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Scaling of interface displacement in a microfluidic comparator

Appl. Phys. Lett. 90, 114109 (2007); doi:10.1063/1.2713800

Published 15 March 2007

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S. A. Vanapalli, D. van den Ende, M. H. G. Duits, and F. Mugele
Physics of Complex Fluids, Department of Science and Technology, MESA+ Institute of Nanotechnology, University of Twente, P. O. Box 217, 7500 AE Enschede, The Netherlands
The authors quantify both experimentally and theoretically the scaling behavior between interface displacement and excess pressure drop in a microfluidic comparator. Unlike previous studies, the authors measure the interface displacement in the outlet channel of the comparator that yields a unique power-law scaling. For an outlet channel width to depth ratio r=3, the authors experimentally determine the scaling exponent to be 0.60±0.01, which is in excellent agreement with theory. In general, the authors find the scaling exponent to increase from 0.51 for square channels (r=1) to 0.93 for very wide channels (r>100). This geometry dependent scaling exponent offers greater sensitivity and flexibility in measurement of hydrodynamic resistance of soft objects. ©2007 American Institute of Physics
History: Received 20 November 2006; accepted 10 February 2007; published 15 March 2007
Permalink: http://link.aip.org/link/?APPLAB/90/114109/1
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KEYWORDS and PACS

Keywords
PACS
  • 47.85.Np
    Fluidics (applied)
  • 47.85.Dh
    Hydrodynamics, hydraulics, hydrostatics (applied)
  • 47.61.Fg
    Flows in micro-electromechanical systems (MEMS) and nano-electromechanical systems (NEMS)
  • 47.60.+i
    Flows in ducts, channels, nozzles, and conduits
  • 07.10.Cm
    Micromechanical devices and systems
  • YEAR: 2007

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PUBLICATION DATA

ISSN:
0003-6951 (print)   1077-3118 (online)
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REFERENCES (17)

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  5. Confocal imaging was done with 20× (for Pi=976 and 2581  Pa) and 100× (for Pi=7660  Pa) objectives at approximately the midplane of the fluidic device. The resulting images were analyzed using IMAGE J software and the interface displacement measured to within an error of ±600  nm.
  6. The three data points due to diffusional broadening were not considered in determining the overall scaling exponent.
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  8. From Fig. 1(a), we estimate alpha as L1W/LW1 and ignore the flow resistance in the comparator region.
  9. J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics (Prentice-Hall, Englewood Cliffs, NJ, 1965), 38, Chap. 2.
  10. R. F. Ismagilov, A. D. Stroock, P. J. A. Kenis, and G. M. Whitesides, Appl. Phys. Lett. 76, 2376 (2000).
  11. This relation was generated by obtaining the calculated values of the exponent m (from the exact velocity profile) for various values of r and using an interpolation scheme to fit the resultant data.
  12. For each channel aspect ratio, beta was determined by fitting a power law to the numerically generated data of DeltaY/W vs DeltaP/Pi in the range 0.01<=DeltaP/Pi<=1. We note that beta increases with increase in the range of DeltaP/Pi and does not deviate by no more than ±0.025 from the values reported in the inset of Fig. 2.
  13. F. H. J. van der Heyden, D. Stein, and C. Dekker, Phys. Rev. Lett. 95, 116104 (2005).
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  15. We estimate the diffusion-limited DeltaY as sqrt(2D tau ), where D is the diffusion coefficient of the dye and tau is the residence time. In our experiments, D[approximate]10−9  m2/s and tau[approximate]0.01  s, which gives DeltaY[approximate]4.5  µm and is comparable to the smallest measurable DeltaY of 5.4  µm.
  16. The hydrostatic head at the inlet of the reference channel was fixed at 548.8  mm and the pressure in the test channel varied until backflow was observed. The pressure for backflow was found to be 172.5±10.7  mm yielding DeltaP/Pi=2.2–2.4. The minor deviation from theory is due to rapid smearing of the interface during backflow.
  17. P. Garstecki, M. J. Fuerstman, and G. M. Whitesides, Nat. Phys.1, 168 (2005).

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