Every group of microorganism utilizes a diverse mechanical strategy to propel through complex environments. These swimming problems deal with the fluid–organism interaction at micro-scales in which Reynolds number is of the order of 10⁻³. By adopting the same propulsion mechanism of so-called Taylor’s sheet, here we address the biomechanical principle of swimming via different wavy surfaces. The passage (containing micro-swimmers) is considered to be passive two-dimensional channel filled with viscoelastic liquid, i.e., Oldroyd-4 constant fluid. For some initial value of unknowns, i.e., cell speed and flow rate of surrounding liquid, the resulting boundary value problem is solved by robust finite difference scheme. This convergent solution is further employed in the equilibrium conditions which will obviously not be satisfied for such crude values of unknowns. These unknowns are further refined (to satisfy the equilibrium conditions) by modified Newton–Raphson algorithm. These computed pairs are also utilized to compute the energy losses. The speed of swimming sheet its power delivered and flow rate of Oldroyd-4 constant fluid are compared for different kinds of wavy sheets. These results are also useful in the manufacturing of artificial (soft) microbots and the optimization of locomotion strategies.

每组微生物都利用不同的机械策略来推动复杂的环境。这些游泳问题涉及在雷诺数为 10 ^-3数量级的微观尺度上的流体-生物相互作用. 通过采用与所谓的泰勒薄片相同的推进机制，我们在这里解决了通过不同波浪表面游泳的生物力学原理。通道（包含微型游泳器）被认为是充满粘弹性液体，即Oldroyd-4 恒定流体的被动二维通道。对于一些未知的初始值，即细胞速度和周围液体的流速，由此产生的边界值问题通过鲁棒有限差分格式求解。该收敛解进一步用于平衡条件，对于这种粗略的未知值显然不满足。这些未知数通过改进的 Newton-Raphson 算法进一步细化（以满足平衡条件）。这些计算出的对也用于计算能量损失。比较了不同类型波浪板的游泳板的速度，其传递的功率和Oldroyd-4恒定流体的流量。这些结果也可用于制造人造（软）微型机器人和优化运动策略。