Analysis of the peristaltic-ciliary flow of Johnson-Segalman fluid induced by peristalsis-cilia of the human fallopian tube

The present prospective theoretical analysis concerns with the peristalsis-cilia induced transport of a developing embryo from ampulla to intramural, in the human fallopian tube. A model of peristalsis-cilia induced flow of the Johnson-Segalman fluid within fallopian tubal fluid in a finite two dimensional narrow tube is developed. We solved highly non-linear PDE emerging from the modeling of proposed model using perturbation method. The series expressions for flow variables like axial and radial velocities, pressure gradient, stream function, volume flow rate and time mean volume flow rate are derived. The numerical integration is performed for appropriate residue time over tube length and pressure difference over wavelength. The analysis delineated that, involved parameters and constants have vice versa effects on axial velocity and appropriate residue time over tube length. Striking features of the pumping characteristics and the trapping phenomenon are discussed in detail. Furthermore, comparison of the peristaltic flow with the peristaltic-ciliary flow and Johnson-Segalman fluid with the linearly viscous fluid is made. It is revealed that appropriate residue time of the Johnson-Segalman fluid in the narrow tube is 3-4 days, which agreed with the time taken by the developing embryo from ampulla to intramural, in the human fallopian tube.