Physical hydrodynamic propulsion model study for creeping viscous flow through a ciliated porous tube

Akbar, NS; Butt, AW; Tripathi, D; Beg, OA

Abstract

The present investigation focuses 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 with viscous forces and therefore very low Reynolds number (Re<<1) is taken into account. The wavelength of metachronal wave is also considered as 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 slip parameter the trapped bolus inside the streamlines increases in size. The study is relevant to biological propulsion of medical micro-machines in drug delivery.

• Journal Article Type: Article
• Acceptance Date: Oct 5, 2016
• Online Publication Date: Feb 16, 2017
• Publication Date: Feb 16, 2017
• Deposit Date: Oct 17, 2016
• Publicly Available Date: Oct 17, 2016
• Journal: Pramana
• Print ISSN: 0304-4289
• Electronic ISSN: 0973-7111
• Publisher: Indian Academy of Sciences
• Peer Reviewed: Peer Reviewed
• Volume: 88
• Issue: 52
• DOI: https://doi.org/10.1007/s12043-016-1354-z
• Publisher URL: http://dx.doi.org/10.1007/s12043-016-1354-z
• Related Public URLs: http://link.springer.com/journal/12043