Abstract
A mathematical model is developed to study the transport mechanism of a Casson fluid flow inspired by the metachronal coordination between the beating cilia in a cylindrical tube. A two-dimensional system of nonlinear equations governing the flow problem is formulated by using axisymmetric cylindrical coordinates and then simplified by employing the long wavelength and low Reynolds number assumptions. Exact solutions are derived for the velocity components, the axial pressure gradient, and the stream function. However, the expressions for the pressure rise and the volume flow rate are evaluated numerically. The features of the flow characteristics such as pumping and trapping are illustrated and discussed with the help of graphs. It is observed that the volume flow rate is influenced significantly by the width of plug flow region H p as well as the cilia length parameter ε. The analysis is also applied and compared with the estimated value of the volume flow rate of epididymal fluid in the ductus efferentes of the human male reproductive tract.
Highlights
The study of fluid transport due to systems of beating cilia has attracted the attention of many researchers due to its applications in bioengineering and medical sciences
Ciliated surfaces are known to have different patterns, depending upon whether the metachronal wave travels in the direction of effective stroke, called symplectic metachronism, or in the opposite direction to the effective stroke known as antiplectic metachronism, which is in the opposite direction of fluid motion
We have examined the role of cilia motion in terms of metachronal waves in the transport of a Casson fluid through an axially symmetric tube
Summary
The study of fluid transport due to systems of beating cilia has attracted the attention of many researchers due to its applications in bioengineering and medical sciences. In 1972, Lardner and Shack [1] developed a model for the flow of a Newtonian viscous fluid due to ciliary activity in the ductus efferentes of the male reproductive tube. They used an envelope over the oscillating cilia to model the metachronal wave. Several models of nonNewtonian fluids have been proposed by various scientists to investigate the flow behavior in certain physiological systems of living bodies This is due to their different rheological characteristics. This analysis offers very interesting applications for the flow control in lab-on-a-chip devices and in tiny biosensors
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