Measurement errors in the mean and fluctuation velocities of spherical grains from a computer analysis of digital images

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  • Haitao Xu
    Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14853
  • Anthony P. Reeves
    Department of Electrical and Computer Engineering, Cornell University, Ithaca, New York 14853
  • Michel Y. Louge
    Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14853

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<jats:p>We outline an algorithm to extract the mean and fluctuation velocities of identical spheres colliding in microgravity from a sequence of digital images. We analyze four kinds of intrinsic errors. The first two artificially reduce the apparent fluctuation velocity. They derive from the inability of the algorithm to track indistinguishable spheres moving with excessive speed, and from invisible collisions occurring between consecutive frames. The third is due to the finite pixel size. The resulting uncertainty in the position of the spheres increases the measured fluctuation velocity. The last arises from the partitioning of the flow domain in strips to calculate velocity profiles. While this last kind of error can always be reduced by increasing the number of images acquired, the first three cannot be made arbitrarily small without improving pixel resolution. Using microgravity experiments and numerical simulations of a shear flow, we illustrate insidious distortions of the mean and fluctuation velocity profiles that originate with the unavoidable errors that we have discussed.</jats:p>

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