Role of substrate softness in stabilizing surface nanobubbles

The contact line pinning and supersaturation theory for the nanobubble stability has attracted extensive concerns from experimental investigators, and some experimenters argue that the contact line pinning is unnecessary. To interpret the experimental observations, we have proposed previously through molecular dynamics simulations that the deformation of soft substrates caused by surface nanobubbles may play an important role in stabilizing surface nanobubbles, while yet no quantitative theory is available for explanation of this mechanism. Here, the detailed mechanism of self-pinning-induced stability of surface nanobubbles is investigated through theoretical analysis. By manipulating substrate softness, we find that the formation of surface nanobubbles may create a deformation ridge nearby their contact lines which leads to the self-pinning effect. Theoretical analysis shows that the formation of nanobubbles on sufficiently rigid substrates or on liquid–liquid interfaces corresponds to a local free energy maximum, while that on the substrates with intermediate softness corresponds to a local minimum. Thus, the substrate softness could regulate the surface nanobubble stability. The critical condition for the self-pinning effect is determined based on contact line depinning, and the effect of gas supersaturation is explored. Finally, the approximate stability range for the surface nanobubbles is also predicted.