The Clustering Instability in Rapid Granular and Gas-Solid Flows

Abstract

Flows of solid particles are known to exhibit a clustering instability—dynamic microstructures characterized by a dense region of highly concentrated particles surrounded by a dilute region with relatively few particles—that has no counterpart in molecular fluids. Clustering is pervasive in rapid flows. Its presence impacts momentum, heat, and mass transfer, analogous to how turbulence affects single-phase flows. Yet predicting clustering is challenging, again analogous to the prediction of turbulent flows. In this review, we focus on three key areas: (a) state-of-the-art mathematical tools used to study clustering, with an emphasis on kinetic theory–based continuum models, which are critical to the prediction of the larger systems found in nature and industry, (b) mechanisms that give rise to clustering, most of which are explained via linear stability analyses of kinetic theory–based models, and (c) a critical review of validation studies of kinetic theory–based models to highlight the accuracies and limitations of such theories.

Maximum Solid Phase Concentration in Geophysical Turbulent Gas‐Particle Flows: Insights From Laboratory Experiments

“…This is consistent with the fact that C max is set by particle clustering, which is caused, along with particle collisions, by hydrodynamic instabilities occurring at the particle scale (Fullmer & Hrenya, 2017). Our results suggest that processes at the particle scale (cf.…”

Scale‐dependent nonequilibrium features in a bubbling fluidized bed

“…[1][2][3][4][5][6][7] These dynamical heterogeneous structures are characterized with wide range of length and time scales. [1][2][3][4][5][6][7] These dynamical heterogeneous structures are characterized with wide range of length and time scales.…”

“…The spatio-temporal evolution of the meso-scale structures, such as bubbles or clusters in a gas-solid fluidized bed, has been a hot area of research in recent decades. [1][2][3][4][5][6][7] These dynamical heterogeneous structures are characterized with wide range of length and time scales. For example, the bubble size was reported to range from the distance between neighboring orifices to the width of bed and its frequency 2 to 14 Hz.…”

Dynamic multiscale method for gas‐solid flow via spatiotemporal coupling of two‐fluid model and discrete particle model

“…The constitutive equations for particulate phase stresses is generally based on the assumption that there is a clear scale separation in granular systems, or from thermodynamic viewpoint the local thermodynamic equilibrium postulate is valid. Unfortunately, this is usually not the case . For example, Continuum method is inadequate due to the existence of Knudsen layer .…”

“…Unfortunately, this is usually not the case. [10][11][12] For example, Continuum method is inadequate due to the existence of Knudsen layer. 13,14 Conversely, DPM treats the fluid as a continuum phase and treats the solid phase as a collection of discrete particles that obeys the Newton's second law.…”