Numerical study of particle mixing in bubbling fluidized beds based on fractal and entropy analysis

The DEM–LES coupling method is used to study the mixing of mono-dispersed identical density particles in bubbling fluidized beds based on the fractal and entropy analysis. A dimensionless function is used to study the microscopic characteristics of mixing interface. A criterion for identification of the boundary of bubbles is proposed and used to investigate the effect of bubble on particle mixing characteristics. Moreover, the Shannon information entropy is used to evaluate the macroscopic level of mixing. It is found that both the mixing interface of particles and the boundary of bubbles in fluidized beds are fractal. The bubble boundary dimension decreases as the fluidization velocity increases. The fractal bubble boundary induces the inhomogeneous characteristics of mixing interfaces of particles. On the other hand, the radial distribution function indicates the universal and intrinsic characteristics of particle mixing, independent of the initial effects after a short segment of evolution. Moreover, the information entropy, which is defined based on the radial distribution function, increases as the fluidization velocity increases. The mean information entropy is a good indication and a credible evaluation on the macroscopic mixing levels under various operating conditions of the beds.