Electro-osmotic flow of couple stress fluids in a micro-channel propagated by peristalsis

Regular Article

Abstract.

A mathematical model is developed for electro-osmotic peristaltic pumping of a non-Newtonian liquid in a deformable micro-channel. Stokes' couple stress fluid model is employed to represent realistic working liquids. The Poisson-Boltzmann equation for electric potential distribution is implemented owing to the presence of an electrical double layer (EDL) in the micro-channel. Using long wavelength, lubrication theory and Debye-Huckel approximations, the linearized transformed dimensionless boundary value problem is solved analytically. The influence of electro-osmotic parameter (inversely proportional to Debye length), maximum electro-osmotic velocity (a function of external applied electrical field) and couple stress parameter on axial velocity, volumetric flow rate, pressure gradient, local wall shear stress and stream function distributions is evaluated in detail with the aid of graphs. The Newtonian fluid case is retrieved as a special case with vanishing couple stress effects. With increasing the couple stress parameter there is a significant increase in the axial pressure gradient whereas the core axial velocity is reduced. An increase in the electro-osmotic parameter both induces flow acceleration in the core region (around the channel centreline) and it also enhances the axial pressure gradient substantially. The study is relevant in the simulation of novel smart bio-inspired space pumps, chromatography and medical micro-scale devices.

