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The effect of soluble surfactant on the transient motion of a buoyancy-driven bubble
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10.1063/1.2912441
/content/aip/journal/pof2/20/4/10.1063/1.2912441
http://aip.metastore.ingenta.com/content/aip/journal/pof2/20/4/10.1063/1.2912441
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Schematic illustration of the computational setup for a buoyancy-driven bubble rising in an axisymmetrical channel with soluble surfactant.

Image of FIG. 2.
FIG. 2.

Spherical bubble. (a) Reynolds number vs nondimensional time for , 2.5, 5, 7.5, 10, and 15, and (b) steady Reynolds number vs nondimensional channel diameter for clean (solid lines) and contaminated (dashed lines) bubbles. ( and .)

Image of FIG. 3.
FIG. 3.

Spherical bubble. The streamlines and the velocity vectors at steady-state in a coordinate system moving with the bubble centroid for (a) a clean bubble and (b) a contaminated bubble. Every third grid points are used in the velocity vector plots. ( and .)

Image of FIG. 4.
FIG. 4.

Spherical bubble. (a) Surface velocity profiles of a clean (solid lines) and a contaminated (dashed lines) bubble, and (b) the interfacial surfactant concentration profiles for the channel diameters , 2.5, 5, and 15 at . ( and .)

Image of FIG. 5.
FIG. 5.

Spherical bubble. The contour plots of constant surfactant concentration in the bulk fluid (left side) and the distribution of the surfactant concentration at the interface (right side) with (left plot) and 1 (right plot) at . Contour levels are the same in both cases. (, , and .)

Image of FIG. 6.
FIG. 6.

Spherical bubble. (a) The surface velocity and (b) interfacial surfactant concentration as a function of arc length measured from the centerline in the counterclockwise direction for , 0.5, and 1 at .

Image of FIG. 7.
FIG. 7.

Spherical bubble. The contour plots of constant surfactant concentration in the bulk fluid (left side) and the distribution of the surfactant concentration at the interface (right side) with (left plot) and 1000 (right plot) at . Contour levels are the same in both cases. (, , and .)

Image of FIG. 8.
FIG. 8.

Spherical bubble. (a) The surface velocity and (b) interfacial surfactant concentration as a function of arc length measured from the centerline in the counterclockwise direction for , 100, 500, and 1000 at . ( and .)

Image of FIG. 9.
FIG. 9.

Spherical bubble. Reynolds number vs time for , , 2.5, and 1.25. ( and .)

Image of FIG. 10.
FIG. 10.

Ellipsoidal bubble. Reynolds number vs time for , 0.1, 0.5, and 1.0. ( and .)

Image of FIG. 11.
FIG. 11.

Ellipsoidal bubble. (a) Surface velocity and (b) interfacial surfactant concentration vs arc length measured from the centerline in the counter-clockwise direction for (solid lines) and 1.0 (dashed lines) at times , 28.4, 48.4, and 67.8. ( and .)

Image of FIG. 12.
FIG. 12.

Ellipsoidal bubble. (Top row) The contour plots of the constant surfactant concentration in the bulk fluid (left side) and the distribution of the surfactant concentration at the interface (right side) with (from left to right) , 0.25, 0.5, and 1.0. (Bottom row) The streamlines and the velocity vectors in a coordinate system moving with the bubble centroid. Every third grid point is used in the vector plots. (, , , , and .)

Image of FIG. 13.
FIG. 13.

Ellipsoidal bubble. Effect of elasticity number on bubble deformation. (, , , and .)

Image of FIG. 14.
FIG. 14.

Ellipsoidal bubble. (a) Surface velocity and (b) interfacial surfactant concentration as a function of nondimensional arc length measured from the centerline in the counterclockwise direction with , 0.25, 0.5, and 1.0. (, , , , and .)

Image of FIG. 15.
FIG. 15.

Ellipsoidal bubble. (a) Surface velocity and (b) interfacial surfactant concentration as a function of arc length measured from the centerline in the counterclockwise direction for (solid lines) and 1000 (dashed lines) at times , 28.4, 48.4, and 67.8. (, , , and .)

Image of FIG. 16.
FIG. 16.

Ellipsoidal bubble. (Top row) The contour plots of the constant surfactant concentration in the bulk fluid (left side) and the distribution of the surfactant concentration at the interface (right side) with (from left to right) , 100, 500, and 1000. (Bottom row) The velocity vectors and the streamlines in a coordinate system moving with the bubble centroid. Every third grid point is used in the vector plots. (, , , , and .)

Image of FIG. 17.
FIG. 17.

Ellipsoidal bubble. (a) Surface velocity and (b) interfacial surfactant concentration as a function of arc length measured from the centerline in the counterclockwise direction for , 100, 500, and 1000. (, , , , and .)

Image of FIG. 18.
FIG. 18.

Ellipsoidal bubble. (Top row) The contour plots of the constant surfactant concentration in the bulk fluid (left side) and the distribution of the surfactant concentration at the interface (right side) with (from left to right) , 1000, and . (Bottom row) The velocity vectors and the streamlines in a coordinate system moving with the bubble centroid. Every third grid point is used in the vector plots. (, , , , and .)

Image of FIG. 19.
FIG. 19.

Ellipsoidal bubble. (a) Surface velocity and (b) interfacial surfactant concentration as a function of arc length measured from the centerline in the counterclockwise direction for , 1000, and . (, , , , and .)

Image of FIG. 20.
FIG. 20.

Dimpled ellipsoidal cap. (a) The contour plots of the constant surfactant concentration in the bulk fluid (left side) and the distribution of the surfactant concentration at the interface (right side). The streamlines and the velocity vectors in a frame of reference moving with the bubble centroid for (b) a contaminated and (c) a clean bubble at . Every eighth grid point is used in the vector plots. (, , , , and .)

Image of FIG. 21.
FIG. 21.

Dimpled ellipsoidal cap. (a) Surface velocity and (b) interfacial surfactant concentration as a function of arc length measured from the centerline in the counterclockwise direction at times , 28.9, 46.2, and 63.5. (, , , , and .)

Image of FIG. 22.
FIG. 22.

Effects of the Eötvös number on the motion of the clean and contaminated bubbles. (a) The steady Reynolds number vs the Eötvös number. (b) The drag coefficient vs the Reynolds number.

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/content/aip/journal/pof2/20/4/10.1063/1.2912441
2008-04-30
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: The effect of soluble surfactant on the transient motion of a buoyancy-driven bubble
http://aip.metastore.ingenta.com/content/aip/journal/pof2/20/4/10.1063/1.2912441
10.1063/1.2912441
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