Shapes of single bubbles in infinite stagnant liquids contaminated with surfactant

Abstract

Aspect ratios of ellipsoidal bubbles in clean and contaminated systems were measured to investigate the effects of surfactant on the bubble aspect ratio. The bubble diameter ranged from 0.80 to 5.8 mm. Air was used for the gas phase and the glycerol-water solutions were used for the liquid phase. The experimental ranges of the Morton number, M, the bubble Reynolds number, Re, the Eötvös number, Eo, the Weber number, We, and the Tadaki number, Ta, were as follows: 10 7 < M < 10 3 , 3.6×10 1 < Re < 1.7× 10 2 , 1.1×10 1 < Eo < 5.9, 5.0×10 3 < We < 3.7 and 5.3×10 2 < Ta < 3.6. Triton X-100 and 1-octanol were used for surfactant. The terminal velocities of bubbles were confirmed to be independent of the surfactant concentration, and therefore, the bubbles were fully-contaminated from the point of view of the terminal velocity. By making use of the aspect ratio data, the applicability of available aspect ratio correlations was examined and an empirical correlation was proposed. The applicability of the proposed correlation was also examined for sodium dodecyl sulphate (SDS) and 1-decanol. As a result, the following conclusions were obtained: (1) the aspect ratio database, which is of use for validating and developing shape correlations, was obtained, (2) the available aspect ratio correlations are not applicable to the present data for fully-contaminated ellipsoidal bubbles, (3) the aspect ratios are well correlated in terms of a combination of the Eötvös and bubble Reynolds numbers, which proves that all the relevant forces, i.e.

Towards a phenomenological model on the deformation and orientation dynamics of finite-sized bubbles in both quiescent and turbulent media

“…As shown by recent experiments (Aoyama et al. 2018), the relationship between the bubble aspect ratio and the Weber number appears to be the same for both clean and contaminated bubbles as long as the respective rise velocity and surface tension are used in the Weber number.…”

Comparison of Two Solvers for Simulation of Single Bubble Rising Dynamics: COMSOL vs. Fluent

“…Drag coefficients of deformed bubbles of ellipsoidal shape were also researched in many studies. The degree of deformation can be determined by the aspect ratio χ, which is the ratio between the ellipse major and minor axes [36]. Moore [32] obtained a correlation in which the aspect ratio is a function of the bubble Weber number (We b = D b ρ U b 2 /σ), where σ is the surface tension.…”

“…The results for water are given in Figure 4A, whereas the data for propanol are given in Figure 4B. Experimental data were only available for water [27,36]. Values of the experimental and theoretical velocities are displayed as a straight line across the time interval, as a single equilibrium value.…”

Deformation characteristics of the bubble in water-biodiesel immiscible fluids

“…Myint [6] used distortion coefficient to describe the deformation of droplet, which was also used for the bubble deformation later. Through theoretical analysis [9,11], experiments [12][13][14][15] and numerical simulations [16][17][18], the researchers proposed the relationship of E by taking into account all the forces on bubble, for example, the viscous, surface tension, buoyancy and inertial force. The forces on bubble are represented by dimensionless parameters Eötvös number (gravity vs surface tension, Eo), Reynolds number (inertial force vs viscous force, Re), Morton number (viscous force vs surface tension, Mo).…”

“…In a single liquid, researchers presented some empirical relations. The correlation proposed by Liu [13] was applicable to the fluids with different viscosities, while Tomiyama's correlation [14,15] was suitable for the fluids with different concentrations. In immiscible fluids, however, the deformation characteristics of bubble have not been reported.…”