Vol.18, No.4, 2021, pp.157-172, doi:10.32604/mcb.2021.015605
The Influence of Drag on Nonlinear Oscillatory Flow through Concentric Annulus
  • B. Umadevi1,*, C. V. Vinay1, P. A. Dinesh2
1 Department of Mathematics, JSS Academy of Technical Education, Bangalore, India
2 Department of Mathematics, Ramaiah Institute of Technology, Bangalore, India
* Corresponding Author: B. Umadevi. Email:
Received 30 December 2020; Accepted 13 August 2021; Issue published 27 October 2021
A mathematical model has been developed to study the effect of particle drag parameter and frequency parameter on velocity and pressure gradient in nonlinear oscillatory two phase flow. The main purpose is to apply the model to study the combined effect of introduction of the catheter and elastic properties of the arterial wall on the pulsatile nature of the blood flow. We model the artery as an isotropic thin walled elastic tube and the catheter as a coaxial flexible tube. Blood is modeled as an incompressible particulate viscous Newtonian fluid. Perturbation technique has been applied to find the approximations for velocity and pressure gradient up to second order. Numerical solutions are investigated with graphical presentations to understand the effects of drag parameter, frequency parameter and phase angle on velocity along radial direction and pressure gradient along axial directions. As the drag parameter increases, mean pressure gradient and mean velocity will be decreased. As frequency parameter increases mean velocity profile bends near the outer wall. Due to elastic nature of artery wall, a thin catheter experience small oscillations and a thick catheter remains stationary inside the artery. Finally, the effect of catheterization on various physiologically important flow rate characteristics—mean velocity, mean pressure gradient are studied for a range of different catheter sizes, particle drag parameter and frequency parameters.
Particle drag; oscillatory flow; catheter
Cite This Article
Umadevi, B., Vinay, C. V., Dinesh, P. A. (2021). The Influence of Drag on Nonlinear Oscillatory Flow through Concentric Annulus. Molecular & Cellular Biomechanics, 18(4), 157–172.
This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.