Stability, Dynamics, and Tolerance to Undersaturation of Surface Nanobubbles

Abstract

The theoretical understanding of surface nanobubbles-nanoscale gaseous domains on immersed substrates-revolves around two contrasting perspectives. One perspective, which considers gas transport in the nanobubbles' vicinity, explains numerous stability-related properties but systematically underestimates the dynamical response timescale by orders of magnitude. The other perspective, which considers gas transport as the bulk liquid equilibrates with the external environment, recovers the experimentally observed dynamical timescale but incorrectly predicts that nanobubbles progressively shrink until dissolution. We propose a model that couples both perspectives, which is capable of explaining the stability, dynamics, and unexpected tolerance of surface nanobubbles to undersaturated environments.

The interplay among gas, liquid and solid interactions determines the stability of surface nanobubbles

“…ζ* is a convenient measure of the tolerance of nanobubbles to degassing. The equilibrium contact angle decreases monotonically with decreasing air concentration in the bulk liquid 16 until it reaches a critical value ζ* at which θ e = 0° (Fig. 3B).…”

“…To resolve the difficulties of the pinning-oversaturation model, Tan, An and Ohl 15,16 suggested that an attractive effective potential ϕ of depth ∼1k B T (k B is the Boltzmann's constant and T is the temperature) exists between the substrate and gas molecules, which leads to the formation of a localized gas-oversaturated layer at the surface. ϕ would rationalize the existence of a permanent local oversaturation sustaining surface nanobubbles, while relaxing the unrealistic requirement that the bulk water is indefinitely oversaturated with gas.…”

“…A) Tolerance of nanobubbles to degassing measured as critical undersaturation ζ*. (B) The equilibrium contact angle vs. oversaturation, showing that θ e decreases monotonically with decreasing air concentration in the bulk liquid16 until at ζ* it reaches θ e = 0°. In particular, in panel B, we report the values of the equilibrium contact angle vs. ζ for the case of the weaker solid-gas interaction.…”

Surface nanobubbles: Theory, simulation, and experiment. A review

“…Later, Lohse and Zhang [55] and Chan et al [35] have assumed only gas transport in the vicinity of the NB. The latter two approaches have been recently coupled into a theoretical model, which can explain the stability and dynamics of surface NBs in undersaturated environments [56]. The framework of the model of Lohse and Zhang [55] has been recently exploited to describe the coarsening process of competitively growing NBs that interact diffusively [57].…”

Effects of Surface Tension on the Stability of Surface Nanobubbles

“…Tan combined the hydrophobic adsorption with contact line pinning-oversaturation theory to explain that bubbles can survive in under-saturated water, and also presented that how hydrophobicity and oversaturation work together to stabilize SNBs [36]. Furthermore, Tan got the timescale ∼1,000 s of bubble evolution with the dynamic gas concentration in water with height of 1 mm [37]. Recently, Petsev argued that the adsorption of gas molecules at the substrate modifies the energy of solid-gas interface, and thus reduces the gas-side contact angles and the pressure inside [38].…”