Flow assessment of the shear rate dependent viscoelastic fluid: Application of biomechanics in growing human embryo transport

Abstract The present paper theoretically accords a biomechanical model with a brief biological and mathematical description of the growing embryo transport in the human fallopian tube. This model incorporates transport mechanisms that involve the pressure gradient at the ampullar region entrance, peristaltic contractions of smooth muscle cells and swaying motions of ciliary cells. Shear rate dependent viscoelastic fluid characterizes the nature of growing embryo and secreted fluid. The pressure gradient at the ampullar region entrance ξ , metachronal wave parameter ∊ , amplitude ratio ϕ , the ratio of shear viscosity at infinity shear rate to shear viscosity at zero shear rate μ ∞ / 0 and Weissenberg number We emerged as flow control parameters. The assessment showed that the fluid model parameters ( μ ∞ / 0 and We) have opposite effects on appropriate residue time, boluses size and local flow behaviour. Progesterone ( P 4 ) and estradiol ( E 2 ), prostaglandin E 2 ( PGE 2 ) and prostaglandin F 2 α ( PGF 2 α ) constraint the fluid motion by controlling the ξ , secretion of the fluid through the goblet cells and amplitudes of both the sinusoidal and the metachronal waves. Furthermore, a comparison between the current results and available literature is made. The relevance of the obtained results with the growing embryo transport in the human fallopian tube is also explored.