An Asymptotic Model of Unsteady Airway Reopening

[+] Author and Article Information
S. Naire, O. E. Jensen

Division of Applied Mathematics, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, U.K.

J Biomech Eng 125(6), 823-831 (Jan 09, 2004) (9 pages) doi:10.1115/1.1632525 History: Received December 04, 2002; Revised June 17, 2003; Online January 09, 2004
Copyright © 2003 by ASME
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Grahic Jump Location
Bubble pressure as a function of time, corresponding to the case with C=3.82 in Fig. 8. The piston accelerates linearly to its final steady speed over start-up times Ts* (s) of 1) 0, 2) 0.6, 3) 1.2, 4) 1.8, and 5) 2.4.
Grahic Jump Location
A physical model of airway reopening. The bubble propagates to the right, peeling apart wet membranes held under longitudinal tension.
Grahic Jump Location
Asymptotic regions for η**≫1.
Grahic Jump Location
Pb/ε versus U for steady flows (solid) for various D and ε=0.14 are compared with Eq. (11) (dashed) and an experimental regression (dashed-dotted, 14). Arrows mark the point at which Hb=D with H<D in X>0. Insets show pushing motion (left) and peeling motion (right).
Grahic Jump Location
Initial membrane displacement (H) and pressure (P) for θ0=0.3
Grahic Jump Location
Pb,U,Hb, and Pmin are plotted as functions of time T for (a) D=10,C=10,ε=0.14, and (b) D=40,C=10,ε=0.14
Grahic Jump Location
(a) Membrane shape, (b) pressure, and (c) normalized flux ahead of the meniscus, corresponding to the case shown in Fig. 5(a)
Grahic Jump Location
Contour plot of percentage excess in Pb from its steady value as a function of the parameters C≥0.1 and D≥5, with ε=0.14
Grahic Jump Location
(a) Bubble pressure as a function of time from 14 with various final steady piston speeds (cm/s) 1) 0.6, 2) 2.33, 3) 4.03, 4) 5.84, 5) 7.35, 6) 8.93. (b) pb* versus t* from numerical simulations for corresponding parameter values D=15.2,ε=0.12, and C=1) 0.57, 2) 2.21, 3) 3.82, 4) 5.54, 5) 6.98, and 6) 8.47




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