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

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 nondimensional parameters describe the problem, the Peclet number 2 Pe Ua D  , the Reynolds number 2 Re Ua   and an electrostatic parameter   2 2 0 0 4 a c q T     . Here U is the mean velocity, a the pipe radius and D the diffusion coefficient due to Brownian motion given by 3π D T Cu d    , where Cu is the Cunninghamfactor     1 2.34 1.05exp 0.39 Cu d d       Here d is the particle diameter and  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.