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TECHNICAL PAPERS: Fluids/Heat/Transport

# A New Drift-Flux Model for Particle Transport and Deposition in Human Airways

[+] Author and Article Information
J. B. Wang

School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798

Alvin C. Lai1

School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798

1

To whom correspondence should be addressed; e-mail: mcklai@ntu.edu.sg

J Biomech Eng 128(1), 97-105 (Sep 13, 2005) (9 pages) doi:10.1115/1.2133763 History: Received May 19, 2005; Revised September 13, 2005

## Abstract

Particle deposition and transport in human airways is frequently modeled numerically by the Lagrangian approach. Current formulations of such models always require some ad hoc assumptions, and they are computationally expensive. A new drift-flux model is developed and incorporated into a commercial finite volume code. Because it is Eulerian in nature, the model is able to simulate particle deposition patterns, distribution and transport both spatially and temporally. Brownian diffusion, gravitational settling, and electrostatic force are three major particle deposition mechanisms in human airways. The model is validated against analytical results for three deposition mechanisms in a straight tube prior to applying the method to a single bifurcation G3-G4. Two laminar flows with Reynolds numbers 500 and 2000 are simulated. Particle concentration contour, deposition pattern, and enhancement factor are evaluated. To demonstrate how the diffusion and settling influence the deposition and transport along the bifurcation, particle sizes from $1nmto10μm$ are studied. Different deposition mechanisms can be combined into the mass conversation equation. Combined deposition efficiency for the three mechanisms simultaneously was evaluated and compared with two commonly used empirical expressions.

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## Figures

Figure 5

Particle concentration contour at plane Z=0 and cross sections B-B′ and C-C′ for micron-size particles. (a) Re=500, dp=3μm; (b) Re=500, dp=10μm; (c) Re=2000, dp=3μm; and (d) Re=2000, dp=10μm.

Figure 6

Deposition enhancement factor (DEF) distribution along the bifurcation wall. (a) Re=500 and (b) Re=2000.

Figure 7

Deposition efficiency ηd for the bifurcation G3-G4 for combined three different deposition mechanisms; Brownian diffusion, gravity settling, and electrostatic image force. Parabolic velocity profile and uniform particle concentration distribution is assumed at the inlet. (a) 1to100nm; (b) 100nmto1μm; and (c) 1to10μm.

Figure 1

Particle deposition efficiency ηd for a straight tube with different inlet and simulation conditions as a function of particle sizes dp. (a) Uniform velocity and particle concentration distribution; (b) parabolic velocity and uniform particle concentration distribution; (c) gravitational settling; and (d) electrostatic image force.

Figure 2

A single bifurcation with locations of cross section for velocity and particle concentration results

Figure 3

Comparison of the axial velocity contours and secondary velocity vector with Comer (22). (a) Present simulation of velocity contour at plane Z=0; (b) Comer’s simulation results at C-C′ cross section; and (c) present simulation results at C-C′ cross section.

Figure 4

Particle concentration contour at plane Z=0 and cross sections B-B′ and C-C′ for nanosize particles. (a) Re=500, dp=1nm; (b) Re=500, dp=100nm; (c) Re=2000, dp=1nm; and (d) Re=2000, dp=100nm.

Figure 8

Comparison of combined deposition efficiency ηd evaluated by the present simulation and by the two empirical expressions. Parabolic velocity profile and uniform particle concentration distribution is assumed at the inlet, Re=500. (a) 1to100nm; (b) 100nmto1μm; and (c) 1to10μm.

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