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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(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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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.
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A physical model of airway reopening. The bubble propagates to the right, peeling apart wet membranes held under longitudinal tension.
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Asymptotic regions for η**≫1.
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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).
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Initial membrane displacement (H) and pressure (P) for θ0=0.3
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(a) Membrane shape, (b) pressure, and (c) normalized flux ahead of the meniscus, corresponding to the case shown in Fig. 5(a)
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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
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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




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