Related Experiment Video
Updated: Jul 31, 2026

Protocol for Biofilm Streamer Formation in a Microfluidic Device with Micro-pillars
Published on: August 20, 2014
Waves in initially stressed fluid-filled thick tubes
1Marmara Research Centre, Department of Mathematics, Gebze-Kocaeli, Turkey.
Abstract:
In this paper, treating the artery as a thick walled cylindrical shell made of an incompressible, elastic and isotropic material and the blood as an incompressible inviscid fluid, by taking the inertia of the wall into account, the propagation of harmonic waves in an initially stressed tube, filled with an inviscid fluid, is studied. Utilizing inner-pressure-inner-cross-sectional-area relation in the linear momentum equation of the fluid, together with the continuity equation, we obtained two nonlinear equation governing the axial velocity and the cross-sectional area of the tube. Assuming that the dynamical motion superposed on large initial static deformation is small, a harmonic wave type of solution to incremental equations is sought and the dispersion relation is obtained as a function of transmural pressure, axial stretch, thickness ratio and the wave number. The wave speed is evaluated numerically for various materials and thickness/radius, and the results are depicted in graphical forms. The result indicates that, due to the inertial component of pressure, the wave is dispersive. The present formulation is compared with some previously published works.
Related Concept Videos
Fluid Pressure over Curved Plate of Constant Width
Stresses under Combined Loadings
The process begins by slicing the tube at critical points and analyzing the internal forces and stress components at these sections, focusing on the centroid. Normal stresses, generated by axial forces and bending moments, are either compressive or tensile and vary across the section from...
Navier–Stokes Equations
Steady, Laminar Flow Between Parallel Plates
Steady, Laminar Flow in Circular Tubes
Turbulent Flow

