Experimental and theoretical investigation of the effect of dissolved surfactant on the dynamics of gas bubble floating-up

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Abstract

We present the results of an experimental and numerical investigation of the floating-up of a solitary gas bubble in the presence and absence of dissolved surfactant at Reynolds numbers Re > 1. An original numerical technique is proposed, which makes it possible to investigate the dynamics of a solitary bubble with account for the effects occurring when a surfactant is introduced into the fluid. The effect of the surfactant concentration on the bubble dimensions, shape, and rise velocity are analyzed. Three stages of the bubble rise in the presence of a surfactant are established; they characterize its accumulation and distribution over the free surface of the bubble.

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About the authors

E. I. Borzenko

National Research Tomsk State University

Author for correspondence.
Email: borzenko@ftf.tsu.ru
Russian Federation, Tomsk

A. S. Usanin

National Research Tomsk State University

Email: borzenko@ftf.tsu.ru
Russian Federation, Tomsk

G. R. Shrager

National Research Tomsk State University

Email: borzenko@ftf.tsu.ru
Russian Federation, Tomsk

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Supplementary files

Supplementary Files
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2. Fig. 1. Distribution of surfactant on the bubble surface in the stagnation angle model.

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3. Fig. 2. Schematic diagram of the experimental setup for studying the process of a single air bubble rising: 1 – cuvette with liquid; 2 – capillary; 3 – hollow metal tube; 4 – syringe; 5 – video camera.

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4. Fig. 3. Dependence of the surface tension coefficient of distilled water at the boundary with air on the concentration of the surfactant: ● – sintanol ALM-10; ○ – sodium lauryl sulfate.

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5. Table 1. Fig. 1

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6. Table 1. Fig. 2

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7. Table 1. Fig. 3

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8. Table 1. Fig. 4

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9. Fig. 4. The ascent rate of a single air bubble with a diameter of 1.3 mm depending on the concentration of the surfactant in distilled water: ● – distilled water-syntanol ALM-10 solution; ○ – distilled water-sodium lauryl sulfate solution; ∆ – data [6] for distilled water-sodium lauryl sulfate solution.

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10. Fig. 5. Solution domain (a) and computational grid (b) in the vicinity of a single gas bubble floating in the presence of a surfactant.

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11. Fig. 6. Dependence of the ascent rate (a) and the ellipticity parameter (b) on time for different values ​​of the initial volume concentration of the surfactant: 1–4 – La = 0, 0.24, 0.6, 1.2.

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12. Fig. 7. Shapes of the free surface at different moments of time for different values ​​of La.

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13. Fig. 8. Distributions of concentration G (a) and Marangoni stresses τM (b) on the free surface from the angle φ at different moments in time (La=1.2): 1–7 – t=1.6, 2.6, 4.6, 11.5, 20, 28.6, 40.

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14. Fig. 9. Radial (a) and axial (b) components of the velocity vector on the free surface depending on the angle ϕ at different moments in time (La=1.2): 1–4 – t=1.6, 4.6, 20.5, 40.

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15. Fig. 10. Streamlines (a) and modified pressure (b) in the vicinity of a rising bubble (t=40).

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16. Fig. 11. Dependence of the ascent speed of a single bubble on time: solid curves – numerical calculation; dots – experimental data: 1, 2 – C0=0, 0.32 mmol/l.

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17. Fig. 12. Dependence of the ellipticity coefficient of a single bubble on time: solid curves – numerical calculation; dots – experimental data: 1, 2 – C0=0, 0.32 mmol/l.

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