A Comprehensive Review on Peristaltic Pumping of Newtonian Fluids in Channels and Tubes with Permeable and Flexible Walls

Peristaltic pumping is a fundamental transport mechanism widely observed in biological systems and extensively applied in engineering and biomedical devices. With a focus on flexible and permeable wall effects, this paper provides a comprehensive and critical assessment of theoretical advancements pertaining to the peristaltic transport of Newtonian fluids in axisymmetric tubes and two-dimensional channels. The classical long-wavelength and low Reynolds number approximations are discussed in detail, highlighting their role in simplifying the governing equations and enabling analytical solutions. Key flow characteristics such as pressure–flow rate relationships, pumping range, reflux, and trapping phenomena are critically reviewed. The paper also summarizes perturbation techniques used to address cases involving finite inertia, small amplitude ratios, and non-negligible wave numbers. Relevant applications in physiological flows—such as ureteral transport, gastrointestinal motion, and blood flow in small vessels—as well as industrial peristaltic pumps are examined through existing literature. By consolidating major theoretical contributions and modeling approaches, this review provides a unified framework for understanding peristaltic pumping mechanisms and identifies directions for future research in biomechanics and fluid transport systems.