Lagrangian tracking of colliding droplets

TL;DR

This paper presents a novel 3D Lagrangian particle tracking algorithm capable of accurately tracking droplet trajectories, detecting collisions, coalescence, and break-up in noisy images, validated against synthetic data.

Contribution

The paper introduces a hybrid Lagrangian tracking algorithm that improves trajectory reconstruction and collision detection accuracy over existing methods.

Findings

Perfectly reproduces more trajectories than other methods.

Detects collisions with 95% accuracy for slow-moving particles.

Identifies overlapping particles in noisy images without temporal data.

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 break-up. 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.