Swimming of spermatozoa through couple stress fluid in an asymmetric human cervical canal is investigated in the present theoretical analysis. A couple of fourth-order partial differential equations arising from the mathematical modelling of the proposed model is solved analytically. Flow variables like pressure gradient, propulsive velocity, mucus velocity and time mean flow rate are analysed for the pertinent parameters. Conspicuous features of the pumping characteristics are explored. It is found that pressure rise facilitates the motion of spermatozoa to fertilize an ovum in the female reproductive tract, whereas pressure drop by inverting the direction of spermatozoa controls the probability of pregnancy. Maximal propulsive velocity of the spermatozoa is reported in the absence of travelling waves along the cervical walls. Minute impact of phase difference on propulsive velocity is evident. An analogy of the current analysis with the existing literature is also made.

中文翻译：

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精子在不对称人类宫颈管中通过夫妇应激流体运输的数学评估。

在目前的理论分析中，研究了精子在不对称的人类宫颈管中通过耦合应力流体游动。对提出的模型的数学建模产生的几个四阶偏微分方程进行了解析求解。分析了压力梯度、推进速度、粘液速度和时间平均流速等流动变量的相关参数。探索了泵送特性的显着特征。研究发现，压力升高促进了精子在女性生殖道中的运动，使卵子受精，而通过反转精子方向的压力下降控制了怀孕的可能性。在没有沿宫颈壁行波的情况下，报告了精子的最大推进速度。相位差对推进速度的微小影响是显而易见的。还对当前分析与现有文献进行了类比。