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A new index, the estimate of the error variance, which can be used to quantify the evolution of the flow patterns when multiphase components or tracers are difficultly distinguishable, was proposed. The homogeneity degree of the luminance space distribution behind the viewing windows in the direct contact boiling heat transfer process was explored. With image analysis and a linear statistical model, the F-test of the statistical analysis was used to test whether the light was uniform, and a non-linear method was used to determine the direction and position of a fixed source light. The experimental results showed that the inflection point of the new index was approximately equal to the mixing time. The new index has been popularized and applied to a multiphase macro mixing process by top blowing in a stirred tank. Moreover, a general quantifying model was introduced for demonstrating the relationship between the flow patterns of the bubble swarms and heat transfer. The results can be applied to investigate other mixing processes that are very difficult to recognize the target.

The study of bubble swarm distributions in a direct-contact heat exchanger was addressed both theoretically and experimentally. But recently developed approach based on uniform design for measuring bubbles uniformity and mixing efficiency within rectangular or square region can not be used to characterise the mixture homogeneity and mixing time within circular region. This paper discussed the difference between rectangular or square region and circular region. A quantitative metric of mixing uniformity is used to characterize the bubble patterns within circular region. Simulation studies are also used to illustrate the proposed methodologies while the experimental case considered demonstrate that the proposed approach evaluated the experimental data rather well. The space-time features of the mixing transient have been successfully derived when the bubble swarms or other objects distribute in a circular region. This work brings new insights to evaluate mixing quality of different systems practically, which has a high degree of accuracy (the percentage of enhancing achieved is about 40%).

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