Controlling kinetics of self-propelled rod-like swimmers near multi sinusoidal substrate

Zeeshan Asghar; Rehman Ali Shah; Amjad Ali Pasha; Mustafa Mutiur Rahman; Muhammad Waris Saeed Khan

doi:10.1016/j.compbiomed.2022.106250

Controlling kinetics of self-propelled rod-like swimmers near multi sinusoidal substrate

Comput Biol Med. 2022 Dec;151(Pt A):106250. doi: 10.1016/j.compbiomed.2022.106250. Epub 2022 Oct 29.

Authors

Zeeshan Asghar¹, Rehman Ali Shah², Amjad Ali Pasha³, Mustafa Mutiur Rahman⁴, Muhammad Waris Saeed Khan²

Affiliations

¹ Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia. Electronic address: zasghar@psu.edu.sa.
² Department of Mathematics and Statistics, International Islamic University, Islamabad, 44000, Pakistan.
³ Aerospace Engineering Department, King Abdulaziz University, Jeddah, 21589, Saudi Arabia.
⁴ Department of Mechanical and Mechatronics Engineering, University of Waterloo, ON, N2L 3G1, Canada.

PMID: 36368110
DOI: 10.1016/j.compbiomed.2022.106250

Abstract

Motility is defined as the movement of cells by some form of self-propulsion. Some organisms motile by using long flagella that quickly rotate to propel them over various surfaces (in swarming and swimming mechanism), while few motile without the aid of flagella (in twitching, sliding and gliding mechanism). Among these modes, gliding motility is adopted by a rod-shaped organism famously known as gliding bacteria. It is hypothesized that in such type of motility, organism motile under their own power by secreting a layer of slime on the substrate. In this study, an active wall is considered as a substrate and a two-dimensional wavy sheet as an organism. Slip effects are also employed in the current work. The physical properties of the slime are governed by a suitable constitutive equation of couple stress model. A sixth order BVP is obtained by utilizing lubrication assumption. For an appropriate fixed pair of flow rate and organism speed the BVP is solved by MATLAB built-in function bvp-5c. This solution is utilized in the mechanical equilibrium conditions which are obviously not satisfied yet. To satisfy these conditions, the pair of flow rate and gliding speed is refined by a root finding algorithm (modified Newton-Raphson method). By employing this numerical scheme, various figures are shown to demonstrate the effect of several associated parameters on organism speed, flow rate, energy expended by the glider, streamlines and longitudinal velocity. It is observed from the graphical results that organism speed and energy consumption is directly proportional to the couple stress parameter and slip effects.

Keywords: Complex undulating sheet; Couple stress fluid; Gliding bacteria; Modified Newton-Raphson method; Slip effects; Soft substrate.

MeSH terms

Algorithms*
Kinetics
Movement*