{"title":"The Influence of Drag on Nonlinear Oscillatory Flow through Concentric Annulus","authors":"B Umadevi, C. V. Vinay, P. A. Dinesh","doi":"10.32604/mcb.2021.015605","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":48719,"journal":{"name":"Molecular & Cellular Biomechanics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Molecular & Cellular Biomechanics","FirstCategoryId":"1087","ListUrlMain":"https://doi.org/10.32604/mcb.2021.015605","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Biochemistry, Genetics and Molecular Biology","Score":null,"Total":0}
引用次数: 0
Abstract
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.
期刊介绍:
The field of biomechanics concerns with motion, deformation, and forces in biological systems. With the explosive progress in molecular biology, genomic engineering, bioimaging, and nanotechnology, there will be an ever-increasing generation of knowledge and information concerning the mechanobiology of genes, proteins, cells, tissues, and organs. Such information will bring new diagnostic tools, new therapeutic approaches, and new knowledge on ourselves and our interactions with our environment. It becomes apparent that biomechanics focusing on molecules, cells as well as tissues and organs is an important aspect of modern biomedical sciences. The aims of this journal are to facilitate the studies of the mechanics of biomolecules (including proteins, genes, cytoskeletons, etc.), cells (and their interactions with extracellular matrix), tissues and organs, the development of relevant advanced mathematical methods, and the discovery of biological secrets. As science concerns only with relative truth, we seek ideas that are state-of-the-art, which may be controversial, but stimulate and promote new ideas, new techniques, and new applications.