Efficiency optimization of micro-swimmers in viscoelastic bio-fluids within complex cervical environments

Biological fluids often harbor motile organisms, making the study of micro-swimming mechanisms within these environments critical for advancing medical applications. This research aims to deepen our understanding of how micro-swimmers interact with their surrounding fluids. Addressing the complexities of these interactions requires an interdisciplinary approach that integrates biology, mathematics, and physics. In this study, we utilize the classical Navier-Stokes equations to model the rheological behavior of mucus, focusing on its representation as a Finitely Extensible Nonlinear Elastic Peterlin (FENE-P) fluid. We analyze three distinct scenarios within bounded channels: passive, simple active, and complex active configurations, all filled with FENE-P mucus. The propulsion in these micro-channels is driven by the movement of spermatozoa and the dynamics of the channel walls, underpinned by key assumptions such as creeping flow and lubrication theory. Conservation of momentum yields a second-order differential equation, which we solve numerically to determine the propulsion speed under specific conditions. Our findings outline the conditions that optimize swimming efficiency, offering valuable insights into the design of artificial micro-swimmers with customizable speeds. These results hold significant potential for applications in biomedical engineering and the development of targeted delivery systems in healthcare.