Development of a coalescence model in gas–solid fluidized bed for the population balance equation

On the role of the macroscopic deformation in liquid film drainage between bubbles

“…On the contrary, a liquid film drainage model with deformable interfaces is commonly used to study the interaction between fluid particles. This kind of model can provide the necessary closure parameters for some reactor simulations 15–19 . Based on the lubrication theory and boundary integral method, Davis et al 8 proposed a liquid film drainage model with partially or fully mobile interface.…”

“…This kind of model can provide the necessary closure parameters for some reactor simulations. [15][16][17][18][19] Based on the lubrication theory and boundary integral method, Davis et al 8 proposed a liquid film drainage model with partially or fully mobile interface. Although it is inevitable to deal with the inherent numerical singularities in the boundary integral equation when using the model, 8 it is still extended in many works.…”

Further developments of the extended quadrature method of moments to solve population balance equations

“…Population Balance Model (PBM) is ubiquitous in industrial applications where multiple phases are involved. For instance, PBM is applied in the modeling of gas–liquid [1] , gas-solid [2] and gas-solid-liquid [3] phases with applications in aerosol technology [4] , petrochemical technology [5] , crystallization technology [6] and fermentation technology [7] to name a few. Population balance is a transport equation that is used to track the dynamics of the evolving particulate phase Number Density Function (NDF) with a given set of internal coordinates (e.g.…”