Abstract
The main purpose of this article is to present a mathematical model of ciliary motion in an annulus. In this analysis, two dimensional flow of a viscous nanofluid is observed in an annulus with ciliated tips. The current theoretical model may be supposed as mathematical illustration to the movement of ciliary motion in the presence of an endoscopic tube (or catheter tube). The inner tube is rigid, while the outer tube takes a metachronal wave. The features of ciliary structures are determined by the dominance of viscous effects over inertial effects using the long-wavelength approximation. Exact solutions have been established for both velocity and temperature profiles, which include nanoparticle effects. The features of the ciliary motion are analyzed by plotting graphs and discussed in detail.
Highlights
Cilia are small hair like structures, which protrude from cell surfaces and play important roles in motility, sensory perception[1] and development[2] in a wide range of eukaryotes including human
The main purpose of this article is to present a mathematical model of ciliary motion in an annulus
Metachronal waves are observed to propagate in all possible directions: in the direction of the effective stroke, in the opposite direction, or even in a perpendicular or oblique direction
Summary
Cilia are small hair like structures, which protrude from cell surfaces and play important roles in motility, sensory perception[1] and development[2] in a wide range of eukaryotes including human. While many human tissues have non-motile or (primary cilia), cilia generally occur one per cell examples of primary cilia can be found in human sensory organs such as the eye and the nose. Another essential feature of ciliated cells is the existence of waves propagating all along the surface. Metachronal waves are observed to propagate in all possible directions: in the direction of the effective stroke (symplectic metachronal waves), in the opposite direction (antiplectic), or even in a perpendicular (laeoplectic or dexioplectic) or oblique direction. The origin of these waves and the mechanisms controlling their formation are not well understood.[5]
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