Effect of impurities in description of surface nanobubbles

Surface nanobubbles emerging at solid-liquid interfaces of submerged hydrophobic surfaces show extreme stability and very small (gas-side) contact angles. In a recent paper 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 nonionic) 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.