Biological interactions between carreau fluid and micro-swimmers in a complex wavy canal with MHD effects

Ali, N; Asghar, Z; Sajid, M; Beg, OA

Abstract

The efficient magnetic swimming of actual or mechanically designed micro-swimmers within bounded regions is reliant on several factors. Few of which are: the actuation of these swimmers via magnetic field, rheology of surrounding liquid (with dominant viscous forces), nature of medium (either porous or non-porous), position (either straight, inclined or declined) and state (either active or passive) of the narrow passage. To witness these interactions, we utilize Carreau fluid with Taylor swimming sheet model under magnetic and porous effects. Moreover, the cervical canal is approximated as a two-dimensional complex wavy channel inclined at certain angle with the horizontal. The momentum equations are reduced by means of lubrication assumption, which finally leads to a fourth order differential equation. MATLAB's built-in bvp4c function is employed to solve the resulting boundary value problem (BVP). The solution obtained via bvp4c is further verified by finite difference method (FDM). In both these methods, the refined values of flow rate and cell speed are computed by utilizing modified Newton-Raphson method. These realistic pairs are further utilized, to calculate the energy delivered by the micro-swimmer. The numerical results are plotted and discussed at the end of the article. Our study explains that the optimum speed of the micro-organism can be achieved by means of exploiting the fluid rheology and with the suitable application of the magnetic field. The peristaltic nature of the channel walls and porous medium may also serve as alternative factors to control the speed of the propeller.

Citation

Ali, N., Asghar, Z., Sajid, M., & Beg, O. (2019). Biological interactions between carreau fluid and micro-swimmers in a complex wavy canal with MHD effects. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 41, 446. https://doi.org/10.1007/s40430-019-1953-y

• Journal Article Type: Article
• Acceptance Date: Aug 31, 2019
• Online Publication Date: Sep 21, 2019
• Publication Date: Sep 21, 2019
• Deposit Date: Sep 3, 2019
• Publicly Available Date: Sep 21, 2020
• Journal: Journal of the Brazilian Society of Mechanical Sciences and Engineering
• Print ISSN: 1678-5878
• Electronic ISSN: 1806-3691
• Publisher: Springer Verlag
• Volume: 41
• Pages: 446
• DOI: https://doi.org/10.1007/s40430-019-1953-y
• Publisher URL: https://doi.org/10.1007/s40430-019-1953-y
• Related Public URLs: https://link.springer.com/journal/40430
• Additional Information: Access Information : This is a post-peer-review, pre-copyedit version of an article published in Journal of the Brazilian Society of Mechanical Sciences and Engineering. The final authenticated version is available online at: http://dx.doi.org/10.1007/s40430-019-1953-y