Extension of kinetic theory to cohesive particle flow

Particle flow is significantly affected by the agglomeration of particles due to the inter-particle force when fine particles, such as Geldartʹs Group C particles, are used. In order to quantify cohesive particle flow behavior, governing equations based on the kinetic theory for cohesive particle flow were developed. In the derivation of the governing equations for cohesive particle flow, we defined a new distribution function of the instantaneous velocity of the particle relative to the average velocity based on the volume fraction of the particulate phase that is conserved upon agglomeration. Furthermore, to account for the effect of diameter growth on agglomeration, we considered the change in number of particles due to agglomeration in the derivation of a new conservation of the number of particles equation. Based on our distribution function, governing equations were derived; namely, mass and momentum plus energy and conservation of number of particles equations for cohesive particle flow. This set of equations is capable of describing cohesive particle flow behavior as well as particle diameter variation due to agglomeration. Finally, to show the validity of our model, we analyzed the homogeneous simple shear flow of particles under the agglomeration condition. The predicted flow properties, such as shear viscosity, normal viscosity, and particle growth, agreed well with the expected trends.