New metrics for measuring 2D uniformity in stirring system based on reconstruction of the particle trajectory

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In industrial mixing systems, the evaluation method is a crucial indicator for measuring mixing uniformity. This study proposes an assessment method that combines a method for positioning using dual cameras and a point pattern density fluctuation (PD) method based on disordered hyperuniformity. This study employs a method for positioning using dual cameras to investigate the motion trajectories of tracer balls and achieve a 3D reconstruction process. The reconstructed 3D systems are cross-sectioned through on the axis of the stirring paddle to form a 2D planar diagram of the tracer ball trajectories. The PD method is used to evaluate the mixing effectiveness of the 2D trajectory points, establishing evaluation metrics for the 2D mixing system. To ensure the accuracy of the PD method, a feasibility analysis was conducted using the conductometry. A relationship model between λ and mixing time was established, with a Pearson correlation coefficient (r) of -0.9867, indicating a strong negative linear correlation. The relationship between the planes and whole 3D space was analyzed in terms of the whole and the discrete perspective, as well as the existing methods were compared with other approaches. This study not only deepens the theoretical understanding of evaluating mixing uniformity but also provides a crucial foundation and theoretical basis for process optimization of stirring systems and design of stirred reactors. It offers valuable references and insights for engineering design and technological improvements in related fields.