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. 2019 Jul 29;9(1):11008.
doi: 10.1038/s41598-019-46883-5.

Bubble Formation and Scale Dependence in Free-Surface Air Entrainment

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Free PMC article

Bubble Formation and Scale Dependence in Free-Surface Air Entrainment

Wangru Wei et al. Sci Rep. .
Free PMC article

Abstract

The air bubble entrainment and self-aeration phenomena in free-surface water flows reveal a rich interplay of fundamental science and engineering, and the size distribution of the entrained bubbles enhances the air-water gas flux, improves the gas transfer, and influences the cavitation erosion protection in high-speed flows. In the present study, we investigate the bubble-formation mechanism of free-surface air entrainment and the related microscopic bubble scale in the laboratory. This paper provides a quantitative description of bubble entrainment. The entrapment deformation of the local free surface over a period follows a power-law scaling and entrains a bubble when the entrapped surface becomes enclosed in the unstable movement period. Both the size scale and shape character of the entrapped free surface determine the size and skewness of the distribution of the air bubble. The entrapment deformation process confirms that the instability behaviour of the local air-water interface results in the onset of bubble entrainment. Further research is necessary to elucidate the instability criterion dominated by the interface instability and promote a new understanding of multiphase flow generation and development.

Conflict of interest statement

Dr Wei’s work was funded by financial support from the National Natural Science Foundation of China (Grant No. 51609162). Professor Xu declares no competing interests. Professor Deng declares no competing interests. Dr Tian declares no competing interests.

Figures

Figure 1
Figure 1
Free-surface entrapped deformation and bubble–entrainment process. (a) High–speed video images of the entire life of the free surface entrapment deformation and air entrainment process. Image sequences are captured at 1/3000 s with 1280 (width) × 344 (height) pixels and a spatial resolution of approximately 4 pixels/mm. The shutter speed is 0.23 μs. (b) Binary image for determining the length scale of the entrapment surface and entrained air bubble. (c) Size scales of the width L, depth y, and radius of curvature r of the entrapped surface throughout the entire lifetime, including the incipient, evolving, instable and air entrainment periods. The radius of curvature at the apex of the entrapped surface r is defined from mathematics as r = 0.125·L·(L/y). The right axis shows the corresponding correlation coefficient Rsquare of the Gaussian–type curve for the entrapment deformation. (d) Comparison of the entrapment deformation with the Gaussian–type curve.
Figure 2
Figure 2
Three groups of air entrainment through the free–surface instability and enclosure with consecutive images (the time interval between two images is 0.33 ms): A, dab = 2.5 mm; B, dab = 4.3 mm; and C, dab = 8.6 mm.
Figure 3
Figure 3
Variation in the radius of curvature in the free-surface deformation process. The ratio of r to critical value rC in the air entrainment lifetime was obtained from eight bubble entrainment events. The equivalent diameter of the bubble size dab ranged from 1.7 to 8.6 mm; each bubble was considered to be a spherical particle with identical areas.
Figure 4
Figure 4
Bubble size spectrum entrained through the free surface. (a) The relationship between the critical radius of curvature rC and the air bubble size dab. The value of d95 is the critical bubble size on the Hinze scale. The envelope line of the maximum value of dab with ln(rC) follows a linear approximation dab = m·[ln(rC) + n·d95] with coefficients m = 2 and n = 3. (b) The relationship between the size scale of the entrapment deformation LC and the air bubble size dab. (c) Normal distribution of the bubble size as a function of LC/yC (the solid line: dab/LC = 0.4 + 1.2·exp{−0.5·[(LC/yC − 1.15)/0.6]2}).
Figure 5
Figure 5
Illustration of the bubble entrainment affected by the surface enclosure.

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