A New Experimental Technique-Magnetic Particle Tracking and Its Application in Granular Flow

Abstract

Granular flows are omnipresent in nature and they have broad scientific and engineering applications. Current study has benefitted a lot from the development of advanced particle tracking technologies. Some technologies are optical based method (e.g. Lagrangian particle tracking), the accuracy of them is high but they have the limitation in an opaque environment or granular flows; Some techniques use radioactive materials for particle tracking, it can be conducted for granular flow but it is very expensive and require special safe training. We present a new development in the magnetic particle tracking (MPT) technology which can capture the motions of a small particle without optical devices and it is free from radioactive materials. Another advantage of MPT is that it can also acquire rotational information of the particle which other techniques can hardly do. The reconstruction process of MPT using a standard optimization approach is very time consuming, therefore limits its application. In this work, two new MPT reconstruction algorithms are examined and the results are compared with the optimization method. The extended Kalman filter (EKF) algorithm has the same accuracy as the optimization method but is orders of magnitude faster. The speed of sequential importance sampling (SIR) approach is between the optimization method and EKF algorithm. The reconstruct trajectory of this technique is compared with high speed cameras, the accuracy of position obtained using EKF is about 0.6% and the uncertainty of orientation is less than 1.5°. These advantages of MPT method with EKF algorithm makes it a great tool for studying granular flows. It is applied to a Couette cell to study the dynamics of a tracer particle in a shear flow. Two experiments are conducted with different granular material for various purposes. One is using smaller copper ball with different shear rate the other is a cylindrical plastic tracer with an aspect ratio of 1 at a constant shear rate. The trajectories of the tracer particle in both experiments show that the grains in a Couette cell with a spilt bottom moves in a layered structure. The velocity of the particle obtained from the cylindrical tracer is higher in the space between the layers, which suggests that the jumping process between layers is fast. The orientation of particle shows that the cylindrical tracer particle has a preference align in specific directions even though with a low aspect ratio and the shear stress should not cause strong alignment. We use a symbolic based method to examine the jumping and flipping process and the result shows that the durance of particle staying in a preferred state is much longer than in the transition process, and the flipping and jumping are more likely to occur simultaneously. The energy distribution of translation and rotation velocity in discrete zones shows in the near center place these two are approximately the same magnitude. The rotational energy is more stable across different radius while the translational energy varies significantly respect to different radius.