Computer aided optimisation of a constant shear-rate micro-channel contraction

Simon Higgins, Gregory J Sheard, Andreas Fouras, Kerry Hourigan


A combination of spectral element computational fluid dynamics simulation and the Levenberg--Marquardt non-linear optimisation algorithm are used to optimise a micro-channel contraction. The Levenberg--Marquardt algorithm finds the optimum contraction profile which minimises changes in the shear rate near the channel centreline. The primary criterion for the design of the micro-channel contraction is a constant shear rate in the flow direction. This is motivated by the need to study living cells in an environment of uniform shear.

  • Popescu, G., Park, Y., Choi, W., Dasari, R. R., Feld, M. S., Badizadegan, K., Imaging red blood cell dynamics by quantitative phase microscopy, Blood Cells, Molecules, and Diseases, 41, 2008, 10--16. doi:10.1016/j.bcmd.2008.01.010
  • Lee, S. S., Yim, Y., Kim, N. J., Ahn, K. H., Lee S. J., et al., Extension flow-induced red blood cell (rbc) deformation in the microchannel of contraction geometry. I. J. Vascular Biomedical Eng., 5, 2007, 8--13.
  • Dobbe, J. G. G., Hardemanb, M. R., Streekstrac, G. J., Strackeec, J., Inceb, C., and Grimbergen, C. A., Analyzing red blood cell-deformability distributions. Blood Cells, Molecules, and Diseases, 28, 2002, 373--284. doi:10.1006/bcmd.2002.0528
  • Linderkamp, O., and Meiselman, H. J., Geometric, osmotic, and membrene mechanical properties of density-separated human red cells, Blood 59, 1982, 1121--1127.
  • Nash, G. B., and Wyard, S. J., Changes is surface area and volume measured by micropipette aspiration for erythrocytes ageing in vivo, Biorheology, 17, 1981, 479--484.
  • Corry, W. D., and Meiselman, H. J., Deformation of human erthrocytes in a centrifugal field, Biophysical Journal, 21, 1978, 19--34
  • Eggleton, C. D., Popel, A. S., Large deformation of red blood cell ghosts in simple shear flow. Physics of Fluids, 10, 1998, 1823--1845. doi:10.1063/1.869703
  • Abkarian, M. and Viallat, A., Vesicles and red blood cells in shear flow. Royal Society Chemistry, 4, 2008, 653--657. doi:10.1039/b716612e
  • Sheard, G. J., Leweke, T., Thompson, M. C., Hourigan, K., Flow around an impulsively arrested circular cylinder. Physics of Fluids, 19, 2007 article number 083601. doi:10.1063/1.2754346
  • Sheard, G. J. and Ryan, K., Pressure-driven flow past spheres moving in a circular tube. J. Fluid Mech., 592, 2007 233--262. doi:10.1017/S0022112007008543
  • Sheard, G. J., Thompson, M. C. and Hourigan, K., From spheres to circular cylinders: the stability and flow structure of bluff ring wakes. J. Fluid Mech., 492, 2003, 147--180. doi:10.1017/S0022112003005512
  • Press, W. H., Teukolsky, S. A. Vetterling, W. T., Flannery, B. P., Numerical Recipes in C: The Art of Scientific Computing, Second Edition. Cambridge University Press, 1988 (ISBN 0-521-43108-5)

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