Applied Mathematics and Mechanics

, Volume 39, Issue 3, pp 437–454 | Cite as

Fallopian tube assessment of the peristaltic-ciliary flow of a linearly viscous fluid in a finite narrow tube



The present theoretical assessment deals with the peristaltic-ciliary transport of a developing embryo within a fallopian tubal fluid in the human fallopian tube. A mathematical model of peristalsis-cilia induced flow of a linearly viscous fluid within a fallopian tubal fluid in a finite two-dimensional narrow tube is developed. The lubrication approximation theory is used to solve the resulting partial differential equation. The expressions for axial and radial velocities, pressure gradient, stream function, volume flow rate, and time mean volume flow rate are derived. Numerical integration is performed for the appropriate residue time over the wavelength and the pressure difference over the wavelength. Moreover, the plots of axial velocity, the appropriate residue time over wavelength, the vector, the pressure difference over wavelength, and the streamlines are displayed and discussed for emerging parameters and constants. Salient features of the pumping characteristics and the trapping phenomenon are discussed in detail. Furthermore, a comparison between the peristaltic flow and the peristaltic-ciliary flow is made as the special case. Relevance of the current results to the transport of a developing embryo within a fallopian tubal fluid from ampulla to the intramural in the fallopian tube is also explored. It reveals the fact that cilia along with peristalsis helps to complete the required mitotic divisions while transporting the developing embryo within a fallopian tubal fluid in the human fallopian tube.


peristaltic-ciliary flow linearly viscous fluid analytic solution human fallopian tube 

Chinese Library Classification


2010 Mathematics Subject Classification

76D05 76D08 92C10 92C35 


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Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsRiphah International UniversityIslamabadPakistan
  2. 2.Department of Mathematics, York CampusPennsylvania State University, YorkYorkUSA

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