{"title":"用Navier-Stokes-Brinkman方程研究人肺胆周层的血流","authors":"Kanognudge Wuttanachamsri, Nattapol Oangwatcharaparkan","doi":"10.5556/j.tkjm.54.2023.3738","DOIUrl":null,"url":null,"abstract":"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. \nHowever, 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. \nThe 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. \nWe 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. \nIncluding 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. \nThe 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.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2021-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"The Flow in Periciliary Layer in Human Lungs with Navier-Stokes-Brinkman Equations\",\"authors\":\"Kanognudge Wuttanachamsri, Nattapol Oangwatcharaparkan\",\"doi\":\"10.5556/j.tkjm.54.2023.3738\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"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. \\nHowever, 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. \\nThe 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. \\nWe 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. \\nIncluding 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. \\nThe 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.\",\"PeriodicalId\":45776,\"journal\":{\"name\":\"Tamkang Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2021-11-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Tamkang Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5556/j.tkjm.54.2023.3738\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tamkang Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5556/j.tkjm.54.2023.3738","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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.
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.