Electro-osmosis Modulated Viscoelastic Embryo Transport in Uterine Hydrodynamics: Mathematical Modelling.

Embryological transport features a very interesting and complex application of peristaltic fluid dynamics. Electro- osmotic phenomena are also known to arise in embryo transfer location. The fluid dynamic environment in em- bryological systems is also known to be non-Newtonian and exhibits strong viscolastic properties. Motivated by these applications, the present article develops a new mathematical model for simulating two-dimensional peristaltic transport of a viscoelastic fluid in a tapered channel under the influence of electro-osmosis induced by asymmet- ric zeta potentials at the channel walls. The robust Jeffrey viscoelastic model is utilized. The finite Debye layer electro-kinetic approximation is deployed. The moving boundary problem is transformed to a steady boundary problem in the wave frame. The current study carries significant physiological relevance with an ever-increasing desire to study intrauterine fluid flow motion in an artificial uterus. The consequences of this model may introduce a new mechanical factor for embryo transport to a successful implantation site. Hydrodynamic characteristics are shown to be markedly influences by the electro-osmosis, the channel taper angle and the phase shift between the channel walls. Furthermore it is demonstrated that volumetric flow rates and axial flow are both enhanced when the electro-osmotic force aids the axial flow for specific values of zeta potential ratio. Strong trapping of the bolus (representative of the embryo) is identified in the vicinity of the channel central line when the electro-osmosis op- poses axial flow.