Strategies for evaluating distributive mixing of multimodal Lagrangian particles with novel bimodal bin count variance

The variance among bin counts is one of the most effective and convenient indices to quantify the degree of spatial distributive mixing. Although it is suitable for evaluating the spatial distribution of unimodal particles, many practical particle-mixing processes involve bimodal or multimodal particle systems. Herein, the variance among bimodal bin counts is introduced as a new mixing index to quantify the degree of distributive mixing of bimodal or multimodal particles. Four bimodal particle-mixing systems are assumed and analyzed to evaluate index performance: balanced versus imbalanced and fully versus partially distributed particle systems. As a result, we suggest practical usage and the most effective variation of variances among conventional bin counts and bimodal bin counts to quantify the four bimodal particle-mixing systems. Furthermore, variations of the method for evaluating multimodal mixing are proposed.