Kinetic Theory of Granular Flow Limitations for Modeling High-Shear Mixing

Abstract

Particulate modeling is often used to describe the kinematics of granular flow in mixers, granulators, and fluidized beds. An improved understanding of the rate processes associated with granulation can prove to be a valuable tool for modeling the evolution of particle size distributions. The kinetic theory of granular flow (KTGF) is a tool developed from the kinetic theory of gases to describe the kinematics found in granular media. Past work has shown that the KTGF can be used to describe the particle motion in a fluidized bed due to the inherently random particle movement caused by the fluid mechanics. Initially, it was thought that kinetic theory would not suffice when describing the kinematics in a high-shear mixer because of the shear motion in the mixer. However, recent work by Nilpawar et al. (in Proceedings: The 8th International Symposium on Agglomeration; The Industrial Pharmacists Group: Bangkok, Thailand, 2005) has shown experimentally that the collision frequency caused by random motion dominates over shear-induced collisions using measurements from the surface of the mixer. The present work attempts to support previous experimental findings by investigating the distributions of particle speed and velocity. The analysis is performed using discrete element modeling (DEM), a tool commonly used to simulate complex granular flow. This work demonstrates that, under idealized conditions, the KTGF is a very adequate means of describing particle flow. As the DEM process model becomes less ideal, the KTGF appears to be less successful in modeling the system.

Simulation of Entrainment by Free‐Falling Bulk Material Depending on Particle‐Size Distribution

“…Bei noch dichteren Partikelströmungen, d. h. vierfacher Kopplung, gewinnen zusätzlich Kräfte durch Partikel/Partikel‐Interaktionen sowie Partikel/Wand‐Interaktionen an Bedeutung. In der Diskrete‐Elemente‐Methode (DEM) werden hierfür Kontaktmodelle anhand physikalischer Modelle wie Feder‐, Dämpfer‐ und Gleitelemente angenähert , , , wobei zwischen sogenannten Soft‐Sphere‐ und Hard‐Sphere‐Modellen differenziert werden muss.…”

“…Zur Betrachtung des Partikelverhaltens in der Simulation bieten sich in der Regel zwei unterschiedliche Modelle an [13]. Einerseits werden bei der Euler-Euler-Betrachtung sowohl die Fluidphase als auch die Partikelphase als Kontinuum betrachtet, wobei für beide Phasen Gleichungen für Massen-, Impuls-und Energieerhaltung aufgestellt und gelöst werden (Navier-Stokes-Gleichungen [12,17,18], wobei zwischen sogenannten Soft-Sphere- [19] und Hard-Sphere-Modellen [20] differenziert werden muss.…”

Numerical simulations of two-component granulation: Comparison of three methods

“…The so-called KTGF kernel is based on the kinetic theory of granular flow (KTGF) and is often used to model granulation (Gantt and Gatzke, 2006). The termv accounts for the granular temperature of the system which increases with increasing size.…”

CFD simulation of the high shear mixing process using kinetic theory of granular flow and frictional stress models

“…The discrete element method (DEM) is shown to be a promising modelling tool for modelling the particulate flow in the mixer (Gantt and Gatzke, 2006;Kuo et al, 2004). In the DEM approach, the motion of every single particle is tracked.…”