8.10. Mixing Index

This script compute the Mixing Index (MI) for particulate systems containing multiple materials. The method quantifies the degree of homogeneity of a granular bed after simulation processing.

Script Details

When running this script in a case that contains results, a new user input window will be prompted (as shown below) and the following input is necessary:

Avaliable geometries: Select the geometry where the particle bed is located.

Figure 8.32: Mix Geometry Selection.

Mix Geometry Selection.

The Mixing Index:

  • evaluates local uniformity per spatial cell

  • compares local composition against the global target composition

  • produces a dimensionless indicator

  • allows both spatial and global mixing assessment

Mathematical Formulation

The formulation follows the method proposed by Govender (2023)[1] and can be applied to Rocky particle statistics exported per spatial cell (bins).

The calculation follows these steps:

  1. Compute global material ratios:

    (8–1)

  2. Determine normalization factors:

    (8–2)

  3. Evaluate each spatial cell independently:

    (8–3)

  4. Compute MaxD per cell:

    (8–4)

    Then:

    (8–5)

  5. Compute SumProb:

    (8–6)

  6. Compute local Mixing Index:

    (8–7)

  7. Compute global Mixing Index:

    (8–8)

Script Output

Figure 8.33: Average Cell Mixing Index.

Average Cell Mixing Index.

Table 8.1: Typical interpretation

MI valueMeaning
~0Segregated
~0.5Partially mixed
~1Ideally homogeneous