FENE-P fluid flow generated by self-propelling bacteria with slip effects

Zeeshan Asghar; Rehman Ali Shah; Wasfi Shatanawi; Nasir Ali

doi:10.1016/j.compbiomed.2022.106386

FENE-P fluid flow generated by self-propelling bacteria with slip effects

Comput Biol Med. 2023 Feb:153:106386. doi: 10.1016/j.compbiomed.2022.106386. Epub 2022 Nov 30.

Authors

Zeeshan Asghar¹, Rehman Ali Shah², Wasfi Shatanawi³, Nasir Ali²

Affiliations

¹ Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia; NUTECH, School of Applied Sciences and Humanities, National University of Technology, Islamabad, 44000, Pakistan. Electronic address: zasghar@psu.edu.sa.
² Department of Mathematics and Statistics, International Islamic University, Islamabad, 44000, Pakistan.
³ Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia; Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan; Department of Mathematics, Faculty of Science, The Hashemite University, P.O. Box 330127, Zarqa, 13133, Jordan. Electronic address: wshatanawi@psu.edu.sa.

PMID: 36587569
DOI: 10.1016/j.compbiomed.2022.106386

Abstract

It is hypothesized that gliding bacteria move by producing waves on their own surface and leave an adhesive slime trail. Slime is basically a viscoelastic slippery material. Based on these observations, we use a mathematical model (of undulating sheet) to examine the locomotion of gliding bacteria over a layer of non-Newtonian slime. The constitutive equations of FENE-P model are employed to characterize the rheological behavior of the non-Newtonian slime. Moreover, substratum beneath the slime is approximated by a multi-sinusoidal sheet. A hybrid computational technique to solve the second order DE with a system of algebraic equations is presented. The speed of organism, flow rate and energy loss at larger values of the involved parameters are simulated using bvp5c in conjunction with a modified Newton-Raphson technique (MNRT). The comparison of soft and rigid substrate, slip and no-slip boundary conditions, Newtonian and non-Newtonian slime is displayed in several figures. Streamlines pattern and velocity of the slime are also drawn for the realistic pairs of speed and flow rate and are thoroughly explained.

Keywords: FENE-P Model; Gliding bacteria; Modified Newton-Raphson method; Slippery soft substrate.

MeSH terms

Bacteria*
Locomotion*
Models, Theoretical