A microcontinuum analysis of the self propulsion of the spermatozoa in the cervical canal

The hydrodynamics of the self propulsion of a spermatozoa, swimming through the mucus filling the cervical channel, is investigated. The mucus is modeled as a micropolar fluid and the spermatozoa as a 2-dimensional sheet swimming at low Reynolds number between two rigid walls. The wavelengths of the propulsive waves passing down the sheet are assumed to be very large compared to the channel spacing, but the amplitude of the propulsive waves is arbitrary. Expressions for the propulsive velocity and the energy expended by the swimming sheet are obtained in terms of various parameters involved. The results are elaborated through graphs. It is found that both the propulsive velocity and the rate of working by the sheet increase as the value of the micropolar parameters $\text{N}$ increases and that of $\text{L}$ decreases.