Mathematical assessment of the spermatozoa transport through couple stress fluid in an asymmetric human cervical canal.

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.