Skip to main content
Log in

Determination of velocity profiles of Bird-Carreau fluids in curvilinear microchannels using random sample consensus

  • Short Communication
  • Published:
Korea-Australia Rheology Journal Aims and scope Submit manuscript

Abstract

Flow features of rheologically complex fluids inside curved microchannels should be meaningfully scrutinized for effective mixing, sorting, and manipulation of nano- and micro-sized colloids or particles. In this study, a particle streak velocimetry method with coordinate transformation is incorporated to depict experimentally the axial velocity profiles of Newtonian and non-Newtonian (Bird-Carreau, BC) fluids in a curvilinear microchannel under constant flow rate conditions. Theoretical velocity distributions for both fluids are favorably substantiated from experimental observations that employ a random sample consensus (RanSAC) algorithm under various channel geometric conditions, demonstrating the good agreement between experiments and simulations previously developed. It is confirmed that the BC fluid showed blunt and non-parabolic profiles in comparison to the Newtonian case at a low Dean number. The suggested algorithm and method for accurately observing microscale flow fields provide useful insights into the elaborate manipulation and processing of non-Newtonian fluids in curved channel devices.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  • Adrian, R.J., 1991, Particle-imaging techniques for experimental fluid mechanics, Annu. Rev. Fluid Mech.23, 261–304.

    Article  Google Scholar 

  • Bayat, P. and P. Rezai, 2017, Semi-empirical estimation of dean flow velocity in curved microchannels, Sci. Rep.7, 13655.

    Article  Google Scholar 

  • Bird, R.B., R.C. Armstrong, and O. Hassager, 1987, Dynamics of Polymeric Liquids: Vol. 1. Fluid Mechanics, 2nd Ed., John Wiley & Sons, New York.

    Google Scholar 

  • Chun, M.-S. and S. Lee, 2005, Flow imaging of dilute colloidal suspension in PDMS-based microfluidic chip using fluorescence microscopy, Colloid. Surf. A267, 86–94.

    Article  CAS  Google Scholar 

  • Chun, M.-S., T.S. Lee, and K. Lee, 2005, Microflow of dilute colloidal suspension in narrow channel of microfluidic-chip under Newtonian fluid slip condition, Korea-Aust. Rheol. J.17, 207–215.

    Google Scholar 

  • De Vriend, H.J., 1981, Velocity redistribution in curved rectangular channels, J. Fluid Mech.107, 423–439.

    Article  CAS  Google Scholar 

  • Dean, W.R., 1927, XVI. Note on the motion of fluid in a curved pipe, Philos. Mag.4, 208–223.

    Article  Google Scholar 

  • Degré, G., P. Joseph, and P. Tabeling, 2006, Rheology of complex fluids by particle image velocimetry in microchannels, Appl. Phys. Lett.89, 024104.

    Article  Google Scholar 

  • Di Carlo, D., D. Irimia, R.G. Tompkins, and M. Toner, 2007, Continuous inertial focusing, ordering, and separation of particles in microchannels, Proc. Natl. Acad. Sci. U. S. A.104, 18892–18897.

    Google Scholar 

  • Fischler, M.A. and R.C. Bolles, 1981, Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography, Commun. ACM24, 381–395.

    Article  Google Scholar 

  • Garcia, M. and S. Pennathur, 2019, A model for inertial particles in curvilinear flows, Microfluid. Nanofluid.23, 63.

    Article  Google Scholar 

  • Khodaparast, S., N. Borhani, G. Tagliabue, and J.R. Thome, 2013, A micro particle shadow velocimetry (μPSV) technique to measure flows in microchannels, Exp. Fluids54, 1474.

    Article  Google Scholar 

  • Lima, R., S. Wada, K. Tsubota, and T. Yamaguchi, 2006, Confocal micro-PIV measurements of three-dimensional profiles of cell suspension flow in a square microchannel, Meas. Sci. Technol.17, 797–808.

