Effect of first order chemical reactions through tissue-blood interface on the partial pressure distribution of inhaled gas

Gas exchange is an essential process to get fresh oxygenated air from the environment. In the human respiratory system, partial pressure is responsible for exchanging gas between tissue-blood capillary (inter capillary). However, the mechanisms of partial pressure distribution in the human respiratory system remain incompletely understood in terms of inter-capillary transmission with tissue porosity and reactive boundary conditions. In this paper, we worked on the spatial (radial) and temporal variations of inhaled gas partial pressure through inter capillary. We assumed that the tissue of alveoli is porous and the material of blood capillary is absorptive and reactive and gas could bear linear first-order kinetic reactions, one is reversible among the material of blood capillary and the other is irreversible into the surrounding tissue. Mathematical modeling is done by using diffusion equation; and the effect of various dimensionless parameters e.g. the Damkohler number (DA), phase partitioning number (α), dimensionless absorption number (Γ) are analyzed. Numerical simulation shows that an increment in porosity does not change convection speed but the diffusion of gas increases in alveolar tissue, resultantly, partial pressure gradient of the gas decreases in tissue and increases in blood capillary. However, by increasing the breathing rate, the partial pressure of the gas inside the blood first decreases, and after some time it increases gradually with the breathing rate. Additionally, the dispersion coefficient advanced toward its steady-state in a short time at absorption rate Γ≤ 0.1 and Damkohler number 1≤DA≤10, while long-time dispersion is achieved at porosity ϵ = 0.9, absorption rate Γ = 1, and phase exchange rate 10