Residual time of sinusoidal metachronal ciliary flow of non-Newtonian fluid through ciliated walls: fertilization and implantation

• Published in: Biomechanics and modeling in mechanobiology Vol. 20; no. 2; pp. 609 - 630
• Main Authors: Zaher, A. Z., Moawad, A. M. A., Mekheimer, Kh. S., Bhatti, M. M.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-04-2021; Springer Nature B.V
• Subjects: Biological and Medical Physics; Biomedical Engineering and Bioengineering; Biophysics; Canals; Capacitation; Engineering; Fertilization; Flow; Fluid flow; Mathematical models; Newtonian fluids; Non Newtonian fluids; Original Paper; Parameters; Space life sciences; Stream functions (fluids); Theoretical and Applied Mechanics; Uterus; Vorticity; Eyring-Powell fluid; Implantation; Fertilization; Peristaltic ciliary flow; Numerical solution (ADM); Residual time
• ISSN: 1617-7959; 1617-7940
• DOI: 10.1007/s10237-020-01405-5

The monitoring of the ciliated walls in the uterine tube has supreme importance in enhancing the sperm to reach the egg (capacitation processes), and at peristaltic ciliary flow has a more favorable residual time along the canal when compared to the peristaltic flow. Based on the importance of this study, a mathematical simulation of this process has been carried out by studying the behavior of a non-Newtonian magnetized fluid with a Darcy flow model with an oscillating wall having an internal ciliated surface. The governing equation is formed with Eyring-Powell fluid (tubal fallopian fluid) without using any approximations and solved using the Adomian analysis method. Using the vorticity formula, the components of the velocity function, pressure gradient, and stream function are obtained. The influence of relevant parameters is explained through diagramming and discussion. We also analyzed the residue time effects on the flow parameters. The results indicate that peristaltic ciliary flow has a more favorable residual time along the canal when compared to peristaltic flow.