Abstract We introduce a new Lagrangian particle tracking algorithm that tracks particles in three dimensions to separations between trajectories approaching contact. The algorithm also detects low Weber number binary collisions that result in coalescence as well as droplet breakup. Particles are identified in two-dimensional high-resolution digital images by finding sets of circles to describe the edge of each body. This allows identification of particles that overlap in projection by over 80% even for noisy images and without invoking additional temporal data. The algorithm builds trajectories from three-dimensional particle coordinates by minimizing a penalty function that is a weighted sum of deviations from the expected particle coordinates using information from four moments in time. This new hybrid algorithm is validated against synthetic data and found to perfectly reproduce more trajectories than other commonly used methods. Collisions are detected with 95% accuracy for particles that move on average less than one tenth the distance to their nearest neighbor. Graphic abstract

中文翻译：

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碰撞液滴的拉格朗日跟踪

摘要 我们介绍了一种新的拉格朗日粒子跟踪算法，该算法在三个维度上跟踪粒子到接近接触的轨迹之间的间隔。该算法还检测导致聚结和液滴破裂的低韦伯数二元碰撞。通过寻找一组圆来描述每个物体的边缘，在二维高分辨率数字图像中识别粒子。这允许识别在投影中重叠超过 80% 的粒子，即使对于嘈杂的图像并且无需调用额外的时间数据。该算法通过使用来自四个时刻的信息来最小化惩罚函数，该函数是与预期粒子坐标的偏差的加权总和，从而从三维粒子坐标构建轨迹。这种新的混合算法针对合成数据进行了验证，发现比其他常用方法可以完美地再现更多的轨迹。对于平均移动不到其最近邻居距离十分之一的粒子，碰撞检测的准确率为 95%。图形摘要