Mobile or Immobile? Rise Velocity of Air Bubbles in High-Purity Water

Abstract

The velocity of bubbles rising in pure liquids is affected by the boundary conditions at the liquid–air interface, with bubbles rising the fastest when the bubble surface is fully mobile. The presence of even very small amounts of surface-active molecules causes tangential immobility at the liquid–air interface and subsequently results in slower bubble rise velocity. The existing literature on the rise velocities of air bubbles in high-purity water does not provide a conclusive picture on whether or not the water–air interface is immobile, with the most discrepancies reported for very small bubbles. This paper presents the first systematic study of bubble rise velocities in high-purity water for a sufficiently wide range of bubble sizes (bubble diameter between 48 μm and 1.5 mm) and for the same experimental conditions, which will allow firm conclusions to be drawn on this issue. For bubbles of diameter 800 μm or larger, the measured rise velocity is in a good agreement with the theoretical predictions for a completely mobile water–air interface, but the velocity starts to deviate from that of mobile bubbles as the size becomes smaller. The smaller the bubble, the closer the rise velocity corresponds to an immobile water–air interface, and for Re < 1, the bubble rise velocity agrees with the Stokes law. We use the rear stagnant cap model to explain why smaller bubbles are significantly more sensitive to any surface-active impurities than larger ones.

Stable-streamlined cavities following the impact of non-superhydrophobic spheres on water

“…For small bubbles and low shear stress close to the Stokes regime even a trace amount of surfactant that does not change the surface tension will fully immobilize the interface and the bubbles behave like rigid particles. [38][39][40][41][42][43][44] For larger deformable bubbles their rise velocity is in agreement with the mobile-surface rise velocity predicted by the Moor theory 45 of stress-free interface bubbles, unless a higher concentration of surfactant is added. [46][47][48] Finally for the larger foam bubbles and higher shear rates, as well as in our falling cavity experiments, even for concentrations of synthetic surfactants above the CMC the interface remains free-slip.…”

“…However this result is in good agreement with the foam rheology investigations that indicate free-slip on bubbles for foams formed using lowsurface-modulus surfactants. [34][35][36] At the same time it is in sharp contrast with the behaviour of micron sizes bubbles in water, in which case even trace amounts of contamination are found to immobilise the interface as evaluated in rising bubble terminal velocity experiments [38][39][40][41] and in bubble interaction in atomic force microscopy (AFM) experiments. 42,43 This behaviour clearly demonstrates that the mobility of the air-water interface strongly depends on the flow regime and related tangential stress applied on the bubbles or cavity interface.…”

The dependence of pool scrubbing decontamination factor on particle number density: modeling based on bubble mass and energy balances

“…Thirdly, with the total particle surface area being <0.1% of the bubble surface area, and the SiO 2 particles used in the experiments being insoluble and hydrophilic, it seems unlikely that the particle deposition and absorption make persistent influence on the bubble surface mobility. Experimental results in literature show that bubbles larger than about 1 mm in diameters (Re > 100-200) are much less sensitive to surface contamination than smaller ones [22][23][24].…”

Bubble Rise Velocity and Surface Mobility in Aqueous Solutions of Sodium Dodecyl Sulphate and n-Propanol

“…The calculations used the values listed in Table 1, which shows density values, and Table 2, which shows dynamic viscosity. The data and discussion on bubble velocities in pure water and in aqueous propanol solutions can be found in the literature [7,36]. Bubble size ranges from 0.5 to 1 mm.…”