Quantitative Evaluation of Mixed States of Granular Systems with Shannon Entropy

Abstract

Technology which can monitor states of granular systems will become a key to optimize manufacturing systems for developing functional materials such as for battery and medicine. Several methods are already available including process tomography and PIV. This paper focuses and discusses mixing index by Shannon Entropy, Shannon mixing index termed in the paper, by comparing the Lacey mixing known as standard mixing index based on statistics and experimental data. The following results are obtained: 1) Shannon mixing index can handle multi-component systems, instead of Lacey mixing index being limited to binary systems. 2) Shannon mixing index can evaluate really small amount of component quantitatively as well as qualitatively, which is not available by statistically based methods. 3) Shannon mixing index can be calculated experimentally by material sampling method, which is comparable to predictions by DEM (Discrete Element Method) simulation. The results obtained through the research indicates that Shannon Entropy can be qualified to the standard mixing index.