Enhancing motility of micro-swimmers via electric and dynamical interaction effects

The purpose of this article is to discuss the motion of five different undulating swimming sheets assisted by an electric field and dynamical interactions. The sine or cosine wavy sheet can be a verge on the spermatozoa's surface. The human cervix is approximated as a rigid two-dimensional channel (with anti-slip effects) under the action of an external electric field. The flow equations of viscus mucus are modeled by using Navier-Stokes equations. The Poisson-Boltzmann equation is employed to simulate the electroosmotic term. Utilizing lubrication and Debye-Huckel approximation, we finally obtained a fourth-order ordinary differential equation with an axial component of velocity as a dependent variable. The closed-form expressions of upper and lower mucus velocity, pressure gradient, and stress components are obtained by utilizing Wolfram Mathematica 13.1. This solution is further used in equilibrium conditions to check whether they are satisfied or not. Off course, conditions will not be satisfied since the guesses are crude. The numerical values of cell speed and flow rate are refined via a root-finding algorithm. These unknowns are further utilized in the formula of work done by the swimmer. The numerical results of cell speed, flow rate, and power delivered are plotted in MATLAB R2022b.