An investigation of non-Newtonian fluid flow due to metachronal beating of cilia in a tube

Abdul M. Siddiqui, A. A. Farooq, M. A. Rana

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

The aim of this study is to explain theoretically the role of ciliary motion on the transport of epididymal fluid through the ductus efferentes of the male reproductive track. For this purpose, a mathematical model has been developed for the flow of a non-Newtonian fluid in an axisymmetric tube due to metachronal wave of cilia motion for the more realistic consequences. Carreau viscous fluid model is considered to see the rheological effects on the pumping characteristics of the flow. Regular perturbation method has been employed to obtain the analytical expressions for the stream function, the velocity field and a relation between the pressure difference and the volume flow rate. It is found that the volume flow rate is influenced significantly by Weissenberg number We and the cilia length parameter ε. The computational results are presented graphically to see the effects of various physical parameters. Finally, the analysis is applied and compared with the observed value of the flow rate of spermatic fluid in the ductus efferentes of the male reproductive track. The volume flow rate is reported closed to the estimated value 6 × 10-3 ml/h in the human ductus efferentes when We = 0.5 and ε is near by 0.25.

Original languageEnglish (US)
Article number1550016
JournalInternational Journal of Biomathematics
Volume8
Issue number2
DOIs
StatePublished - Mar 12 2015

Fingerprint

Non Newtonian flow
Non-Newtonian Flow
Non-Newtonian Fluid
Flow Rate
Fluid Flow
Tube
Flow rate
Fluids
Fluid
Motion
Stream Function
Fluid Model
Perturbation Method
Viscous Fluid
Velocity Field
Computational Results
Mathematical Model
Mathematical models
Closed

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Applied Mathematics

Cite this

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abstract = "The aim of this study is to explain theoretically the role of ciliary motion on the transport of epididymal fluid through the ductus efferentes of the male reproductive track. For this purpose, a mathematical model has been developed for the flow of a non-Newtonian fluid in an axisymmetric tube due to metachronal wave of cilia motion for the more realistic consequences. Carreau viscous fluid model is considered to see the rheological effects on the pumping characteristics of the flow. Regular perturbation method has been employed to obtain the analytical expressions for the stream function, the velocity field and a relation between the pressure difference and the volume flow rate. It is found that the volume flow rate is influenced significantly by Weissenberg number We and the cilia length parameter ε. The computational results are presented graphically to see the effects of various physical parameters. Finally, the analysis is applied and compared with the observed value of the flow rate of spermatic fluid in the ductus efferentes of the male reproductive track. The volume flow rate is reported closed to the estimated value 6 × 10-3 ml/h in the human ductus efferentes when We = 0.5 and ε is near by 0.25.",
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An investigation of non-Newtonian fluid flow due to metachronal beating of cilia in a tube. / Siddiqui, Abdul M.; Farooq, A. A.; Rana, M. A.

In: International Journal of Biomathematics, Vol. 8, No. 2, 1550016, 12.03.2015.

Research output: Contribution to journalArticle

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