Eur. Phys. J. Plus (2021) 136: 693
https://doi.org/10.1140/epjp/s13360-021-01669-5

Regular Article

Dynamical interaction effects on soft-bodied organisms in a multi-sinusoidal passage

¹ NUTECH, School of Applied Sciences and Humanities, National University of Technology, 44000, Islamabad, Pakistan
² Department of Mathematics and Statistics, International Islamic University, 44000, Islamabad, Pakistan
³ Department of Mathematics, Northern University, 24100, Nowshera, KPK, Pakistan
⁴ School of Mathematics and Statistics, Beijing Institute of Technology, 100081, Beijing, China

^a zeeshanasghar@nutech.edu.pk, zee.qau5@gmail.com

Received: 1 January 2020
Accepted: 6 June 2021
Published online: 27 June 2021

Abstract

Soft nano-robots are transportable in a hydrodynamic environment (governed by Stokes equations) just like propelling spermatozoa in the female genital tract. In biomedicine, these artificial crawlers which are useful for drug delivery, diagnostic, or therapeutic purposes are controlled via electric and magnetic sensors. In addition to the fluid rheology, these external forces tend to reduce/enhance the speed of sperm cells to control fertility. To investigate such effects on active swimmers we calculate the speed of an undulating sheet propelling through non-Newtonian Couple stress fluid. The swimmers are assumed to be bounded in a multi-sinusoidal channel with magnetic effects. The dynamical interaction of the micelles aligned along the wall of the channel is also considered. After utilizing Galilean transformation, dimensionless variables, stream function, low Reynolds, and long-wavelength approximations on momentum equation, one arrives at the sixth-order ordinary differential equation with six boundary conditions involving two unknowns, i.e., flow rate and organism speed. This BVP is solved analytically via Wolfram Mathematica 12.0.1. The unknowns satisfying the dynamic equilibrium conditions are simulated (numerically) via the modified Newton–Raphson method. Consequently, work done by the microorganism is also computed. In the end, the results obtained through the hybrid solution approach are compared with the existing results and discussed in detail.