A Theoretical and Experimental Study of an Oscillatory Flow Through a Compliant Tube

Periodic flows are ubiquitous in biological and industrial systems. A theoretical and experimental study of an oscillatory flow through a finite compliant tube is reported. A horizontally submerged elastic PDMS tube is mounted between two fixed ends, each instrumented with a pressure sensor. Two rigidly connected piston-cylinder assemblies, such that their motions are out of phase, ensure that the amount of fluid pushed into the tube from one end is identical to the amount pulled out from the other, thereby making the flow purely oscillatory. The tube's shape is monitored with a high-speed camera. The instantaneous tube profile is obtained by processing the footage frames offline in MATLAB. A model is developed to describe the tube's wall radial motion. The resulting equation is solved analytically for small deformations to obtain the predicted local deformation history. For radial deformations within ~10%, the analytical solution agreed well with observation. A complete solution for the flow field is then proposed within the said deformation limit. This study showcases a setup where a compliant tube's flow conditions are measured in tandem with its deformation, offering a unique avenue through which fluid-structure interaction models in compliant ducts can be tested and refined.