用Navier-Stokes-Brinkman方程研究人肺胆周层的血流

IF 0.7 Q2 MATHEMATICS Tamkang Journal of Mathematics Pub Date : 2021-11-10 DOI:10.5556/j.tkjm.54.2023.3738
Kanognudge Wuttanachamsri, Nattapol Oangwatcharaparkan
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引用次数: 1

摘要

在人的呼吸道中,吸入的空气常被粉尘、化学喷雾等奇异颗粒污染,可能使人患上呼吸道疾病。然而,人体有一个先天的免疫系统,通过分泌粘液来捕获外来颗粒,这些颗粒通过免疫系统中上皮细胞表面的微小毛发的运动从体内移除。含有细小毛发或纤毛的这一层被称为纤毛周层。本文利用Navier-Stokes-Brinkman方程计算了纤毛跳动时PCL内流体的运动速度。我们采用伽辽金有限元法来确定数值解。对于方程的稳定线性情况,数值结果与精确解很好地吻合。包括时间导数和非线性项,我们表明液体的速度受到固体速度的影响,这符合流体流动的物理意义。该结果可作为黏液层的底边界条件,以求得黏液在人体肺部的流速。
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The Flow in Periciliary Layer in Human Lungs with Navier-Stokes-Brinkman Equations
In the human respiratory tract, air breathed in is often contaminated with strange particles such as dust and chemical spray, which may cause people respiratory diseases. However, the human body has an innate immune system that helps to trap the debris by secreting mucus to catch the foreign particles, which are removed from the body by the movement of tiny hairs lining on the surface of the epithelial cells in the immune system. The layer containing the tiny hairs or cilia is called Periciliary Layer (PCL). In this research, we find the velocity of the fluid in the PCL moved by a ciliary beating by using the Navier-Stokes-Brinkman equations. We apply the Galerkin finite element method to determine numerical solutions. For the steady linear case of the equation, the numerical result is in good agreement with an exact solution. Including the time derivative and nonlinear terms, we show that the velocity of the liquid is affected by the velocity of the solid, which follows the physical meaning of the fluid flow. The result can be applied as a bottom boundary condition of the mucous layer to be able to find the velocity of mucus in the human lungs.
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来源期刊
CiteScore
1.50
自引率
0.00%
发文量
11
期刊介绍: To promote research interactions between local and overseas researchers, the Department has been publishing an international mathematics journal, the Tamkang Journal of Mathematics. The journal started as a biannual journal in 1970 and is devoted to high-quality original research papers in pure and applied mathematics. In 1985 it has become a quarterly journal. The four issues are out for distribution at the end of March, June, September and December. The articles published in Tamkang Journal of Mathematics cover diverse mathematical disciplines. Submission of papers comes from all over the world. All articles are subjected to peer review from an international pool of referees.
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