Acta Mechanica

, Volume 229, Issue 7, pp 2861–2881 | Cite as

Biomechanics of the swimming of self-propelling spermatozoa through slippery human cervical canal

  • Ahsan Walait
  • A. M. Siddiqui
  • M. A. Rana
Original Paper


The present theoretical investigation is concerned with the biomechanics of the swimming of self-propelling spermatozoa through the slippery human cervical canal. Partial differential equations arising from the mathematical modelling of the proposed model along with slip boundary conditions are solved analytically. Expressions for pressure gradient, propulsive velocity, mucus velocity and time mean flow rate are analysed for the pertinent parameters. Salient features of the pumping characteristics are explored. It is interesting to note that maximal slippage on the upper cervical wall and zero slippage on the lower cervical wall maximize the probability of the spermatozoa to fertilize an ovum. It is found that a pressure rise facilitates the motion of spermatozoa to fertilize an ovum in the female reproductive tract, whereas a pressure drop inverts the direction of spermatozoa to the vagina and controls the probability of pregnancy.

Mathematics Subject Classification

76Zxx 35Q92 92C10 58D30 35Q30 


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The authors wish to express their very sincere thanks to the reviewers for their valuable suggestions and comments.


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsRiphah International UniversityIslamabadPakistan
  2. 2.Department of MathematicsPennsylvania State UniversityYorkUSA

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