Deposition of charged nano-particles in the human airways including effects from cartilaginous rings

Abstract

This paper presents a numerical study of the deposition of spherical charged nano-particles caused by convection, Brownian diffusion and electrostatics in a pipe with a cartilaginous ring structure. The model describes the deposition of charged particles in the different generations of the tracheobronchial tree of the human lung. The upper airways are characterized by a certain wall structure called cartilaginous rings which modify the particle deposition when compared to an airway with a smooth wall. The problem is defined by solving Naver-Stokes equations in combination with a convective-diffusion equation and Gauss law for electrostatics. Three non- dimensional parameters describe the problem, the Peclet number Pe = 2 ū a/D , the Reynolds number Re = ū a/v and an electrostatic parameter α = α 2 c 0 q 2 /(4 ε 0 κT ) . Here U is the mean velocity, a the pipe radius and D the diffusion coefficient due to Brownian motion given by D = κTCu /3 πμd , where Cu is the Cunningham-factor Cu =1+ λ/d (2.34+1.05exp(-0.39 d/λ )) Here d is the particle diameter and λ the mean free path of the air molecules. Results are provided for generations G4-G16 of the human airways. The electrostatic parameter is varied to model different concentrations and charge numbers.