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

doi:10.1007/s10483-018-2305-9

摘要/Abstract

摘要：

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.

关键词: peristaltic-ciliary flow, debonding, metal matrix composites, elastoplasticity, Generalized, human fallopian tube, analytic solution, linearly viscous fluid

Abstract:

Key words: debonding, metal matrix composites, elastoplasticity, Generalized, linearly viscous fluid, peristaltic-ciliary flow, human fallopian tube, analytic solution

中图分类号:

H. ASHRAF, A. M. SIDDIQUI, M. A. RANA. Fallopian tube assessment of the peristaltic-ciliary flow of a linearly viscous fluid in a finite narrow tube[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(3): 437-454.

参考文献

[1] Eddy, C. A. and Pauerstein, C. J. Anatomy and physiology of the fallopian tube. Clinical Obstetrics and Gynecology, 23(4), 1177-1193(1980)
[2] Yeung, W. S. B., Lee, C. K. F., and Xu, J. S. The oviduct and development of the preimplantation embryo. Reproductive Medicine Review, 10(1), 21-44(2002)
[3] Ghazal, S., Makarov, J. K., and de Jonge, C. J. Egg transport and fertilization. Global Library of Women's Medicine, 2014(2014) https://doi.org/10.3843/GLOWM.10317
[4] Fauci, L. J. and Dillon, R. Biofluidmechanics of reproduction. Annual Review of Fluid Mechanics, 38, 371-394(2006)
[5] Jones, R. E. and Lopez, K. H. Human Reproductive Biology, Elsevier, Burlington, 253-260(2006)
[6] Kolle, S., Reese, S., and Kummer, W. New aspects of gamete transport, fertilization, and embryonic development in the oviduct gained by means of live cell imaging. Theriogenology, 73, 786-795(2010)
[7] Sokol, E. R. Clinical anatomy of the uterus, fallopian tubes, and ovaries. Global Library of Women's Medicine, 2011(2011) https://doi.org/10.3843/GLOWM.10001
[8] Carlson, B. M. Human Embryology and Developmental Biology, Elsevier, Philadelphia, 36-37(2014)
[9] Ezzati, M., Djahanbakhch, O., Arian, S., and Carr, B. R. Tubal transport of gametes and embryos:a review of physiology and pathophysiology. Journal of Assisted Reproduction and Genetics, 31(10), 1337-1347(2014)
[10] Wakeley, P. W. Optimisation and Properties of Gamete Transport, Ph. D. dissertation, University of Birmingham, 139-166(2008)
[11] Leese, H. J. The formation and function of oviduct fluid. Journal of Reproduction and Fertility, 82, 843-856(1988)
[12] Leese, H. J., Tay, J. I., Reischl, J., and Downing, S. J. Formation of fallopian tubal fluid:role of a neglected epithelium. Reproduction, 121, 339-346(2001)
[13] Lyons, R. A., Saridogan, E., and Djahanbakhch, O. The reproductive significance of human fallopian tube cilia. Human Reproduction Update, 12(4), 363-372(2006)
[14] Siddiqui, A. M., Farooq, A. A., and Rana, M. A. Hydromagnetic flow of Newtonian fluid due to ciliary motion in a channel. Magnetohydrodynamics, 50(3), 109-122(2014)
[15] Sadaf, H. and Nadeem, S. Influences of slip and Cu-blood nanofluid in a physiological study of cilia. Computer Methods and Programs in Biomedicine, 131, 169-180(2016)
[16] Buthaud, H. The Influences of Unsymmetry, Wall Slope and Wall Motion on Peristaltic Pumping at Small Reynolds Number, M. Sc. dissertation, The Johns Hopkins University Baltimore Maryland 21218, 9-24(1971)
[17] Nadeem, S. and Shahzadi, I. Mathematical analysis for peristaltic flow of two phase nanofluid in a curved channel. Communications in Theoretical Physics, 64(5), 547-554(2015)
[18] Nadeem, S. and Shahzadi, I. Single wall carbon nanotube (SWCNT) analysis on peristaltic flow in an inclined tube with permeable walls. International Journal of Heat and Mass Transfer, 97, 794-802(2016)
[19] Nadeem, S. and Shahzadi, I. Inspiration of induced magnetic field on nano hyperbolic tangent fluid in a curved channel. AIP Advances, 6(1), 015110-015125(2016)
[20] Shahzadi, I. and Nadeem, S. Stimulation of metallic nanoparticles under the impact of radial magnetic field through eccentric cylinders:a useful application in biomedicine. Journal of Molecular Liquids, 225, 365-381(2017)
[21] Shahzadi, I., Sadaf, H., Nadeem, S., and Saleem, A. Bio-mathematical analysis for the peristaltic flow of single wall carbon nanotubes under the impact of variable viscosity and wall properties. Computer Methods and Programs in Biomedicine, 139, 137-147(2017)
[22] Shahzadi, I. and Nadeem, S. Inclined magnetic field analysis for metallic nanoparticles submerged in blood with convective boundary condition. Journal of Molecular Liquids, 230, 61-73(2017)
[23] Shahzadi, I. and Nadeem, S. Impinging of metallic nanoparticles along with the slip effects through a porous medium with MHD. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 39(7), 2535-2560(2017)
[24] Shahzadi, I. and Nadeem, S. Impact of curvature on the mixed convective peristaltic flow of shear thinning fluid with nanoparticles. Canadian Journal of Physics, 94(12), 1319-1330(2016)
[25] Shahzadi, I., Nadeem, S., and Rabiei, F. Simultaneous effects of single wall carbon nanotube and effective variable viscosity for peristaltic flow through annulus having permeable walls. Results in Physics, 7, 667-676(2017)
[26] Eytan, O. and Elad, D. Analysis of intra-uterine fluid motion induced by uterine contractions. Bulletin of Mathematical Biology, 61, 221-236(1999)
[27] Eytan, O., Jaffa, A. J., and Elad, D. Peristaltic flow in a tapered channel:application to embryo transport within the uterine cavity. Medical Engineering and Physics, 23, 473-482(2001)
[28] Yaniv, S., Jaffa, A. J., Eytan, O., and Elad, D. Simulation of embryo transport in a closed uterine cavity model. Eurpian Journal of Obstetrics and Gynecology and Reproductive Biology, 144(1), 50-60(2009)
[29] Blake, J. R., Vann, P. G., and Winet, H. A model for ovum transport. Journal of Theoretical Biology, 102, 145-166(1982)
[30] Papanastasiou, T. C. Applied Fluid Mechanics, P T R Prentice Hall, Inc., A Paramount Communications Company Englewood Cliffs, New Jersey, 309-310(1994)
[31] Siddiqui, A. M., Ashraf, H., Walait, A., and Haroon, T. On study of horizontal thin film flow of Sisko fluid due to surface tension gradient. Applied Mathematics and Mechanics (English Edition), 36(7), 847-862(2015) https://doi.org/10.1007/s10483-015-1952-9