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Effects of gravity, inertia, and surfactant on steady plug propagation in a two-dimensional channel
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10.1063/1.2762256
/content/aip/journal/pof2/19/8/10.1063/1.2762256
http://aip.metastore.ingenta.com/content/aip/journal/pof2/19/8/10.1063/1.2762256
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

(Color online) (a) An initial liquid plug is instilled in the parent tube and splits into two daughter tubes with pressure and gravity driven. (b) With the gravity acts on the plug with an angle to the flow direction, the prebifurcation asymmetry already exists on the plug.

Image of FIG. 2.
FIG. 2.

The schematic of the computational model for liquid plug propagation in a liquid-lined 2D channel. The gravity is acting at an angle with the axis on the plug. The pressure difference drives the liquid plug of length at constant speed with the gravitational force. The precursor films are uniformly coated: , and the mass are conserved: .

Image of FIG. 3.
FIG. 3.

(Color online) A sample computation grid around the plug core region for . The staggered grid is used, pressure is stored in the grid points and the velocities are stored on the centers of the control surfaces.

Image of FIG. 4.
FIG. 4.

The streamlines, the pressure fields, the corresponding wall pressure and wall shear stress vs for , , , : (a) with no gravity, ; (b) ; (c) . In the plug domain, the solid lines with arrows are streamlines while the dashed lines are lines of constant pressure. S1–S6 are locations of the stagnation points. Points A and C are the recirculation centers; B and D are the vertical edges of the recirculations. and are the upper and lower vortex strength. The axis on the left is , shown as solid lines while the axis on the right is , shown as dashed lines.

Image of FIG. 5.
FIG. 5.

The streamlines, the pressure fields, and vs for (a), (b), and (c) at , , , and .

Image of FIG. 6.
FIG. 6.

The streamlines, the pressure fields, and vs for =0 (a), (b), (c), and (d) at , , , and .

Image of FIG. 7.
FIG. 7.

The ratio of the upper to lower trailing film thickness (a) and the mass left behind in the trailing films (b) vs Bo for different at , , , and .

Image of FIG. 8.
FIG. 8.

The streamlines, the pressure fields, and vs for (a), 0.1 (b), and 0.3 (c) at , , , and .

Image of FIG. 9.
FIG. 9.

The ratio of the upper to lower trailing film thickness (a) and the mass left behind (b) vs Ca for different Bo at , , and .

Image of FIG. 10.
FIG. 10.

The streamlines, the pressure fields, and vs (a); the surfactant concentration with velocity vectors (b) in the plug with surfactant at , , , , with . In (a), the solid lines with arrows are streamlines and the dashed lines are that for constant pressure; in (b), the dashed lines are for constant concentrations and the solid lines with arrows are velocity vectors.

Image of FIG. 11.
FIG. 11.

The interface position, (a) for the rear interface and (b) for the front; and interfacial surfactant concentration along the interface arc , (c) for the rear and (d) for the front, at , , , , with different .

Image of FIG. 12.
FIG. 12.

The interface position and interfacial surfactant concentration along the interface arc at , , , , with different , 0.3, and 0.6.

Image of FIG. 13.
FIG. 13.

The ratio of the upper to lower trailing film thickness (a), the mass left behind (b) vs Bo for different values of , and the pressure drop vs C0 for , 0.3, and 0.6 at , , and .

Image of FIG. 14.
FIG. 14.

The streamlines, the pressure fields, and vs at , , and for (a) and (b).

Image of FIG. 15.
FIG. 15.

The ratio of the upper to lower trailing film thickness (a) and the mass left behind after the plug propagation (b) vs Bo for different Re and Ca at , .

Image of FIG. 16.
FIG. 16.

Comparison of , , , and vs for different conditions of Bo, Re, and .

Image of FIG. 17.
FIG. 17.

The volume ratio Vr vs Bo for different and (a), and Vr vs Ca for different Bo with (b) at and .

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/content/aip/journal/pof2/19/8/10.1063/1.2762256
2007-08-29
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Effects of gravity, inertia, and surfactant on steady plug propagation in a two-dimensional channel
http://aip.metastore.ingenta.com/content/aip/journal/pof2/19/8/10.1063/1.2762256
10.1063/1.2762256
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