Effect of first order chemical reactions on the dispersion coefficient associated with laminar flow through fibrosis affected lung

Abstract

In this paper, we worked on the effective area average concentration and dispersion coefficient associated with the unsteady flow, to understand the dispersion in the fibrosis-affected lung. We assumed that the tube wall (i.e. alveolar or pulmonary capillary wall) is thicker than its normal size due to fibrosis and chemical species may go through linear first-order kinetic reactions, one is reversible phase exchange with the wall material and other is irreversible absorption into the tube wall. By considering diffusivity as a function of thickness, the dispersion can be calculated by the distribution of concentration of gas along a tube. Mathematical modeling is done by using diffusion equation; and effects of various dimensionless parameters e.g., the Damkohler number (DA), phase partitioning number (α), dimensionless absorption number (Γ), thickness and permeability of wall are observed. Numerical simulation shows that the diffusion rate through the respiratory wall is decreased significantly as the thickness of wall increases, while it increased with the increment in the porosity of wall, the concentration of species increased when the tube wall thickness increases; which cause reduction in the spread of the species; additionally, the dispersion coefficient achieves the steady-state values in a very short time when 0 < DA ⩽1 and absorption rate < 1, while for 1 < DA ⩽20 and absorption rate = 1 long time dispersion is achieved.