Mathematical Modeling of Casson type Biofluid transport in a Gynecological reproductive-tract

Source abstract

Transport within the female reproductive tract is governed by the coupled action of ciliary activity, smooth-muscle contractility and luminal tubal fluid. The fallopian tube is a seromuscular organ with infundibular, ampullary, isthmic and intramural regions; coordinated ciliary motion, muscular activity and tubal fluid contribute to transport. This study develops a reduced-order continuum model in which a Casson-type constitutive law represents a yield-stress biological fluid. The incompressible continuity and Navier–Stokes equations are formulated in a two-dimensional deformable channel. A travelling-wave transformation, long-wavelength approximation and low-Reynolds-number limit reduce the PDE system to a nonlinear ODE boundary-value problem. The ODEs are written in first-order form and solved using classical fourth-order Runge–Kutta integration with a shooting procedure. Dimensionless parameters include Reynolds number, wave-number ratio, amplitude ratio and a Casson/yield-stress parameter. Illustrative computations demonstrate velocity-profile flattening, plug-region formation, pressure-gradient modulation, pressure rise and RK4 convergence. The framework is intended for mechanistic research on reproductive-tract transport and should not be interpreted as a clinical predictive model.