The influence of surface tension on the diffusion-controlled growth or dissolution of spherical gas bubbles

Abstract

Surface tension can markedly affect the growth or dissolution of small gas bubbles but, even when spherical symmetry is maintained and the interfacial concentration assumed constant, generally valid analytical solutions for the change of size with time cannot be obtained; approximations of limited validity are therefore often used. However, accurate and efficient methods for computing the diffusion-controlled growth or dissolution of spheres in such conditions have recently been developed; the results obtained when interfacial solute concentration is assumed constant have been published and validated by comparing them, where possible, with the equivalent analytical solutions. This paper extends that work to include the effects of a constant surface tension, for both Henry’s and Sievert’s laws. The numerical results are valid for as wide a range of parameters as is likely to be needed and are compared with the few analytical solutions available for particular cases. It is shown that, when surface tension is introduced, a complete description of the problem requires an additional saturation parameter as well as the dimensionless surface tension. It is also shown that Henry’s and Sievert’s laws can have very different effects on dissolving bubbles: when Sievert’s law applies a higher surface tension can increase time for a bubble to dissolve but this paradox can be resolved by examining the competing effects involved.

Self-similar growth of a gas bubble induced by localized heating: the effect of temperature-dependent transport properties

“…The inertia and viscous terms which contain time derivatives of the bubble radius R can be ignored due to the slow growth of the bubble and also because only moderately viscous solvents are examined here. These terms are known to be important in the early stages of boiling applications, where typical growth rates are of the order of mm/ s. The contribution of surface tension to the bubble evolution has been studied in detail by Cable and Frade (1998). They found that for bubbles with radius 20 times larger than the critical one the effect of surface tension is negligible.…”

Bubble dynamics during the non-isothermal degassing of liquids. Exploiting microgravity conditions

“…The bubble pressure is the sum of the gas pressure P g and vapor pressure P L . Surface tension σ has an effect only at the very early stages of growth [30], being insignificant in the period of practical importance for which then P b =P ∞ . The normal velocity u n of the liquid on the surface of a bubble which grows keeping constant not its center but a particular point of its surface (contact point with the heater), is…”

Micro bubble formation and bubble dissolution in domestic wet central heating systems

“…[14,15,16]. Two principal mechanisms are known to govern the bubble dissolution process, these being the solution of the gas into the liquid at the bubble fluid interface and the diffusion of dissolved gas away from the interface into the outer phase of infinite extent.…”

“…Most studies on bubble dissolution in under saturated solutions have been done for isolated gas bubbles and are based on the Epstein and Plesset gas diffusion model. [14,15,16] The theoretical interpretation of these experiments has been based on the consideration of an isolated sphere in spherically symmetrical conditions. Hence, at under saturated conditions the bubble dissolves at a rate controlled by the diffusion of gas through the liquid.…”