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. 2020 Jun 22;10:10102. doi: 10.1038/s41598-020-66887-w

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© The Author(s) 2020

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Mechanism of forward transport (pumping) driven by peristalsis in fluids and solids. (a) The movement of fluid (the dots represent fluid particles) driven by peristaltic compression of the walls of a 2D tube. The fluid movement in this figure is calculated using the Navier-Stokes equation with zero traction (pressure) at the two ends of the tube. (b) The pressure field in the tube in the deformed state. The fluid is displaced by the moving walls and this creates high pressure at the neck of wall movement. The pressure difference is same for retrograde and anterograde flow. However, the resistance is large posterior to the site of contraction. Compared to anterograde flow, retrograde flow needs the fluid to flow through a narrower tube. This results in a greater anterograde flow (magenta dots in a) compared to retrograde flow (green dots in a). (c) The movement of a solid bolus (yellow ellipse) driven by peristaltic motion of the walls of a 2D tube. The contact forces between the moving walls and the solid bolus are responsible for forward transport. The position of the solid bolus with respect to the dotted lines shows that the solid is moved forward. (a) was generated with MATLAB 2019b(https://www.mathworks.com/products/matlab.html). (b) was generated with COMSOL Multiphysics 5.4 (http://comsol.com). (c) was drawn in Adobe Illustrator 23.0(https://www.adobe.com/products/illustrator.html).