Journal of computational fluids engineering (한국전산유체공학회지)

Korean Society of Computational Fluids Engineering (한국전산유체공학회)
권호 표지
DOI QR코드

DOI QR Code

STOKES FLOW THROUGH A MICROCHANNEL WITH PROTUBERANCES OF STAGGERED ARRANGEMENT

엇갈린 배열의 돌출물들이 존재하는 마이크로채널 내의 스톡스 유동

  • Son, Jeong Su (School of Mechanical Engineering, Chonnam National Univ.) ;
  • Jeong, Jae-Tack (School of Mechanical Engineering, Chonnam National Univ.)
  • Received : 2015.11.06
  • Accepted : 2015.11.17
  • Published : 2015.12.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this study, the Stokes flow in the microchannel is analysed where the semicircular protuberances with constant spacing are attached on the upper and lower walls with staggered arrangement. For the low Reynolds number flow in microchannel, Stokes approximation is used and the periodicity and symmetry of the flow are considered to determine the stream function and pressure distribution in the flow field by using the method of least squared error. As results, the streamline patterns and pressure distributions in the flow field are shown for some specific values of the size and spacing of the protuberances, and shear stress distributions on the surface of semicircular protuberances are plotted. Especially, for an important physical property, the average pressure gradient along the microchannel is obtained and compared with that for the case of in-phase arrangement of the upper and lower protuberances. And, for the small clearance between the protuberances of upper and lower walls or between the protuberances and the opposite wall, the average pressure gradient is derived from the lubrication theory and compared with that of the present study.

Keywords

References

  1. 2012, Nguyen, N.-T., Micromixers Fundamentals Design and Fabrication, Second Ed., Elsevier, Waltham, pp.321-342.
  2. 2010, Berthier, J. and Silberzan, P., Microfluidics for Biotechnology, Second Ed., Artech House, Norwood, pp.17-72.
  3. 2009, Sun, Z.-X., Li, Z.-Y., He, Y.-L. and Tao. W.-Q., "Coupled solid (FVM) - fluid (DSMC) simulation of micro-nozzle with unstructured-grid," Micro-Nano fluids, Vol.7, pp.621-631. https://doi.org/10.1007/s10404-009-0418-5
  4. 2001, Wang, C.Y., "Flow in a Channel With Longitudinal Tubes," J. Fluids Eng.-Trans. ASME, Vol.123, pp.157-160. https://doi.org/10.1115/1.1335496
  5. 1997, Wang, C.Y., "Stokes Flow Through a Transversely Finned Channel," J. Fluids Eng.-Trans. ASME, Vol.119, pp.110-114. https://doi.org/10.1115/1.2819095
  6. 2014, Inasawa, A., Floryan, J.M. and Asai, M., "Flow Recovery Downstream from a Surface Protuberance," Theor. Comput. Fluid Dyn., Vol.28, pp.427-447. https://doi.org/10.1007/s00162-014-0321-x
  7. 2010, Pozrikidis, C., "Stokes Flow through a Permeable Tube," Arch.. Appl. Mech., Vol.80, pp.323-333. https://doi.org/10.1007/s00419-009-0319-9
  8. 1993, Davis, A.M.J., "Periodic blocking in parallel shear or channel flow at low Reynolds number," Phys. Fluids, Vol.5, pp.800-809. https://doi.org/10.1063/1.858628
  9. 2013, Meftah, M. B. and Mossa, M., "Prediction of Channel Flow Characteristics through Square Arrays of Emergent Cylinders," Phys. Fluids, Vol.25, 045102. https://doi.org/10.1063/1.4802047
  10. 2006, Kirsh, V.A., "Stokes flow in periodic systems of parallel cylinders with porous permeable shells," Colloid. J., Vol.68, pp.173-181. https://doi.org/10.1134/S1061933X06020086
  11. 2006, Jeong, J.-T., "Two dimensional Stokes flow through a slit in a microchannel with slip," J. Phys. Soc. Jpn., Vol.75, No.9, 094401. https://doi.org/10.1143/JPSJ.75.094401
  12. 2013, Jeong, J.-T. and Yoon, S.-H., "Two-Dimensional Stokes Flow around a Circular Cylinder in a Microchannel," J. Mech. Sci. Technol., Vol.28, pp.573-579.
  13. 2014, Jeong, J.-T. and Jang, C.-S., "Slow motion of a circular cylinder in a plane Poiseuille flow in a microchannel," Phys. Fluids, Vol.26, No.12, 123104. https://doi.org/10.1063/1.4903477
  14. 2015, Son, J.S. and Jeong, J.-T., "Stokes flow through a microchannel with protuberances of constant spacing," Trans. Korean Soc. Mech. Eng. B, Vol.39, pp.335-341. https://doi.org/10.3795/KSME-B.2015.39.4.335
  15. 2010, Cengel, Y.A. and Cimbala, J.M., Fluid Mechanics Fundamentals and Applications, McGraw-Hill, New York, pp.419-475.
  16. 2011, Kreyszig, E., Advanced Engineering Mathematics, Wiley, Hoboken, pp.473-539.
  17. 2012, Chapra, S.C., Numerical Methods for Engineers, McGraw-Hill, New York, pp.336-344.
  18. 1964, Moffatt, H.K., "Viscous and Resistive Eddies near a Sharp Corner," J. Fluid Mech., Vol.18, pp.1-18. https://doi.org/10.1017/S0022112064000015
  19. 2000, Day, R.F. and Stone, H.A., "Lubrication Analysis and Boundary Integral Simulations of a Viscous Micropump," J. Fluid Mech., Vol.416, pp.197-216. https://doi.org/10.1017/S002211200000879X