized beds, for which the particulate phase transitions between the viscous and plastic regimes, are good reminders of this limitation. In recent years, tremendous effort has been devoted to finding new ways to describe the effects of sustained solids friction and dense flow rheology. This article provides a perspective on this matter from the viewpoint of gas-solid fluidization and discusses advances in describing the dilute-to-dense transition in a continuum framework. Four innovative approaches prevail to extend or supersede the existing kinetic theory: (i) including effective restitution coefficients, (ii) coupling local granular rheological correlations, (iii) introducing rotational granular energy, and (iv) combining non-local laws. While their reliability is still far from that of a Eulerian-Lagrangian approach, they lay a promising foundation for developing a rigorous description of granular media that merges the classical frameworks of continuous fluid and soil mechanics. The progress of continuum formulations does not compete with multi-scale modeling platforms with an applied focus. Ultimately, combining both is a prerequisite to developing new solid stress models that will improve not only the performance of macroscopic models, but also our understanding of granular physics.