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Research Papers

Carousel Effect in Alveolar Models

[+] Author and Article Information
F. E. Laine-Pearson

Department of Mathematics,  University of Surrey, Guildford GU2 7XH, United Kingdomf.laine-pearson@surrey.ac.uk

P. E. Hydon

Department of Mathematics,  University of Surrey, Guildford GU2 7XH, United Kingdomp.hydon@surrey.ac.uk

J Biomech Eng 130(2), 021016 (Apr 03, 2008) (6 pages) doi:10.1115/1.2903429 History: Received December 18, 2006; Revised June 28, 2007; Published April 03, 2008

Experimental work over the past decade has shown that recirculation in alveoli substantially increases the transport of particles. We have previously shown that, for nondiffusing passive particles, this can be understood with the aid of Moffatt’s famous corner flow model. Without wall motion, passive particles recirculate in a regular fashion and no chaos exists; however, wall motion produces extensive chaotic flow. Aerosols typically do not follow this flow as they are fundamentally different from fluid particles. Here, we construct a simple model to study diffusing particles in the presence of recirculation. We assume that all particles are passive, that is to say that they do not significantly alter the underlying flow. In particular, we consider particles with high Péclet number and neglect inertial effects. We modify the Lagrangian system for corner eddies to accommodate diffusing particles. Particle transport is governed by Langevin equations. Ensembles of diffusing particles are tracked by numerical integration. We show that transport of diffusing particles is enhanced by sufficiently strong underlying recirculation through a mechanism that we call the “carousel effect.” However, as the corner is approached, the recirculation rapidly decreases in intensity, favoring motion by diffusion. Far from the corner’s apex, recirculation dominates. For real alveoli, the model indicates that sufficiently strong recirculation can enhance transport of diffusing particles through the carousel effect.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Moffatt’s corner eddies with corner angle of 20deg. Two eddies are shown; the left-hand eddy and the right-hand eddy are illustrated by three and five representative curves, respectively.

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Figure 2

Moving the walls perturbs the eddies of Fig. 1. This Poincaré section shows that some of the eight representative curves have changed in structure. In particular, for the right-hand eddy, the inner most curve has changed shape but is still regular, the next curve out from the center has been replaced by a chain of islands, and the other three curves have been replaced by chaotic paths. More detailed Poincaré sections are found in Ref. 6.

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Figure 3

The inner three curves of the right-hand eddy of Fig. 1. The eddy is bound on each side by a separatrix.

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Figure 4

Two example trajectories of particles released from point A with Pe=1000 (shown in black and gray, respectively)

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Figure 5

Crossing times for ensembles of 400 particles released from point A

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Figure 6

The crossing times for 400 particles released from points A, B, and C with Pe=10,000

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Figure 11

Step 1: Particle goes around on eddy (carousel). Step 2: Many particles diffuse off the eddy and cross the finish line.

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Figure 10

The crossing times for diffusion alone (that is, K=0) for 400 particles released from points A, B, and C with Pe=1000

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Figure 9

Two examples of pure two-dimensional random walk (that is, K=0) starting from point C with Pe=10,000 (shown in black and gray, respectively)

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Figure 7

The crossing times for 400 particles released from points A, B, and C with Pe=1000

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Figure 8

The time it takes for a particle released from y=0 to complete a revolution when diffusion is not present (that is, Pe=∞)

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