
This study applies the three-dimensional Ripley’s L function to quantitatively assess solid-liquid mixing homogeneity in a stirred tank. The figure presents the DEM-VOF simulated mixing system together with a qualitative representation of the Ripley’s L curves, illustrating the evolution of particle distributions from clustering to dispersion and enabling a multiscale characterization of spatial organization during agitation. Comparative analysis under identical operating conditions demonstrates that the 45° pitched-blade turbine impeller achieves the most rapid homogenization, as indicated by the shorter time progress bar.
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