(630f) An Index to Characterize Particle Mixing at Different Scales

Characterizing the mixing and segregation of particles which may differ in type, size or density is important in many chemical engineering applications, and has been extensively studied for more than half a century. This has resulted in a large number of mixing indices (~40) which are used, with varying levels of success, to characterize mixing in granular and gas-solid flows. In spite of the extensive literature on this topic, none of the existing mixing indices explicitly account for the fact that the level of mixing or segregation can vary depending on the scale at which the system is observed, which is conveniently characterized by a sampling volume. It is useful to classify these scales into three ranges: (i) the microscale representing sampling volumes with a characteristic length scale in the range O(1-10 d_p), where d_p is the particle diameter, (ii) the mesoscale representing sampling volumes with a characteristic length scale in the range O(10-100 d_p), and (iii) the macroscale representing sampling volumes on the scale of the device. Here we describe a new mixing index that explicitly accounts for the phenomenon of scale-dependent mixing, and is based on the average solid volume fraction fields corresponding to the different particle types obtained from multifluid multiphase computational fluid dynamics (mCFD) simulations or experiment. The performance of this scale-dependent mixing index (SDMI) is characterized using synthetic fields as well as data obtained from multifluid mCFD simulations of biomass mixing in sand in a fluidized bed reactor. Care is taken to distinguish grid-independence of the mCFD results from scale-dependence in the mixing index, resulting in a robust approach which can be applied to well-resolved as well as potentially under-resolved simulations or experimental data. Extension of the SDMI to discrete particle counts encountered in other multiphase flow simulation approaches such as Euler-Lagrange and particle-resolved direct numerical simulations is also discussed.