Surface Nanobubbles Are Stabilized by Hydrophobic Attraction

The remarkably long lifetime of surface nanobubbles has perplexed researchers for two decades. The current understanding is that both contact line pinning and supersaturation of the ambient liquid are strictly required for the stability of nanobubbles, yet experiments show nanobubbles surviving in open systems and undersaturated environments. We find that this discrepancy can be addressed if the effects of an attractive hydrophobic potential at the solid substrate on the spatial distribution of the gas concentration is taken into account. We also show that, in our model, only substrate pinning is strictly required for stabilization; while hydrophobicity and supersaturation both aid stability, neither is mandatory—the absence of one can be compensated by an excess of the other.

Figure 1

(a) Schematic of a surface nanobubble. To generalize the gas transport problem to a nonhomogeneous distribution of the dissolved gas concentration, it is helpful to divide the bubble into vertical slices of thickness $dz$. Ignoring the dissolved gas concentration of the ambient liquid, the bottommost slices have the largest radii and, thus, make the largest contribution to gas exchange. (b) Concentration distribution of the gas as a function of separation $z$ from solid hydrophobic (blue line) and hydrophilic (orange) substrates, based on Eq. (7).

Figure 2

Dynamical response of a nanobubble with initial footprint radius $L=100\mathrm{nm}$ and initial contact angle $\theta =20°$ for a liquid with far-field concentration $c_{\infty }=2c_{\mathrm{sat}}$. The curves are for hydrophobic (${\varphi }_0/k_{B}T=-2$, blue line) and hydrophilic (${\varphi }_0/k_{B}T=2$, orange) substrates in the current theory, and the equivalent condition ($\zeta =1$) in the Lohse-Zhang theory is shown as a black dashed line.

Figure 3

Equilibrium contact angles of nanobubbles in liquids with varying $c_{\infty }/c_{\mathrm{sat}}$ in the (a) present theory and (b) Lohse-Zhang theory. Each curve represents one value of dissolved gas concentration $c_{\infty }/c_{\mathrm{sat}}$ in the liquid. The substrate is assumed hydrophobic (${\varphi }_0/k_{B}T=-2$). In the Lohse-Zhang model, nanobubbles are stable only in supersaturated liquid ($c/c_{\mathrm{sat}}>1$ or $\zeta >0$).

Figure 4

Equilibrium contact angles of surface nanobubbles with radius $L=100\mathrm{nm}$ as a function of the substrate potential (hydrophobic potentials, ${\varphi }_0<0$; hydrophilic potentials, ${\varphi }_0>0$). Each curve represents a single value of dissolved gas concentration $c_{\infty }/c_{\mathrm{sat}}$. Nanobubbles are stable on hydrophobic substrates, and moreover, the equilibrium angle increases with hydrophobicity. In the opposite direction, increasing the hydrophilicity introduces a threshold $c_{\infty }$ for which stable nanobubbles can be expected.