Advertisement

Rheological effects of biomimetic propulsion on fluid flow: An application of bio-engineering

  • Khurram Javid
  • Mohsan Hassan
  • M. Imran AsjadEmail author
  • Irfan Ali
  • Abdul Nazib
Review
  • 24 Downloads

Abstract.

In the current article, we have studied few rheological phenomena related to the fluid transportation in various forms of flow geometries and motion of the fluid based upon the peristaltic propulsions of the boundary walls. This study is productive for mechanical engineers to design devices that are used as a remedy of complex cardiovascular treatments. This study deals with the flow of a viscous fluid through the complex paths due to the biomimetic propulsions of the boundary walls of geometries. Firstly, due to the complex nature of flow regimes, the continuity and momentum equations are governed into the form of curvilinear coordinates. Secondly, the governing equations are transformed from the laboratory frame to the wave frame by introducing a linear mathematical relation between these two frames. Thirdly, similarity transformations are utilized to convert the system of equations into the dimensionless form and at the last, these equations will reduce into the four ODEs in terms of stream function after using long wavelength approximation. The analytical solution of the governing equation is acquired by applying integration rules and mathematical values of integrating constants are obtained by using Mathematica 10 software. The significant impacts of physical parameters such as curvature parameter and non-uniform parameter in the velocity profile, pumping and trapping phenomena’s are argued expansively through graphs to the various forms of flow regimes. Physical characteristics of simple wavy walls and complex wavy walls of the curved channels are also highlighted in detail in the wave frame of reference. Moreover, a comparison among the straight channel and the curved channel is also emphasized. The results of the current study may be useful in designing the complex instruments which are used in medical engineering and treatment of physiological systems. Comprehensive information about the transportation of bio-fluids in the uniform as well as non-uniform vessels or arteries is obtained from the present study. This study provides dynamic information, to the mechanical engineers, to enhance the performance of the peristaltic micro-pumps.

