Ensuring adequate statistics in particle tracking experiments

Abstract

Particle tracking techniques such as magnetic particle tracking, radioactive particle tracking and positron emission particle tracking are widely used in academia and industry to image the dynamics of particulate and multiphase systems. These techniques can provide detailed data concerning a range of important, whole-field quantities based only on the time-averaged dynamics of a small number of tracer particles. However, in order for this data to be reliable, the duration over which these time-averages are taken must be suitably long. Further, the ‘minimum averaging time’ required to produce good statistics depends sensitively on the system in question and, at present, cannot be determined a priori in advance of an experiment. In this paper, we take a step toward resolving this issue, using discrete element method simulations of a simple vibrofluidised granular bed to develop a series of scaling laws relating said minimum averaging time to a variety of key system variables. The scaling laws developed may be used by future experimentalists to predict the required averaging time for each given system during an experimental campaign, thus improving both the efficiency with which particle tracking techniques may be applied, and the reliability of the data produced thereby.