Effective and powerful techniques to characterize the quality of a mixture with multiple components have been recently reviewed and linked with mixing mechanisms using 2-D images. However, there is no universally accepted method against experimental data in 3-D domains so far. In this paper, we introduce two novel statistical metrics for defining and characterizing homogeneity of mixture in 3-D domain using centered L-2-star discrepancy (CD) and wrap-around L-2-star discrepancy (WD). The CD and WD can be alternatives and superior to other 2-D approaches because they both exhibits some advantages such as permutation invariance, rotation invariance (reflection invariance) and the ability to measure projection uniformity. The feasibility of those developed techniques was verified by simulation and gas-liquid-particle mixture flowing in a gas-stirred liquid reactor with top-air injection. Experimental results are presented of gas-liquid two-phase flow by two indices (CD and WD) and correlation with operating conditions. The study led to a different approach to assessing mixing behaviors in 3-D domains. (C) 2018 Elsevier B.V. All rights reserved.