A study on the resonance of sputum plug in the airway oscillation

Abstract

With reference to the asymmetrical two-dimensional stenosis model used in my previous paper, a mathematical model for the evaluation of the efficiency on the resonant amplitude of the oscillation of the plug of sputum has been presented. The viscous property of the sputum is assumed to obey the Casson fluidity which was introduced to represent the non-Newtonian blood flow. Using the symbols as [A=height of the plug; l=the width; R=l/A; ρ=density of the sputum: T=the surface tension: E=the elasticity; fc=the yield stress; ηc=viscosity of the sputum at a very high shear rate; r=radius of the airway; ωR=the angular frequency of the oscillation of the plug at resonance; PX=amplitude of the oscillation of the pressure gradient; A_PR= the amplitude at resonant amplitude of the oscillation of the plug], the results have become clear as follows.