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Analytical and numerical study of creeping flow generated by active spermatozoa bounded within a declined passive tract

  • Z. Asghar
  • N. Ali
  • M. Sajid
Regular Article
  • 13 Downloads

Abstract.

The fluid-swimmer interaction is effective in two ways, i.e. the rheology of the surrounding fluid assists/resists the swimming mechanism and an efficient swimming generates an enhanced fluid flow. In particular the swimming of spermatozoa consists in biorheological hydrodynamic propulsion at low Reynolds numbers, where the viscous damping by far dominates over inertia. In this paper, we study the self-propulsion of a spermatozoon in the human cervix. The organism is modeled as a self-propelling infinite sheet and the cervix is simulated as a two-dimensional channel composed of two rigid walls. We assumed that the cervical walls are declined at a certain angle to the horizontal. The cervical fluid is characterized by the non-Newtonian Carreau model which exhibits shear rate-dependent viscosity, a characteristic of cervical medium. The amplitude of the waves traveling down the declined sheet surface is arbitrary while their wavelength is assumed larger than the declined channel spacing. The flow equations are formulated under this assumption. The analytic expressions of pressure gradient and velocity of the fluid are obtained by utilizing the perturbation technique. These expressions (effective for small values of Carreau parameters) are used in dynamics equilibrium conditions to calculate cell speed and power losses. The propulsive speed and power delivered by the spermatozoa at larger values of the rheological parameters are computed by employing the implicit finite deference technique combined with the Broyden method (modified secant method). The most striking result of the present study is that the optimum speed can be achieved by suitably adjusting the rheological parameters of the cervical fluid and likewise a fast moving organism can generate a better fluid flow.

References

  1. 1.
    G.I. Taylor, Proc. R. Soc. Lond. A 209, 447 (1951)ADSCrossRefGoogle Scholar
  2. 2.
    G.I. Taylor, Proc. R. Soc. Lond. A 211, 225 (1952)ADSCrossRefGoogle Scholar
  3. 3.
    G.J. Hancock, Proc. R. Soc. Ser. A 217, 96 (1953)ADSGoogle Scholar
  4. 4.
    J. Gray, G.J. Hancock, J. Exp. Biol. 32, 802 (1955)Google Scholar
  5. 5.
    J.E. Drummond, J. Fluid Mech. 25, 787 (1966)ADSCrossRefGoogle Scholar
  6. 6.
    M.J. Lighthill, SIAM Rev. 18, 161 (1975)CrossRefGoogle Scholar
  7. 7.
    E.O. Tuck, J. Fluid Mech. 31, 305 (1968)ADSCrossRefGoogle Scholar
  8. 8.
    C. Brennen, J. Fluid Mech. 65, 799 (1974)ADSCrossRefGoogle Scholar
  9. 9.
    A.J. Reynolds, J. Fluid Mech. 23, 241 (1965)ADSCrossRefGoogle Scholar
  10. 10.
    W.J. Shack, T.J. Lardner, Bull. Math. Biol. 36, 435 (1974)CrossRefGoogle Scholar
  11. 11.
    D.F. Katz, J. Fluid Mech. 64, 33 (1974)ADSCrossRefGoogle Scholar
  12. 12.
    E. Odeblad, Adv. Exp. Med. Biol. 89, 217 (1977)CrossRefGoogle Scholar
  13. 13.
    R.E. Smelser, W.J. Shack, T.J. Lardner, J. Biomech. 7, 349 (1974)CrossRefGoogle Scholar
  14. 14.
    J.B. Shukla, B.R.P. Rao, R.S. Parihar, J. Biomech. 11, 15 (1978)CrossRefGoogle Scholar
  15. 15.
    J.B. Shukla, P. Chandra, R. Sharma, J. Biomech. 21, 947 (1988)CrossRefGoogle Scholar
  16. 16.
    G. Radhakrishnamacharya, R. Sharma, Nonlinear Anal. Model. 12, 409 (2007)Google Scholar
  17. 17.
    T.K. Chaudhury, J. Fluid Mech. 95, 189 (1979)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    J. Rutlant, M. Lopez-Bejar, P. Santolaria, J. Yaniz, F. Lopez-Gatius, J. Anat. 201, 553 (2002)CrossRefGoogle Scholar
  19. 19.
    D. Philip, P. Chandra, Arch. Appl. Mech. 66, 90 (1995)ADSCrossRefGoogle Scholar
  20. 20.
    E. Lauga, Phys. Fluids 19, 083104 (2007)ADSCrossRefGoogle Scholar
  21. 21.
    N.J. Balmforth, D. Coombs, S. Pachmann, Q. J. Mech. Appl. Math. 63, 267 (2010)CrossRefGoogle Scholar
  22. 22.
    M. Sajid, N. Ali, A.M. Siddiqui, Z. Abbas, T. Javed, J. Porous Media 17, 59 (2014)CrossRefGoogle Scholar
  23. 23.
    M. Sajid, N. Ali, O. Anwar Bég, A.M. Siddiqui, J. Mech. Med. Biol. 17, 1750009 (2017)CrossRefGoogle Scholar
  24. 24.
    N. Ali, M. Sajid, Z. Abbas, O. Anwar Bég, J. Mech. Med. Biol. 17, 1750054 (2017)CrossRefGoogle Scholar
  25. 25.
    Z. Asghar, N. Ali, M. Sajid, J. Braz. Soc. Mech. Sci. Eng. 40, 475 (2018)CrossRefGoogle Scholar
  26. 26.
    J.R. Vélez-Cordero, Eric Lauga, J. Non-Newton. Fluid Mech. 199, 37 (2013)CrossRefGoogle Scholar
  27. 27.
    T. Hayat, N. Saleem, N. Ali, Commun. Nonlinear Sci. Numer. Simul. 15, 2407 (2010)ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    M. Waqas, M.I. Khan, T. Hayat, A. Alsaedi, Comput. Methods Appl. Mech. Eng. 324, 640 (2017)ADSCrossRefGoogle Scholar
  29. 29.
    M. Waqas, A. Alsaedi, S.A. Shehzad, T. Hayat, S. Asghar, J. Braz. Soc. Mech. Sci. Eng. 39, 3005 (2017)CrossRefGoogle Scholar
  30. 30.
    R.H. Reddy, A. Kavitha, S. Sreenadh, R. Saravana, Int. J. Mech. Mater. Eng. 41, 240 (2011)Google Scholar
  31. 31.
    T. Hayat, N. Aslam, M.I. Khan, A. Alsaedi, Microsyst. Technol. (2018)  https://doi.org/10.1007/s00542-018-4017-9
  32. 32.
    N. Ali, Z. Asghar, O. Anwar Bég, M. Sajid, J. Theor. Biol. 397, 22 (2016)CrossRefGoogle Scholar
  33. 33.
    Z. Asghar, N. Ali, M. Sajid, Math. Biosci. 290, 31 (2017)MathSciNetCrossRefGoogle Scholar
  34. 34.
    Z. Asghar, N. Ali, O. Anwar Bég, T. Javed, Results Phys. 9, 682 (2018)ADSCrossRefGoogle Scholar
  35. 35.
    Z. Asghar, N. Ali, Can. J. Phys. (2018)  https://doi.org/10.1139/cjp-2017-0906

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsInternational Islamic UniversityIslamabadPakistan

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