, Volume 8, Issue 3, pp 723–734 | Cite as

Electro-osmotic Flow of Non-Newtonian Biofluids Through Wavy Micro-Concentric Tubes

  • Kh. S. Mekheimer
  • R. E. Abo-Elkhair
  • A. M. A. MoawadEmail author


Most biofluids are non-Newtonian fluids with complex flow behaviors; for instance, human blood and DNA samples are shear thinning fluids (Jeffery model). The electro-kinetic transport of such fluids by microperistaltic pumping has been a topic of interest in biomedical engineering and other medical fields. This type of fluid transport requires sophisticated mathematical models and numerical simulations. Motivated by these developments, this study analyzed the simultaneous effects of an electric double layer (EDL) and a transverse magnetic field on the peristaltic flow and transport of blood. However, electro-osmotic flow is most significant when in micro channels/tubes. A constitutive relation is proposed to describe the electro-osmotic flow in the gap between two micro-coaxial horizontal pipes. Under low Reynolds number, long wavelength and Debye linearization approximations, the Poisson-Boltzmann equation, and governing equations are derived with the appropriate boundary conditions. The expressions for the electric potential, stream function, axial velocity, shear wall stress, and axial pressure gradient are obtained. The pressure rise and frictional force per wavelength are numerically evaluated and briefly discussed. The computational evidence suggests that the electric potential is an increasing function of the EDL thickness. Additionally, axial flow is accelerated by a positive electric field and decelerated by a negative electric field. Finally, the bolus size is reduced as the axial external electric field changes from the positive to negative direction.


