The sperm propelling mechanism has been proposed as a possible resource for soft micro-robots in confined spaces, with potential applications in biomedical engineering. Human sperm cells essentially swim through the non-Newtonian liquid (cervical mucus) to reach their target. Thus, sperm cells swimming through non-Newtonian fluids is not vital only for physiology, but also for the fabrication of swimming micro-robots. Inspired by these remarkable applications, we examine the basic mechanics of spermatozoa motility using an undulating sheet model. This undulating sheet is bounded between two rigid walls which is self-propeling in the negative axial direction. The liquid around the spermatozoa is taken as Carreau fluid with electro-osmotic properties. The application of the lubrication approximation results in the reduction of momentum equations. The resulting ODE is solved numerically via the finite difference method and MATLAB’s built-in routine bvp5c. The unknowns that are present in the boundary conditions are refined by the root-finding algorithm. Power losses, cell speed, flow rate, velocity of the fluid, and streamline pattern are visualized by graphs. The findings of this study have important implications for the designing and optimization of electrically controlled microswimmers.

精子推进机制已被提议作为有限空间中软体微型机器人的可能资源，在生物医学工程中具有潜在的应用。人类精子细胞本质上是游过非牛顿液体（宫颈粘液）到达目标。因此，精子细胞在非牛顿流体中游泳不仅对于生理学至关重要，而且对于游泳微型机器人的制造也至关重要。受这些非凡应用的启发，我们使用起伏的片层模型研究了精子活力的基本机制。该波状片材被限制在两个刚性壁之间，该刚性壁在负轴向方向上自推进。精子周围的液体被视为具有电渗特性的卡罗液。润滑近似的应用导致动量方程的简化。生成的 ODE 通过有限差分法和 MATLAB 的内置例程 bvp5c 进行数值求解。边界条件中存在的未知数通过寻根算法进行细化。功率损失、细胞速度、流速、流体速度和流线模式通过图表可视化。这项研究的结果对于电控微型游泳器的设计和优化具有重要意义。