Non-Newtonian fluid model analysis due to metachronal waves of cilia: A physiological mathematical model

Abstract

The Phan–Thien–Tanner non-Newtonian model of fluid flow is considered to mathematically model the cilia governed flow inside human body. The collective action of cilia generates a rhythmic motion in form of metachronal wave travelling along the wall of channel. We used the necessary assumptions to non-dimensionalize this complex problem and exact solutions are obtained for the cilia governed flow problem. The graphical results are also incorporated to further discuss these solutions in detail. The wavy movements developed because of rhythmic actions of cilia are evident in pressure gradient graphs. Further, a parabolic flow pattern is also observed in this ciliated channel flow problem. Streamlines disclose the trapping phenomenon and the multiple pumping regions can be seen in intrigued pressure rise graphical solutions. Cilia-generated peristaltic flow is very important for mucus clearance in the respiratory tract, ovum transit in the reproductive system, nutrient digestion, fluid circulation in the brain, and pathogen removal in different tissues.

Keywords

• Ciliary motion
• Planner channel
• Phan–Thien–Tanner fluid
• Exact solutions