Surfactant Transport Over Airway Liquid Lining of Nonuniform Depth

[+] Author and Article Information
H. A. R. Williams, O. E. Jensen

Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, United Kingdom

J Biomech Eng 122(2), 159-165 (Nov 18, 1999) (7 pages) doi:10.1115/1.429637 History: Received September 03, 1999; Revised November 18, 1999
Copyright © 2000 by ASME
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A schematic cross section of a small airway under compression, showing air (A), liquid lining (L), mucosa (M) surrounded by a ring of smooth muscle, at (a) large and (b) small fluid volumes
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Equilibrium liquid lining inside a cylindrical airway: (a) lining of uniform depth; (b) an eccentric lumen with a nonuniform annular lining; (c) lining forming a rivulet with zero contact angle
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A snapshot of a localized monolayer spreading along a channel of nonuniform depth, indicating (top) the concentration distribution along y=0 and y=1, and (bottom) a plan view of the monolayer (shaded), showing the contour Γ=0 (the monolayer’s leading edge, where the flow is fully two dimensional) and two typical contours of constant concentration in the long bulk region where either Γt<0 or Γt>0
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The downward-sloping lines show the surfactant distribution Γ(x, 0, 50) computed using the full model (Eq. (1), solid) and the simplified model (Eq. (4), dashed), with ε=0.5. Also shown are the corresponding film depth distributions h(x, 0, 50) (solid) and h0(0)=1.5 (dashed).
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The function I(y; ε)−I(y; ε) (with I given by Eq. (15)) is plotted for values of ε=0.1 (solid), 0.3, 0.5, 0.7, 0.9, and 0.99.
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The monolayer’s leading edge (solid lines) at t=50 for ε=0, 0.25, 0.5, and 0.75, computed using Eq. (4). The dashed line gives the fitted function x=4.104+0.313 I(y; ε).
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The difference in monolayer length along the deepest and shallowest parts of the channel D(t)=Ld(t)−Ls(t) plotted for ε=0.25, 0.5, and 0.75 using the full model (Eq. (1), solid) and the simplified model (Eq. (4), dashed)
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A schematic illustration of a localized monolayer (shaded) spreading over a rivulet of thickness h(y)=1+cos(πy), showing three typical contours of constant surfactant concentration. In the bulk region the monolayer concentration is approximately uniform in the transverse direction.




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