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Applied Mathematics and Mechanics

, Volume 39, Issue 3, pp 395–408 | Cite as

Fluid flow driven along microchannel by its upper stretching wall with electrokinetic effects

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Abstract

We develop a mathematical model to describe the flow in a microchannel driven by the upper stretching wall of the channel in the presence of electrokinetic effects. In this model, we avoid imposing any unphysical boundary condition, for instance, the zero electrostatic potential in the middle of the channel. Using the similarity transformation, we employ the homotopy analysis method (HAM) to get the analytical solution of the model. In our approach, the unknown pressure constant and the integral constant related to the electric potential are solved spontaneously by using the proper boundary conditions on the channel walls, which makes our model consistent with the commonly accepted models in the field of fluid mechanics. It is expected that our model can offer a general and proper way to study the flow phenomena in microchannels.

Keywords

microchannel electrokinetic effect stretching wall electro-viscous flow model 

Chinese Library Classification

O361 

2010 Mathematics Subject Classification

76D05 76M55 65D99 

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Notes

Acknowledgements

This work is supported in part by the Australian Research Council through a Discovery Early Career Researcher Award to Qiang SUN.

References

  1. [1]
    Qu, W. and Mudawar, I. Experimental and numerical study of pressure drop and heat transfer in a single-phase micro-channel heat sink. International Journal of Heat and Mass Transfer, 45, 2549–2565 (2002)CrossRefGoogle Scholar
  2. [2]
    Vafai, K. and Khaled, A. R. A. Analysis of flexible microchannel heat sink systems. International Journal of Heat and Mass Transfer, 48, 1739–1746 (2005)CrossRefMATHGoogle Scholar
  3. [3]
    Figeys, D. and Pinto, D. Lab-on-a-chip: a revolution in biological and medical sciences. Analytical Chemistry, 72, 330–335 (2000)CrossRefGoogle Scholar
  4. [4]
    Tripathi, D., Sharma, A., and Bég, O. A. Electrothermal transport of nanofluids via peristaltic pumping in a finite micro-channel: effects of Joule heating and Helmholtz-Smoluchowski velocity. International Journal of Heat and Mass Transfer, 11, 138–149 (2017)CrossRefGoogle Scholar
  5. [5]
    Eringen, A. C. Simple microfluids. International Journal of Engineering Science, 2, 205–217 (1964)MathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    Pfahler, J., Harley, J., Bau, H., and Zemel, J. Liquid transport in micron and submicron channels. Sensors and Actuators A: Physical, 22, 431–434 (1990)CrossRefGoogle Scholar
  7. [7]
    Mala, G. M., Li, D. Q., and Dale, J. D. Heat transfer and fluid flow in microchannels. International Journal of Heat and Mass Transfer, 40, 3079–3088 (1997)CrossRefMATHGoogle Scholar
  8. [8]
    Mala, G. M., Li, D.Q., Werner, C., Jacobasch, H. J., and Ning, Y. B. Flow characteristics of water through a microchannel between two parallel plates with electrokinetic effects. International Journal of Heat and Fluid Flow, 18, 489–496 (1997)CrossRefGoogle Scholar
  9. [9]
    Ren, L. Q., Qu, W. L., and Li, D. Q. Interfacial electrokinetic effects on liquid flow in microchannels. International Journal of Heat Mass Transfer, 44, 3125–3134 (2001)CrossRefMATHGoogle Scholar
  10. [10]
    Berman, A. S. Laminar flow in channels with porous walls. Journal of Applied Physics, 24, 1232–1235 (1953)MathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    Sellars, J. R. Laminar flow in channels with porous walls at high suction Reynolds numbers. Journal of Applied Physics, 26, 489–490 (1955)CrossRefMATHGoogle Scholar
  12. [12]
    Taylor, G. I. Fluid flow in regions bounded by porous surfaces. Proceedings of the Royal Society of London Seriers A, 234, 456–475 (1956)CrossRefMATHGoogle Scholar
  13. [13]
    Proudman, I. An example of steady laminar flow at large Reynolds number. Journal of Fluid Mechanics, 9, 593–602 (1960)MathSciNetCrossRefMATHGoogle Scholar
  14. [14]
    Shrestha, G. M. Singular perturbation problems of laminar flow in a uniformly porous channel in the presence of a transverse magnetic field. Quarterly Journal of Mechanics and Applied Mathematics, 20, 233–246 (1967)CrossRefMATHGoogle Scholar
  15. [15]
    Skalak, F. M. and Wang, C. Y. On the nonunique solutions of laminar flow through a porous tube or channel. SIAM Journal on Mathematical Analysis, 34, 535–544 (1978)MathSciNetMATHGoogle Scholar
  16. [16]
    Brady, J. F. and Acrivos, A. Steady flow in a channel or tube with an acceleration surface velocity: an exact solution to the Navier-Stokes equations with reverse flow. Journal of Fluid Mechanics, 112, 127–150 (1981)MathSciNetCrossRefMATHGoogle Scholar
  17. [17]
    Brady, J. F. Flow development in a porous channel and tube. Physics and Fluids, 27, 1061–1067 (1984)CrossRefGoogle Scholar
  18. [18]
    Watson, E. B. B., Banks, W. H. H., Zaturska, M. B., and Drazin, P. G. On transition to chaos in two-dimensional channel flow symmetrically driven by accelerating walls. Journal of Fluid Mechanics, 212, 451–485 (1990)MathSciNetCrossRefMATHGoogle Scholar
  19. [19]
    Dauenhauer, E. C. and Majdalani, J. Exact self-similarity solution of the Navier-Stokes equations for a porous channel with orthogonally moving walls. Physics of Fluids, 15, 1485–1495 (2003)MathSciNetCrossRefMATHGoogle Scholar
  20. [20]
    Liao, S. J. Beyond Perturbation: Introduction to the Homotopy Analysis Method, Chapman & Hall/CRC Press, Boca Raton (2003)CrossRefGoogle Scholar
  21. [21]
    Chung, T. J. Computational Fluid Dynamics, Cambridge University Press, Cambridge (2002)CrossRefMATHGoogle Scholar
  22. [22]
    Hunter, R. J. Zeta Potential in Colloid Science: Principles and Applications, Academic Press, New York (1981)Google Scholar
  23. [23]
    Burgreen, D. and Nakache, F. R. Electrokinetic flow in ultrafine capillary slits. Journal of Physical Chemistry B, 68, 1084–1091 (1964)CrossRefGoogle Scholar

Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, State Key Lab of Ocean Engineering, School of Naval Architecture, Ocean and Civil EngineeringShanghai Jiao Tong UniversityShanghaiChina
  2. 2.Department of MathematicsBabeş-Bolyai UniversityCluj-NapocaRomania
  3. 3.Particulate Fluids Processing Centre, Department of Chemical EngineeringThe University of MelbourneParkvilleAustralia

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