Knudsen Gas Provides Nanobubble Stability

We provide a model for the remarkable stability of surface nanobubbles to bulk dissolution. The key to the solution is that the gas in a nanobubble is of Knudsen type. This leads to the generation of a bulk liquid flow which effectively forces the diffusive gas to remain local. Our model predicts the presence of a vertical water jet immediately above a nanobubble, with an estimated speed of $\sim 3.3\mathrm{m}/\mathrm{s}$, in good agreement with our experimental atomic force microscopy measurement of $\sim 2.7\mathrm{m}/\mathrm{s}$. In addition, our model also predicts an upper bound for the size of nanobubbles, which is consistent with the available experimental data.

Figure 1

Knudsen gas streaming and nanobubble geometry. (a) The broken symmetry created between one solid surface and one “leaky” liquid-gas interface leads to bulk upwards flow in the Knudsen gas. (b) The tangential component of the bulk Knudsen gas flow drives a bulk liquid flow due to the continuity of shear stress at the liquid-gas interface. (c) Finally, due to conservation of mass, this gas-rich liquid stream circulates upwards at the bubble apex and back around to the three-phase line, effectively transporting the diffusive outfluxing gas back to the three-phase line for reentry [14].

Figure 2

(a) Three-dimensional topological image ($1\mu \mathrm{m}\times 1\mu \mathrm{m}\times 100\mathrm{nm}$) of one of the nanobubbles investigated in this study. The nanobubble was created by depositing room temperature ultrapure (Millipore) water on HOPG, also at room temperature. The water had been thoroughly degassed before supersaturating it with 300% argon, resulting in a bubble with radius of curvature $R\approx 1.4\mu \mathrm{m}$ and contact angle $\theta \approx 20°$. The nanobubble was topologically imaged regularly over $\sim 12\mathrm{h}$ to confirm that its size was not changing with time. (b) Cross-sectional line scan (blue) of the nanobubble in (a), with feedback-disabled noncontact-mode force-field measurements (red), taken at 250 to 600 nm above the substrate, in steps of 50 nm. At 250 nm from the substrate ($\sim 160\mathrm{nm}$ above the nanobubble’s apex) the AFM cantilever was deflected upwards by a $\sim 1\mathrm{nN}$ force, which decreased in magnitude with increasing cantilever-substrate separation until it became smaller than the AFM resolution ($\sim 5\mathrm{pN}$) at 550 nm. The force ordinate on the right-hand side of the image is for the bottommost force-field measurement. The proceeding force-field measurements have the same scale, but with their zeros offset according to the height at which they were recorded (left-hand ordinate). We recalibrated the AFM cantilever to the substrate between each force-field measurement in order to maintain accurate separation with minimal drift for each scan.