References

  1. 1.
    D. Acheson, Elementary Fluid Dynamics (Oxford University Press, Oxford, 1990)Google Scholar
  2. 2.
    J. Lighthill, Mathematical Bio Fluid Dynamics (SIAM, Philadelphia, 1975)Google Scholar
  3. 3.
    J. Lighthill, Waves in Fluids (Cambridge University Press, Cambridge, 1980)Google Scholar
  4. 4.
    J. West, Respiratory Physiology: The Essentials (Williams & Wilkins, Baltimore, 1985)Google Scholar
  5. 5.
    J. Blazek, Computational Fluid Dynamics: Principles and Applications, 2nd Ed. (Elsevier, New York, 2005)Google Scholar
  6. 6.
    A.L. Chorin, A Mathematical Introduction to Fluid Mechanics, 3rd Ed. (Springer, New York, 1993)zbMATHCrossRefGoogle Scholar
  7. 7.
    R. Darby, Chemical Engineering Fluid Mechanics, 2nd Ed. (Marcel Dekker, New York, 2001)Google Scholar
  8. 8.
    E. Feireisl, Dynamics of Viscous Compressible Fluids (Oxford University Press, New York, 2004)Google Scholar
  9. 9.
    T.W. Latham, Fluid Motion in a Peristaltic Pump, MS thesis, MIT, Cambridge (1966)Google Scholar
  10. 10.
    J.C. Burns, T. Parkes, J. Fluid Mech. 29, 731 (1967)ADSCrossRefGoogle Scholar
  11. 11.
    A.H. Shapiro, M.Y. Jaffrin, S.L. Weinberg, J. Fluid Mech. 37, 799 (1969)ADSCrossRefGoogle Scholar
  12. 12.
    W.M. Bayliss, E.H. Starling, J. Physiol. 24, 99 (1899)CrossRefGoogle Scholar
  13. 13.
    Y.C. Fung, C.S. Yih, J. Appl. Mech. 35, 669 (1968)ADSCrossRefGoogle Scholar
  14. 14.
    F. Yin, Y.C. Fung, J. Appl. Mech. 36, 579 (1969)ADSCrossRefGoogle Scholar
  15. 15.
    S. Takabatake, K. Ayukawa, J. Fluid Mech. 122, 439 (1982)ADSCrossRefGoogle Scholar
  16. 16.
    S. Takabatake, K. Ayukawa, A. Mori, J. Fluid Mech. 193, 269 (1988)ADSCrossRefGoogle Scholar
  17. 17.
    N. Ali, Y. Wang, T. Hayat, M. Oberlack, Can. J. Phys. 87, 1047 (2009)ADSCrossRefGoogle Scholar
  18. 18.
    T.D. Brown, T.K. Hung, J. Fluid Mech. 83, 249 (1977)ADSCrossRefGoogle Scholar
  19. 19.
    T.K. Hung, T.D. Brown, J. Fluid Mech. 73, 77 (1976)ADSCrossRefGoogle Scholar
  20. 20.
    T. Hayat, N. Ali, Appl. Math. Mod. 32, 761 (2008)CrossRefGoogle Scholar
  21. 21.
    S. Srinivas, R. Gayathri, Appl. Math. Comput. 215, 185 (2009)MathSciNetGoogle Scholar
  22. 22.
    K.S. Mekheimer, Y. Abd Elmaboud, Physica A 372, 1657 (2008)Google Scholar
  23. 23.
    A. Ebaid, Phys. Lett. A 372, 4493 (2008)ADSCrossRefGoogle Scholar
  24. 24.
    K.K. Raju, R. Devanathan, Rheol. Acta 13, 944 (1974)CrossRefGoogle Scholar
  25. 25.
    N. Ali, Y. Wang, T. Hayat, M. Oberlack, Biorheology 45, 611 (2008)Google Scholar
  26. 26.
    N. Ali, Y. Wang, T. Hayat, M. Oberlack, Can. J. Phys. 87, 1047 (2009)ADSCrossRefGoogle Scholar
  27. 27.
    N. Ali, T. Javed, Z. Naturforsch. 68a, 515 (2013)ADSCrossRefGoogle Scholar
  28. 28.
    W.R. Dean, Phil. Mag. 4, 208 (1927)CrossRefGoogle Scholar
  29. 29.
    W.R. Dean, Phil. Mag. 5, 673 (1928)CrossRefGoogle Scholar
  30. 30.
    H. Sato, T. Kawai, T. Fujita, M. Okabe, Trans. Jpn. Soc. Mech. Eng. B 66, 679 (2000)CrossRefGoogle Scholar
  31. 31.
    N. Ali, M. Sajid, T. Hayat, Z. Naturforsch. A 65a, 191 (2010)ADSCrossRefGoogle Scholar
  32. 32.
    N. Ali, M. Sajid, T. Javed, Z. Abbas, Int. J. Heat Mass Transfer 53, 3319 (2010)CrossRefGoogle Scholar
  33. 33.
    N. Ali, K. Javid, M. Sajid, O.A. Beg, Comput. Methods Biomech. Biomed. Eng. 19, 614 (2016)CrossRefGoogle Scholar
  34. 34.
    S. Hina, T. Hayat, A. Alsaedi, Int. J. Heat Mass Transfer 55, 351 (2012)Google Scholar
  35. 35.
    S. Hina, M. Mustafa, T. Hayat, A. Alsaedi, ASME J. Appl. Mech. 80, 024501 (2013)ADSCrossRefGoogle Scholar
  36. 36.
    T. Hayat, S. Hina, A.A. Hendi, S. Asghar, Int. J. Heat Mass Transfer 54, 5126 (2011)CrossRefGoogle Scholar
  37. 37.
    V.K. Narla, K.M. Prasad, J.V. Ramanamurthy, Chin. J. Eng. 2013, 582390 (2013)CrossRefGoogle Scholar
  38. 38.
    J.V. Ramanamurthy, K.M. Prasad, V.K. Narla, Phys. Fluids 25, 091903 (2013)ADSCrossRefGoogle Scholar
  39. 39.
    A. Kalantari, K. Sadeghy, S. Sadeqi, Ann. Trans. Nordic Rheol. Soc. 21, 11155 (2013)Google Scholar
  40. 40.
    N. Ali, K. Javid, M. Sajid, A. Zaman, T. Hayat, Int. J. Heat Mass Transfer 94, 500 (2016)CrossRefGoogle Scholar
  41. 41.
    N. Ali, M. Sajid, Z. Abbas, T. Javed, Eur. J. Mech.-B/Fluids 29, 387 (2010)ADSMathSciNetCrossRefGoogle Scholar
  42. 42.
    A.M. Sobh, H.H. Mady, J. Appl. Sci. 8, 1085 (2008)ADSCrossRefGoogle Scholar
  43. 43.
    Kh.S. Mekheimer, Arab. J. Sci. Eng. 54, 532 (2005)Google Scholar
  44. 44.
    M. Mishra, A.R. Rao, Z. Angew. Math. Phys. 54, 532 (2003)MathSciNetCrossRefGoogle Scholar
  45. 45.
    E.F. Elshehawey, E.M. Elghazy, A. Ebaid, Appl. Math. Comput. 182, 140 (2006)MathSciNetGoogle Scholar
  46. 46.
    D. Tripathi, A. Yadav, O. Anwar Beg, R. Kumar, Microvasc. Res. 117, 28 (2018)CrossRefGoogle Scholar
  47. 47.
    Kh.S. Mekheimer, Appl. Math. Comput. 153, 763 (2004)MathSciNetGoogle Scholar
  48. 48.
    S. Noreen, Biomater. Med. Appl. 1, 1 (2017)Google Scholar
  49. 49.
    T.F. Zien, S. Ostrach, J. Biomech. 3, 63 (1970)CrossRefGoogle Scholar
  50. 50.
    M.J. Manton, Fluid Mech. 68, 467 (1975)ADSCrossRefGoogle Scholar
  51. 51.
    T. El-Bashir, Fluid Flow at Small Reynolds Number: Numerical Applications (Hikari, 2006)Google Scholar
  52. 52.
    M.Y. Jaffrin, A.H. Shapiro, Annu. Rev. Fluid Mech. 3, 13 (1971)ADSCrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  • Khurram Javid
    • 1
  • Mohsan Hassan
    • 2
  • M. Imran Asjad
    • 3
    Email author
  • Irfan Ali
    • 4
  • Abdul Nazib
    • 1
  1. 1.Department of MathematicsNorthern UniversityNowshera, KPKPakistan
  2. 2.Department of MathematicsCOMSATS University Islamabad (CUI)Lahore CampusPakistan
  3. 3.Department of MathematicsUniversity of Management and TechnologyLahorePakistan
  4. 4.Department of MathematicsSukkur Institute of Business AdministrationSukkur, SindhPakistan

Personalised recommendations