References

  1. 1.
    Y. Kang, S.C. Tan, C. Yang, X. Huang, Sens. Actuators A: Phys. 133, 375 (2007)CrossRefGoogle Scholar
  2. 2.
    L. Jiang, J.C. Mikkelsen, J.-M. Koo, D. Huber, S. Yao, L. Zhang, P. Zhou, J.G. Maveety, R. Prasher, J.G. Santiago, T.W. Kenny, K.E. Goodson, IEEE Trans. Compon. Packag., Manufact. Technol. 25, 347 (2002)CrossRefGoogle Scholar
  3. 3.
    Y.K. Suh, S. Kang, Electroosmotic Pump, in Encyclopedia of Microfluidics and Nanofluidics, edited by D. Li (Springer, US, 2014) pp. 1--13Google Scholar
  4. 4.
    S. Zeng, C.-H. Chen, J.C. Mikkelsen, J.G. Santiago, Sens. Actuators B 79, 107 (2001)CrossRefGoogle Scholar
  5. 5.
    C.C. Huang, M.Z. Bazant, T. Thorsen, Lab Chip 10, 80 (2010)CrossRefGoogle Scholar
  6. 6.
    S. Liu, Q. Pu, J.J. Lu, J. Chromatogr. A 1013, 57 (2003)CrossRefGoogle Scholar
  7. 7.
    D. Rinderknecht, M.A. Gharib, Acta Futura 6, 9 (2013)Google Scholar
  8. 8.
    M.A. Benjaminson, S. Lehrer, D.A. Macklin, Acta Astron. 43, 329 (1998)CrossRefGoogle Scholar
  9. 9.
    V.K. Stokes, Theory of Fluids with Microstructure - An Introduction (Springer-Verlag, New York, 1984)Google Scholar
  10. 10.
    J. Lin, Comput. Struct. 79, 801 (2001)CrossRefGoogle Scholar
  11. 11.
    M. Nabhani, M. El Khilfi, B. Bou-Said, Tribology Int. 54, 116 (2013)CrossRefGoogle Scholar
  12. 12.
    D. Tripathi, Transp. Porous Media 92, 559 (2012)MathSciNetCrossRefGoogle Scholar
  13. 13.
    D. Pal, N. Rudraiah, R. Devanathan, Bull. Math. Biol. 50, 329 (1988)CrossRefGoogle Scholar
  14. 14.
    D. Tripathi, O. Anwar Bég, J. Mech. Med. Biol. 12, 1250088 (2012)CrossRefGoogle Scholar
  15. 15.
    Y.C. Fung, C.S. Yih, ASME J. Appl. Mech. 35, 669 (1968)ADSCrossRefGoogle Scholar
  16. 16.
    M.Y. Jaffrin, A.H. Shapiro, Annu. Rev. Fluid Mech. 3, 13 (1971)ADSCrossRefGoogle Scholar
  17. 17.
    T.D. Brown, T.K. Hung, J. Fluid Mech. 83, 249 (1977)ADSCrossRefGoogle Scholar
  18. 18.
    Y. Bar-cohen, Z. Chatig, Piezoelectrically-actuated miniature peristaltic pump, Caltech-Jet Propulsion Laboratory, Technical Report, Pasadena, California, USA (1991)Google Scholar
  19. 19.
    V. Shkolnikov, J. Ramunas, J.G. Santiago, Sens. Actuators A: Phys. 160, 141 (2010)CrossRefGoogle Scholar
  20. 20.
    E.F. Elsehawey, K.S. Mekheimer, J. Phys. D: Appl. Phys. 27, 1163 (1994)ADSCrossRefGoogle Scholar
  21. 21.
    K.S. Mekheimer, Y. Abdelmaboud, Phys. A: Stat. Mech. Appl. 387, 2403 (2008)CrossRefGoogle Scholar
  22. 22.
    V.P. Rathod, N.G. Sridhar, M. Mahadev, Adv. Appl. Sci. Res. 3, 2326 (2012)Google Scholar
  23. 23.
    K. Ramesh, M. Devakar, J. Fluids 2015, 163832 (2015)CrossRefGoogle Scholar
  24. 24.
    Y. Abdelmaboud, K.S. Mekheimer, A.I. Abdellateef, ASME J. Heat Transf. 135, 044502 (2013)CrossRefGoogle Scholar
  25. 25.
    D. Tripathi, O. Anwar Bég, Math. Biosci. 246, 72 (2013)MathSciNetCrossRefGoogle Scholar
  26. 26.
    S.-X. Li et al., Colloids Surf. A 470, 240 (2015)CrossRefGoogle Scholar
  27. 27.
    A.A. Siddiqui, A. Lakhtakia, Proc. R. Soc. London A 465, 501 (2009)ADSCrossRefGoogle Scholar
  28. 28.
    A.M. Afonso, M.A. Alves, F.T. Pinho, J. Eng. Math. 71, 15 (2011)CrossRefGoogle Scholar
  29. 29.
    J.J. Sousa, F.T. Pinho, M.A. Alves, Microfluidics Nanofluidics 10, 107 (2011)CrossRefGoogle Scholar
  30. 30.
    G.H. Tang, X.F. Li, Y.L. He, W.Q. Tao, J. Non-Newtonian Fluid Mech. 157, 133 (2009)CrossRefGoogle Scholar
  31. 31.
    G.H. Tang, P.X. Ye, W.Q. Tao, J. Non-Newtonian Fluid Mech. 165, 1536 (2010)CrossRefGoogle Scholar
  32. 32.
    X.X. Li, Z. Yin, Y.J. Jian, L. Chang, J. Su, A.S. Liu, J. Non-Newtonian Fluid Mech. 188, 43 (2012)CrossRefGoogle Scholar
  33. 33.
    M. Rezaei, A.R. Azimian, D. Toghraie, Phys. A: Stat. Mech. Appl. 426, 25 (2015)CrossRefGoogle Scholar
  34. 34.
    G.C. Shit, A. Mondal, A. Sinha, P.K. Kundu, Phys. A: Stat. Mech. Appl. 449, 437 (2016)CrossRefGoogle Scholar
  35. 35.
    G.C. Shit, A. Mondal, A. Sinha, P.K. Kundu, Phys. A: Stat. Mech. Appl. 462, 1040 (2016)CrossRefGoogle Scholar
  36. 36.
    M.F. El-Sayed, M.H. Haroun, D.R. Mostapha, J. Appl. Mech. Tech. Phys. 55, 565 (2014)ADSMathSciNetCrossRefGoogle Scholar
  37. 37.
    P. Goswami, J. Chakraborty, A. Bandopadhyay, S. Chakraborty, Microvascular Res. 103, 41 (2015)CrossRefGoogle Scholar
  38. 38.
    S. Chakraborty, J. Phys. D: Appl. Phys. 39, 5356 (2006)ADSCrossRefGoogle Scholar
  39. 39.
    D. Tripathi, S. Bhushan, O. Anwar Bég, Colloids Surf. A 506, 32 (2016)CrossRefGoogle Scholar
  40. 40.
    N. Rudraiah, B.M. Shankar, C.O. Ng, Spec. Top. Rev. Porous Media 2, 11 (2011)CrossRefGoogle Scholar
  41. 41.
    B.M. Shankar, J. Kumar, I.S. Shivakumara, Appl. Math. Modell. 40, 5462 (2016)CrossRefGoogle Scholar
  42. 42.
    N. Rudraiah, K.S. Mallika, N. Sujatha, J. Appl. Fluid Mech. 9, 71 (2016)CrossRefGoogle Scholar
  43. 43.
    N.S. Akbar, M. Raza, R. Ellahi, Eur. Phys. J. Plus 129, 155 (2014)CrossRefGoogle Scholar
  44. 44.
    N.S. Akbar, S.U. Rahman, R. Ellahi, S. Nadeem, Eur. Phys. J. Plus 129, 256 (2014)CrossRefGoogle Scholar
  45. 45.
    A. Zeeshan, R. Ellahi, M. Hassan, Eur. Phys. J. Plus 129, 261 (2014)CrossRefGoogle Scholar
  46. 46.
    N.S. Akbar, M. Raza, R. Ellahi, Eur. Phys. J. Plus 129, 185 (2014)CrossRefGoogle Scholar
  47. 47.
    R. Ellahi, M.M. Bhatti, I. Pop, Int. J. Numer. Methods Heat Fluid Flow 26, 1802 (2016)CrossRefGoogle Scholar
  48. 48.
    A.C. Eringen, Microcontinuum Field Theories: II Fluent Media (Springer, New York, 2001)Google Scholar
  49. 49.
    N.B. Naduvinamani, A. Siddangouda, Proc. IMechE Part J: J. Eng. Tribol. 221, 525 (2007)CrossRefGoogle Scholar
  50. 50.
    S.C. Cowin, Adv. Appl. Mech. 14, 279 (1974)CrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Dharmendra Tripathi
    • 1
  • Ashu Yadav
    • 1
  • O. Anwar Bég
    • 2
  1. 1.Department of Mechanical EngineeringManipal University JaipurRajasthanIndia
  2. 2.Fluid Mechanics and Propulsion, Department of Mechanical and Aeronautical EngineeringSalford UniversitySalfordUK

Personalised recommendations