Mathematical modelling of ciliary propulsion of an electrically conducting Johnson-Segalman physiological fluid in a channel with slip

Manzoor, N; Beg, OA; Maqbool, K; Shaheen, S

Abstract

Bionic systems frequently feature electromagnetic pumping and offer significant advantages over conventional designs via intelligent bio-inspired properties. Complex wall
features observed in nature also provide efficient mechanisms which can be utilized in biomimetic
designs. The characteristics of biological fluids are frequently non-Newtonian in nature. In many natural systems super-hydrophobic slip is witnessed. Motivated by these phenomena, in the present article, we present a mathematical model for the cilia-generated propulsion of an electrically-conducting viscoelastic physiological fluid in a ciliated channel under the action of an externally
applied static magnetic field. The rheological behavior of the fluid is simulated with the Johnson-Segalman constitutive model which allows internal wall slip. The regular or coordinated movement of the ciliated edges (which line the internal walls of the channel) is represented by a metachronal wave motion in the horizontal direction which generate a two-dimensional velocity profile with the parabolic profile in the vertical direction. This mechanism is imposed as a periodic moving velocity boundary condition which generates propulsion in the channel flow. Under the
classical lubrication approximation (long wavelength and low Reynolds' number), the boundary value problem is rendered non-dimensional and solved analytically with a perturbation technique. The influence of the geometric, rheological (slip and Weissenberg number) and magnetic
parameters on the velocity, pressure gradient and the pressure rise (evaluated via the stream function in symbolic software) are presented graphically and interpreted at length.

Citation

Manzoor, N., Beg, O., Maqbool, K., & Shaheen, S. (2019). Mathematical modelling of ciliary propulsion of an electrically conducting Johnson-Segalman physiological fluid in a channel with slip. Computer Methods in Biomechanics and Biomedical Engineering, 22(7), 685-695. https://doi.org/10.1080/10255842.2019.1582033

• Journal Article Type: Article
• Acceptance Date: Feb 10, 2019
• Online Publication Date: Mar 4, 2019
• Publication Date: Mar 4, 2019
• Deposit Date: Mar 13, 2019
• Publicly Available Date: Mar 4, 2020
• Journal: Computer Methods in Biomechanics and Biomedical Engineering
• Print ISSN: 1025-5842
• Electronic ISSN: 1476-8259
• Publisher: Taylor and Francis
• Volume: 22
• Issue: 7
• Pages: 685-695
• DOI: https://doi.org/10.1080/10255842.2019.1582033
• Publisher URL: https://doi.org/10.1080/10255842.2019.1582033
• Related Public URLs: https://www.tandfonline.com/toc/gcmb20/current