The Velocity of PCL Fluid in Human Lungs with Beaver and Joseph Boundary Condition by Using Asymptotic Expansion Method

Poopra Poopra,Wuttanachamsri Wuttanachamsri

doi:10.3390/math7060567

Poopra Poopra, Wuttanachamsri Wuttanachamsri

Open Access

https://doi.org/10.3390/math7060567

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Journal: Mathematics	Publication Date: Jun 24, 2019
Citations: 3	License type: CC BY 4.0

Affiliation: King Mongkut's Institute of Technology Ladkrabang

Abstract

Humans breathe air into the respiratory system through the trachea, but with all the pollutants in our environment (both outside and inside), the air we breathe may not be clean. When that is so, the respiratory system secretes mucus to trap dirt that is inhaled through the nostrils. The respiratory tract contains hair-like structures in the epithelial tissue, called cilia: These wave back and forth to help expel particles of dust, dirt, mucus, and contaminants from the body. Cilia are found in this layer (a porous medium) and the fluid in this layer is called the periciliary layer (PCL). This study aims to determine the velocity of the PCL fluid flow in motile cilia. Usually, fluids move due to pressure changes, but in this study, the velocity of solids or of the cilia moves the PCL fluid. Stokes‐Brinkman equations are used to determine the velocity of PCL fluid flow when cilia form an angle with the horizontal plane. The Beavers and Joseph boundary condition is applied in this study. The asymptotic expansion method is adapted in order to determine the velocity of PCL from the movement of the cilia.

Highlights

The human body contains numerous cilia, which are omnipresent inside and outside of the body.Cilia are hair-like organelles that provide locomotion to liquids throughout the body
We studied the fluid flow in the periciliary layer (PCL) of the respiratory tract using the of asymptotic expansion method to determine the velocity of PCL fluid
The PCL is divided into two domains: the free fluid and the porous medium domains

Summary

Introduction

The human body contains numerous cilia, which are omnipresent inside and outside of the body. Cilia are hair-like organelles that provide locomotion to liquids throughout the body. This study focuses on cilia inside the body, in the respiratory system. The human respiratory system is illustrated, with labeling of the nose, trachea, and lungs. We breathe in and out all the time, and as we inhale, some dust and pathogens will enter the body. The human body has a defense mechanism to protect against these foreign particles. In a closer look at the immune system, a diagram representing a cross-section of the trachea is displayed, and Figure 3 shows a close-up view of the trachea In a closer look at the immune system, a diagram representing a cross-section of the trachea is displayed in Figure 2, and Figure 3 shows a close-up view of the trachea

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