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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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Figures

Grahic Jump Location
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*.
Grahic Jump Location
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=∞.
Grahic Jump Location
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.
Grahic Jump Location
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).
Grahic Jump Location
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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