Fluid Mechanics and Transport Phenomena

Telescopic time-scale bridging for modeling dispersion in rapidly oscillating flows

  1. Ram K. Balachandran1,
  2. Jaijeet Roychowdhury2,
  3. Kevin D. Dorfman3,
  4. Victor H. Barocas4,*

Article first published online: 30 AUG 2011

DOI: 10.1002/aic.12721

Issue

AIChE Journal

AIChE Journal

Volume 58, Issue 7, pages 1987–1997, July 2012

Additional Information

How to Cite

Balachandran, R. K., Roychowdhury, J., Dorfman, K. D. and Barocas, V. H. (2012), Telescopic time-scale bridging for modeling dispersion in rapidly oscillating flows. AIChE J., 58: 1987–1997. doi: 10.1002/aic.12721

Author Information

  1. 1

    Dept. of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455

  2. 2

    Dept. of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA 94720

  3. 3

    Dept. of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455

  4. 4

    Dept. of Biomedical Engineering, University of Minnesota, Minneapolis, MN 55455

*Dept. of Biomedical Engineering, University of Minnesota, Minneapolis, MN 55455

Publication History

  1. Issue published online: 7 JUN 2012
  2. Article first published online: 30 AUG 2011
  3. Accepted manuscript online: 7 JUL 2011 07:44AM EST
  4. Manuscript Revised: 11 MAY 2011
  5. Manuscript Received: 26 JAN 2011

Funded by

  • Institute for Engineering and Medicine at the University of Minnesota
  • National Institute for Health. Grant Number: R03 EB007815

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Keywords:

  • saccadic motion;
  • envelope tracking;
  • vitreous liquefaction

Abstract

Analytical solution of dispersion in rapidly oscillating flows becomes infeasible in complex geometries. Simulation over long durations can be prohibitively expensive when there is a wide separation between the oscillation and dispersion time scales. Here, we present a methodology based on an implicit envelope-tracking scheme coupled with telescopic projections. A test problem, with a known analytical solution, was simulated, and the effect of Péclet number on the dispersivities was investigated. The solution was unaffected by the time steps for telescopic projections while increasing Péclet numbers introduced errors. The error was found to decrease with mesh refinement, but a small inherent error was observed. The method was also applied to a practical problem of interest to us: drug dispersion due to sloshing in the vitreous humor of the eye. Relative to single-scale solution, the method, when applied to the vitreous sloshing problem, produced speedup values of up to 100. © 2011 American Institute of Chemical Engineers AIChE J, 2012

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