Corrections to long wavelength approximation of peristalsis viscous fluid flow within a wavy channel


Chinese Journal of Physics, vol.89, pp.340-354, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 89
  • Publication Date: 2024
  • Doi Number: 10.1016/j.cjph.2024.03.030
  • Journal Name: Chinese Journal of Physics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, zbMATH
  • Page Numbers: pp.340-354
  • Keywords: Drag, Finite wave number corrections, Long wavelength approximation, Peristalsis, Perturbation solutions, Pressure gradient, Velocity field
  • Hacettepe University Affiliated: Yes


This research paper delves into the pumping phenomenon of peristaltic motion within a wavy, straight channel. Our aim is to provide analytical solutions for the well-established long wavelength and small Reynolds number approximation. To achieve this, we derive third-order corrections to the ideal leading-order solutions. These closed-form solutions encompass the axial and transverse velocity components, pressure rise and axial pressure gradients, and drag force along the wavy channel. Additionally, we elucidate the trapping phenomena of viscous flowing boluses through stream function contours. Notably, these exact solutions enable the analysis of peristalsis with finite wave numbers and moderate Reynolds numbers, eliminating the need for numerical simulations of the full Navier–Stokes equations at such physical parameters. Our simulations reveal that the pumping region is significantly influenced by short wavelength and moderate Reynolds number corrections. Further, the corrections enhance the drag force, and cell divisions within the boluses are observed at higher Reynolds numbers. The analytical derivations provided save researchers from the need for full simulations of the complex equations to acquire the key insights and contributions to capture the essence of the physical peristalsis mechanism inside wavy channels.