Mathematical analysis of flow of non-Newtonian fluid due to metachronal beating of cilia in a tube and its physiological applications

Abstract

In the present paper, the ciliary flow of seminal fluid (non-Newtonian fluid) in the vas deferens (ductus efferentes) of the male reproductive tract is examined through a mathematical model. The rheological behavior of seminal fluid is described as a Hershel–Bulkley fluid. The momentum equations governing the flow of Herschel–Bulkley model are simplified by considering long wave-length and low Reynolds number approximations. The analytical solutions are obtained for velocity profile, flow rate, pressure gradient and flow impedance. The variation of plug core radius with respect to the cilia length (ε), the measure of the eccentricity of the elliptical motion (α), the wave number (β) and the time-mean flow rate (Qav) is reported for the first time. The time-mean flow rates obtained from the present study are compared with their experimental values of the transport of seminal fluid through the rhesus monkey reproductive track and the ductus efferentes of the male reproductive tract, respectively. It is observed that the theoretical values of time-mean flow rates for seminal fluid (Herschel–Bulkley fluid) have been found to be in good agreement with the experimental results.