Physical hydrodynamic propulsion model study on creeping viscous flow through a ciliated porous tube
- 127 Downloads
The present investigation focusses on a mathematical study of creeping viscous flow induced by metachronal wave propagation in a horizontal ciliated tube containing porous media. Creeping flow limitations are imposed, i.e. inertial forces are small compared to viscous forces and therefore a very low Reynolds number (Re ≪ 1) is taken into account. The wavelength of metachronal wave is also considered to be very large for cilia movement. The physical problem is linearized and exact solutions are developed for the differential equation problem. Mathematica software is used to compute and illustrate numerical results. The influence of slip parameter and Darcy number on velocity profile, pressure gradient and trapping of bolus are discussed with the aid of graphs. It is found that with increasing magnitude of the slip parameter, the trapped bolus inside the streamlines increases in size. The study is relevant to biological propulsion of medical micromachines in drug delivery.
KeywordsViscous fluid ciliated tube porous medium Darcy number permeability low Reynolds number hydrodynamic slip biomimetic propulsion.
Authors are thankful to the reviewer for useful suggestions to improve the manuscript.
- T Y Wu, Reflections for resolution to some recent studies on fluid mechanics, in: Advances in engineering mechanics – Reflections and outlooks (World Scientific, Singapore, 2006)Google Scholar
- Ye Wang, Yang Gao and Hans M Wyss, Microfluid Nanofluid 18, 167 (2015)Google Scholar
- M A Sleigh, The biology of cilia and flagella (MacMillan, New York, USA, 1962)Google Scholar
- T Y Wu, Fluid mechanics of ciliary propulsion, Proc. Tenth Annual Meeting of the Society of Engineering Science (Yale University, Connecticut, USA, 1973)Google Scholar
- M A Sleigh and E Aiello, Acta. Protozool. 11, 265 (1972)Google Scholar
- H Agarwal and A Uddin, Indian J. Pure Appl. Math. 15, 1128 (1984)Google Scholar
- C E Miller, An investigation of the movement of Newtonian liquids initiated and sustained by the oscillation of mechanical cilia, Aspen Emphysema Conf. (Aspen, Colorado, USA, 1967)Google Scholar
- G A Truskey, F Yuan and D F Katz, Transport phenomena in biological systems (Pearson, New Jersey, 2004)Google Scholar
- K Vafai, Handbook of porous media (Begell House, New York, USA, 2003)Google Scholar
- O Coussy, Mechanics of porous continua (Butterworths, USA, 1993)Google Scholar
- D Tripathi and O Anwar Bég, J. Mech. Med. Biol. 12(5), 1250088 (2012)Google Scholar
- Noreen Sher Akbar and Z H Khan, Int. J. Biomath. 8(2), 1550026 (2015)Google Scholar
- Noreen Sher Akbar, Int. J. Biomath. 8(2), 1550023 (2015)Google Scholar