    Article  CAS  Google Scholar 

  • Lochab, V., A. Yee, M. Yoda, A.T. Conlisk, and S. Prakash, 2019, Dynamics of colloidal particles in microchannels under combined pressure and electric potential gradients, Microfluid. Nanofluid.23, 134.

    Article  CAS  Google Scholar 

  • McClain, M.A., C.T. Culbertson, S.C. Jacobson, N.L. Allbritton, C.E. Sims, and J.M. Ramsey, 2003, Microfluidic devices for the high-throughput chemical analysis of cells, Anal. Chem.75, 5646–5655.

    Article  CAS  Google Scholar 

  • Nekoubin, N., 2018, Electroosmotic flow of power-law fluids in curved rectangular microchannel with high zeta potentials, J. Non-Newtonian Fluid Mech.260, 54–68.

    Article  CAS  Google Scholar 

  • Nivedita, N., P. Ligrani, and I. Papautsky, 2017, Dean flow dynamics in low-aspect ratio spiral microchannels, Sci. Rep.7, 44072.

    Article  Google Scholar 

  • Patankar, S.V., 1980, Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York.

    Google Scholar 

  • Paul, P.H., M.G. Garguilo, and D.J. Rakestraw, 1998, Imaging of pressure- and electrokinetically driven flows through open capillaries, Anal. Chem.70, 2459–2467.

    Article  CAS  Google Scholar 

  • Shen, S., L. Kou, X. Zhang, D. Wang, Y. Niu, and J. Wang, 2018, Regulating secondary flow in ultra-low aspect ratio microchannels by dimensional confinement, Adv. Theory Simul.1, 1700034.

    Article  Google Scholar 

  • Stone, H.A., A.D. Stroock, and A. Ajdari, 2004, Engineering flows in small devices: Microfluidics toward a lab-on-a-chip, Annu. Rev. Fluid Mech.36, 381–411.

    Article  Google Scholar 

  • Thangam, S. and N. Hur, 1990, Laminar secondary flows in curved rectangular ducts, J. Fluid Mech.217, 421–440.

    Article  CAS  Google Scholar 

  • Volpe, A., P. Paiè, A. Ancona, R. Osellame, P.M. Lugarà, and G. Pascazio, 2017, A computational approach to the characterization of a microfluidic device for continuous size-based inertial sorting, J. Phys. D: Appl. Phys.50, 255601.

    Article  Google Scholar 

  • Yang, W.J., 1989, Handbook of Flow Visualization, Hemisphere Publishing Co., New York.

    Google Scholar 

  • Yoon, K., H.W. Jung, and M.-S. Chun, 2017, Secondary flow behavior of electrolytic viscous fluids with Bird-Carreau model in curved microchannels, Rheol. Acta56, 915–926.

    Article  CAS  Google Scholar 

  • Yoon, K., H.W. Jung, and M.-S. Chun, 2020, Secondary Dean flow characteristics of inelastic Bird-Carreau fluids in curved microchannels, Korea-Aust. Rheol. J.32, 61–70.

    Article  Google Scholar 

  • Yun, J.H., M.-S. Chun, and H.W. Jung, 2010, The geometry effect on steady electrokinetic flows in curved rectangular microchannels, Phys. Fluids22, 052004.

    Article  Google Scholar 

Download references

Acknowledgements

This research was supported by the KIST Institutional Program (project No. 2E29720 and No. 2E30580) provided to M.-S. Chun and by the National Research Foundation of Korea (NRF) of Korea grant (No. 2016R1A5A1009592 and No. 2017R1E1A1A01075107) provided to H.W. Jung.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Hyun Wook Jung or Myung-Suk Chun.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yoon, K., Jung, H.W. & Chun, MS. Determination of velocity profiles of Bird-Carreau fluids in curvilinear microchannels using random sample consensus. Korea-Aust. Rheol. J. 32, 159–164 (2020). https://doi.org/10.1007/s13367-020-0015-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13367-020-0015-4

Keywords

Navigation