An IFDM analysis of low Reynolds number flow generated in a complex wavy curved passage formed by artificial beating cilia

Abstract

Mother nature utilizes an assembly of beating cilia to transport liquid in various circumstances. The arrays of these hair-like cellular appendages also aid in propelling microorganisms like spermatozoa and paramecium. In our implicit finite difference analysis, we present a pumping performance of a curved channel comprising mucus flow induced via active cilium. The non-Newtonian mucus is modelled as Carreau fluid model. The undulating cilia attached with curved walls are assumed to be complex wavy. The tips of these cilia form a complex wavy peristaltic curved passage with porous medium effects. Well-known continuity and momentum equations (in curvilinear coordinates) are utilized to model the flow problem. Cilia-driven flow is creeping which is based on low Reynolds number assumption. Moreover, long wavelength assumption is also employed in this analysis. The reduced fourth-order BVP is solved via implicit finite difference method (IFDM). The computed results are plotted by using MATLAB (2021a). The mucus velocity is plotted at three different cross-sections and flow rates. Moreover, velocity of mucus, pressure gradient, pressure rise, and level curves are also expounded for various rheological, porous and cilia-based parameters. A special case of straight passage is also presented in the graphical result section.