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TECHNICAL PAPERS: Fluids/Heat/Transport

Steady Propagation of a Liquid Plug in a Two-Dimensional Channel

[+] Author and Article Information
Hideki Fujioka, James B. Grotberg

Department of Biomedical Engineering, University of Michigan, Ann Arbor, Michigan 48109 USA

J Biomech Eng 126(5), 567-577 (Nov 23, 2004) (11 pages) doi:10.1115/1.1798051 History: Received March 04, 2004; Revised May 20, 2004; Online November 23, 2004
Copyright © 2004 by ASME
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References

Figures

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A sketch of the liquid plug model. A pressure difference between the front and back air finger, ΔP*=P1*−P2*, drives the liquid plug of the length LP* with constant speed U within a two-dimensional channel of half width H lined by a precursor film of thickness h2*. For steady state h2* is equal to the trailing film thickness at the rear end boundary h1*.
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An example of a two-dimensional grid generated in the domain. A staggered grid is used where the pressure p is stored at the center of each cell and the velocity components are stored at control surfaces.
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Comparison with other studies for the trailing film thickness h1 as a function of Ca at Re=0. The square points represent the results of the present study for LP=2. The broken line 27, the dashed line 40, and the solid line 25 represents the trailing film thickness of leading meniscus for a semi-infinite bubble, i.e., LP=∞.
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The trailing film thickness, h1 versus Ca for different LP at Re=0
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Streamlines and pressure fields inside the liquid plug at Ca=0.05 and Re=0, for (a) LP=0.25, (b) LP=1, and (c) LP=2. The directed lines represent the flow field, and the dashed lines denote lines of constant pressure. S1,S2,S3, and S4 are the locations of the stagnation points.
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Streamlines and pressure fields inside the liquid plug at Ca=0.4 and Re=0 for (a) LP=0.25, (b) LP=1, and (c) LP=2      
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The effect of inertia (Re) on the trailing film thickness h1 at λ=1000 for different LP. The point at Re=50 represents h1 for a semi-infinite bubble propagation 27.
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Axial velocity profiles at the middle cross-section of the liquid plug (x=0) at Re=50, λ=1000 for different values of LP. The curve of “parabolic” is u=−1+32(1−h1)(1−y2) with h1=h1 (LP=2).
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The streamlines and pressure fields inside the liquid plug at Re=50 and λ=1000, for (a) LP=0.25, (b) LP=1, and (c) LP=2
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The streamlines and pressure fields inside the liquid plug at Re=80 and λ=1000, for (a) LP=0.25, (b) LP=1, and (c) LP=2
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The dimensionless macroscopic pressure gradient ΔP/LP versus Re at λ=1000 for different LP
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The wall shear stress, τ distribution, versus x for LP=2, λ=1000, and Re=40, 60, and 80
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Velocity vectors distribution in the capillary wave for LP=2, Re=50, and λ=1000

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