Deposition of submicron charged particles in turbulent pipe flow with an application to the trachea

H Åkerstedt


The paper presents a study of the deposition of submicron charged spherical particles caused by convection, Brownian and turbulent diffusion in a pipe with a smooth wall and with a cartilaginous ring wall structure. The model is supposed to describe deposition of charged particles in generation 0 (trachea) of the human respiratory airways. The flow is modeled with a SST-turbulence model combined with a convective-diffusion equation including electric field migration for the particles, and Poisson’s equation for the determination of the electrostatic potential in terms of the space-charge density of the particles. An approximate analytical solution is derived for the case of a smooth pipe which is used to verify the numerical solutions obtained from using the commercial software Comsol Multiphysics. Numerical results of deposition rates are also provided for the case of a pipe with a cartilaginous ring wall structure.

Full Text:



Melandri C, Tarroni G, Prodi V, De Zaiacomo T,Formignani M, Lombardi CC. Deposition of charged particles in the human airways. J Aerosol Sci. 1983;14(5):657-669.

Melandri C, Prodi V, Tarroni G, et al. On the deposition of unipolarly charged particles in the human respiratory tract. Inhaled Part.1975;4 Pt 1:193-201.

Bailey A. The inhalation and deposition of charged particles within the human lung. J Electrostatics. 1997;42(1):25-32.

Bailey A, Hashish A, Williams T. Drug delivery by inhalation of charged particles.J Electrostatics. 1998;44(1):3-10.

Balachandran W, Machowski W, Gaura E, Hudson C. Control of drug aerosol in human airways using electrostatic forces. J Electrostatics.1997;40–41:579-584.

Xi J, Si X, Longest W. Electrostatic charge effects on pharmaceutical aerosol deposition in human Nasal–Laryngeal airways. Pharmaceutics. 2014;6(1):26-35.

Koullapis PG, Kassinos SC, Bivolarova MP,Melikov AK. Particle deposition in a realistic geometry of the human conducting airways: Effects of inlet velocity profile, inhalation flow rate and electrostatic charge. J Biomech. Crossref

Åkerstedt,H.O., Deposition of charged nanoparticles in the human airways including effects from cartilaginous rings. NaturalScience. Vol 3,No.10,884-88,(2011)

Högberg SM, Åkerstedt HO, Lundström TS, Freund JB. Respiratory deposition of fibers in the non-inertial Regime—Development and application of a semi-analytical model. Aerosol Science and Technology. 2010;44(10):847-860

Högberg SM, Åkerstedt HO, Holmstedt E, Staffan Lundström T, Sandström T. Time-dependent deposition of micro- and nanofibers in straight model airways. Journal of Fluids Engineering. 2012;134(5):051208-051208.

Åkerstedt, H.O., Högberg, S.M., Lundström ,T.S. An asymptotic approach of Brownian deposition of nanofibres in pipe flow. Theor. Comput. Fluid Dyn. (2012) Crossref

Holmstedt E, Åkerstedt HO, Lundström TS, Högberg SM. Modelling transport and deposition efficiency of oblate and prolate nano- and micro-particles in a virtual model of the human airway. Journal of Fluids Engineering. 2016.

Liu, B.Y.H.& Agarwal, J.K. Experimental observation of aerosol deposition in turbulent flow. Aerosol Sci. 1974,5,145-155

Guha A.Transport and deposition of particles in turbulent and laminar flow. Ann Rev of Fluid Mech. 2008. Crossref

Derevich, I.V.& Zaichik, L.I. Particle deposition from a turbulent flow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti I Gaza, No.5, pp.96-104, September-October, 1988.

Durbin PA. Near-wall turbulence closure modeling without “damping functions”. Theor Comput Fluid Dyn. 1991;3(1):1-13.

Schlichting H, Gersten,K. Boundary-layer theory. 8th edition, Springer (2000)

Yu C. P. Precipitation of unipolarly charged particles in cylindrical and spherical vessels. J Aerosol Sci.1977,8,237-41

Hashish A.H., Bailey A.G., Williams T.J. Modelling the effect of charge on selective deposition of particles in a diseased lung using aerosol boli. Phys.Med.Biol. 39 (1994) 2247-2262


Copyright (c) 2018 H Åkerstedt

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.