Electro-osmotic flow Magnetic field Jeffrey fluid Endoscope 


  1. 1.
    Hunter, R.J. (1989). Foundations of colloid science. UK: Oxford University Press.Google Scholar
  2. 2.
    Kang, Y., Tan, S.C., Yang, C., Huang, X. (2007). Electrokinetic pumping using packed microcapillary. Sensors and Actuators A: Physical, 133, 375–382.CrossRefGoogle Scholar
  3. 3.
    Yang, H., Jiang, H., Ramos, A., García-Sánchez, P. (2009). AC Electrokinetic pumping on symmetric electrode arrays. Microfluidics and Nanofluidics, 7, 767.CrossRefGoogle Scholar
  4. 4.
    Sayar, E., & Farouk, B. (2012). Multi-field analysis of a piezoelectric valveless micropump: effects of actuation frequency and electric potential. Smart Materials and Structures, 075002, 21.Google Scholar
  5. 5.
    Tripathi, D., Bhushan, S., Anwar Bg, O. (2017). Analytical study of electro-osmosis modulated capillary peristaltic hemodynamics, Journal of Mechanics, 17, (03). 1750052 (22 pages).
  6. 6.
    Abo-Elkhair, R.E., Mekheimer, Kh.S., Moawad, A. M. A. (2017). Combine impacts of electrokinetic variable viscosity and partial slip on peristaltic MHD flow through a micro-channel, Iran J Sci Technol Trans Sci.
  7. 7.
    Mekheimer, Kh.S. (2008). Effect of the induced magnetic field on peristaltic flow of a couple stress fluid. Physics Letters A, 372, 4271–4278.CrossRefGoogle Scholar
  8. 8.
    Abo-Elkhair, R. E., Mekheimer, Kh. S., Moawad, A. M. A. (2017). Cilia walls influence on peristaltically induced motion of magneto-fluid through a porous medium at moderate Reynolds number: numerical study. Journal of the Egyptian Mathematical Society, 25(2), 238–251.MathSciNetCrossRefGoogle Scholar
  9. 9.
    Ealshahed, M., & Haroun, M. H. (2005). Peristaltic transport of Johnson-Segalman fluid under effect of a magnetic field. Mathematical Problems in Engineering, 6(8), 663–677.MathSciNetCrossRefGoogle Scholar
  10. 10.
    Hayat, T., Nisar, Z., Ahmad, B., Yasmin, H. (2015). Simultaneous effects of slip and wall properties on MHD peristaltic motion of nanofluid with Joule heating. Journal of Magnetism and Magnetic Materials, 395, 48–58.CrossRefGoogle Scholar
  11. 11.
    Akbar, N. S., Tripathi, D., Anwar Bég, O. (2016). Modelling nanoparticle geometry effects on peristaltic pumping of medical magnetohydrodynamic nanofluids with heat transfer. Journal of Mechanics, 16(2), 1650088.1–1650088.20.Google Scholar
  12. 12.
    Ebaid, A. (2008). A new numerical solution for the MHD peristaltic flow of a biofluid with variable viscosity in circular cylindrical tube via Adomian decomposition method. Physics Letters A, 372(32), 5321–5328.MathSciNetCrossRefGoogle Scholar
  13. 13.
    Hayat, T., Shafique, M., Tanveer, A., Alsaedi, A. (2016). Magnetohydrodynamic effects on peristaltic flow of hyperbolic tangent nanofluid with slip conditions and Joule heating in an inclined channel. Int. J. Heat Mass Transf., 102, 54–63.CrossRefGoogle Scholar
  14. 14.
    Tripathi, D., & Anwar Bg, O. (2012). A study of unsteady physiological magneto-fluid flow and heat transfer through a finite length channel by peristaltic pumping. Proceedings of the Institution of Mechanical Engineers, Part H-j. Engineering in Medicine, 226, 631–644.CrossRefGoogle Scholar
  15. 15.
    Hayat, T., Farooq, S., Ahmad, B., Alsaedi, A. (2016). Homogeneous-heterogeneous reactions and heat source/sink, effects in MHD peristaltic flow of micropolar fluid with Newtonian heating in a curved channel. Journal of Molecular Liquids, 223, 469–488.CrossRefGoogle Scholar
  16. 16.
    Bhatti, M.M., Zeeshan, A., Ijaz, N., Anwar Bg, O., Kadir, A. (2016). Mathematical modelling of nonlinear thermal radiation effects on EMHD peristaltic pumping of viscoelastic dusty fluid through a porous medium channel, Engineering Science and Technology, (in press).
  17. 17.
    Ramos, A. (2008). Electrohydrodynamic and magneto-hydrodynamic micropumps. In Hardt, S., & Schönfeld, F. (Eds.) Microfluidics Technologies for Miniaturized Analysis Systems (pp. 59–116).Google Scholar
  18. 18.
    Tripathi, D., Bhushan, S., Anwar Bg, O. (2016). Transverse magnetic field driven modification in unsteady peristaltic transport with electrical double layer effects. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 506, 32–39.CrossRefGoogle Scholar
  19. 19.
    El Naby, A. E. H. A., & El Misiery, A. E. M. (2002). Effects of an endoscope and generalized Newtonian fluid on peristaltic motion. Applied Mathematics and Computation, 128(1), 19–35.MathSciNetCrossRefGoogle Scholar
  20. 20.
    Mekheimer, K. S. (2008). Peristaltic flow of a couple stress fluid in an annulus: application of an endoscope. Physica A: Statistics, Mechanics and Applied, 387(11), 2403–2415.CrossRefGoogle Scholar
  21. 21.
    Mekheimer, K. S., & Abd Elmaboud, Y. (2008). The influence of heat transfer and magnetic field on peristaltic transport of a Newtonian fluid in a vertical annulus: application of an endoscope. Physics Letters A, 372, 1657–1665.CrossRefGoogle Scholar
  22. 22.
    Akbar, N. S., & Nadeem, S. (2012). Characteristics of heating scheme and mass transfer on the peristaltic flow for an Eyring-Powell fluid in an endoscope. International Journal of Heat and Mass Transfer, 55(1), 375–383.CrossRefGoogle Scholar
  23. 23.
    Bhatti, M. M., Zeeshan, A., ljaz, N. (2016). Slip effects and endoscopy analysis on blood flow of particle-fluid suspension induced by peristaltic wave. Journal of Molecular Liquids, 218, 240–245.CrossRefGoogle Scholar
  24. 24.
    El-dabe, N. T. M., Moatimid, G. M., Hassan, M. A., Mostapha, D. R. (2016). Electrohydrodynamic peristaltic flow of a viscoelastic Oldroyd fluid with a mild stenosis: application of an endoscope. Journal of Applied Mechanics and Technical Physics, 57(1 ), 38–54.MathSciNetCrossRefGoogle Scholar
  25. 25.
    Akbar, N. S., & Nadeem, S. (2011). Jeffrey fluid model for blood flow through a tapered artery with a stenosis. J. Mech. Med. Biol., 11(3), 529–545.CrossRefGoogle Scholar
  26. 26.
    Hunter, R. (1981). Zeta potential in colloid science: principles and applications. London: Academic.Google Scholar
  27. 27.
    Hayat, T., Mahomed, F. M., Asghar, S. (2005). Peristaltic flow of magnetohydrodynamic Johnson-Segalman fluid. Nonlinear Dynamics, 40, 375–385.MathSciNetCrossRefGoogle Scholar
  28. 28.
    Mekheimer, Kh. S. (2002). Peristaltic transport of a couple-stress fluid in a uniform and non-uniform channels. Biorheology, 39, 755–765.Google Scholar
  29. 29.
    Mekheimer, Kh. S., Hemada, K. A., Raslan, K. R., Abo-Elkhair, R. E., Moawad, A. M. A. (2014). Numerical study of a non-linear peristaltic transport: application of Adomian decomposition method(ADM). Gen. Math. Notes, 20, 22–49.Google Scholar
  30. 30.
    Mekheimer, Kh. S. (2005). Peristaltic transport through a uniform and non-uniform Annulus. Arabian J. for Science and Engineering, 30(1A), 1–15.Google Scholar
  31. 31.
    Mekheimer, K.S. (2003). Non- linear peristaltic transport of MHD flow in an inclined planar channel. Arabian J. for Science and Engineering, 28(2A), 183–201.Google Scholar
  32. 32.
    Shapiro, A. H., Jaffrin, M. Y., Weinberg, S. L. (1969). Peristaltic pumping with long wavelength at low Reynolds number. Journal of Fluid Mechanics, 37, 799–825.CrossRefGoogle Scholar
  33. 33.
    Mekheimer, Kh. S., & El Kot, M. A. (2012). Mathematical modeling of axial flow between two eccentric cylinders: application on the injection of eccentric catheter through stenotic arteries. International Journal of Non-Linear Mechanics, 47, 927– 937.CrossRefGoogle Scholar
  34. 34.
    Hayat, T., & Ali, N. (2008). Peristaltic motion of a Jeffrey fluid under the effect of a magnetic field in a tube. Communications in Nonlinear Science and Numerical Simulation, 13, 1343–1352.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Kh. S. Mekheimer
    • 1
  • R. E. Abo-Elkhair
    • 1
  • A. M. A. Moawad
    • 1
    Email author
  1. 1.Mathematical Department, Faculty of ScienceAl-Azhar UniversityNasr CityEgypt

Personalised recommendations