Effect of impurities in description of surface nanobubbles

Abstract

Surface nanobubbles emerging at solid-liquid interfaces of submerged hydrophobic surfaces show extreme stability and very small (gas-side) contact angles. In a recent study Ducker (W. A. Ducker, Langmuir 25, 8907 (2009).) conjectured that these effects may arise from the presence of impurities at the air-water interface of the nanobubbles. In this paper we present a quantitative analysis of this hypothesis by estimating the dependence of the contact angle and the Laplace pressure on the fraction of impurity coverage at the liquid-gas interface. We first develop a general analytical framework to estimate the effect of impurities (ionic or non-ionic) in lowering the surface tension of a given air-water interface. We then employ this model to show that the (gas-side) contact angle and the Laplace pressure across the nanobubbles indeed decrease considerably with an increase in the fractional coverage of the impurities, though still not sufficiently small to account for the observed surface nanobubble stability. The proposed model also suggests the dependencies of the Laplace pressure and the contact angle on the type of impurity.3

Effect of impurities in the description of surface nanobubbles: Role of nonidealities in the surface layer

“…The model is next employed to study the effect of impurities on surface nanobubbles. The most important result obtained from the present calculations, in context of surface nanobubbles, is that the nonideality effects ensure that even relatively weak impurity coverage (much smaller than that corresponding to the ideality-based model [19]) can lead to significant alteration of gas-side contact angle and Laplace pressure of surface nanobubbles. Though the Laplace pressure is still high enough to forbid stability (and hence the nanobubble superstability puzzle is still unsolved), the gas-side contact angle shows values close to experimental results [2,7,20] even for substantially reduced impurity coverage.…”

“…As experiments on surface nanobubbles are invariably carried out in an extremely clean environment, one can expect the presence of only trace amount of impurities in the system. In this light, the present nonideality-based model not only provides a more acceptable foundation (in comparison to our previous ideality-based model [19]) for delineating the role of impurities on surface nanobubbles [20], but also provides a satisfactory explanation on how impurities, even in trace amounts, can lead to anomalously small nanobubble contact angles.…”

“…Great scientific interest in surface nanobubbles stems from the fact that unlike macroscopic or even microscopic bubbles, many of their reported properties (the properties of surface nanobubbles that are typically of concern are their gas-side contact angle θ and radius R b ; see Fig. 1 of [19] as well as Fig. 1 provided here) cannot be trivially explained from surface tension values for the media involved.…”

“…The nonideality effects arise from the enthalpic, entropic, and ionic interactions between the surface-adsorbed impurity molecules, and become particularly relevant at surface coverage values at which impurity effects are found to become important for an ideal nanobubble air-water interface [19]. The nonideality based model presented in this paper is thus much broader and more general in scope than our previous simplified ideality based model [19]. The present model is first validated by making it reproduce the reported experimental results of surfactant-induced lowering of surface tension of simple air-water interfaces.…”

“…To address this issue we recently provided a general mathematical framework that pinpoints the effect of impurities (soluble) on the lowering of the surface tension of any general air-water interface and used this model to quantify the effect of impurities in the alteration of surface nanobubble properties [19]. Assuming ideal interactions at the impurity-covered nanobubble air-water interface (we may interchangeably call the nanobubble air-water interface the nanobubble surface layer), the model predicted significant reductions in gas-side contact angles (to values that matched experimental results [2,7,20]) and Laplace pressure (the Laplace pressure, though, is not lowered significantly to justify nanobubble superstability) for substantial impurity surface coverage [19].…”