Preferred sizes and ordering in surface nanobubble populations

Two types of homogeneous surface nanobubble populations, created by different means, are analyzed statistically on both their sizes and spatial positions. In the first type (created by droplet deposition, case A) the bubble size $R$ is found to be distributed according to a generalized gamma law with a preferred radius $R^{\ast }=20\text{nm}$. The radial distribution function shows a preferred spacing at $\sim 5.5R^{\ast }$. These characteristics do not show up in comparable Monte Carlo simulated configurations of random packings of hard disks with the same size distribution and the same density, suggesting a structuring effect in the nanobubble formation process. The nanobubble size distribution of the second population type (created by ethanol-water exchange, case B) is a mixture of two clearly separated distributions, hence, with two preferred radii. The local ordering is less significant, due to the looser packing of the nanobubbles.

Figure 1

(Color online) AFM topography images of the solid-liquid interface of the substrates. In cases A1 and A2 gas-equilibrated MilliQ-water was put on the substrate without explicit use of local oversaturation. In cases B1 and B2 the result is shown after a local and temporal oversaturation has been applied. Each scale bar corresponds to $1\mu \text{m}$.

Figure 2

Probability distribution of the nanobubble diameter $D$ in both case A (top) and case B (bottom). Each case is represented by two unique images (1 and 2, respectively), of which the total size distribution is shown. The bars depict experimental data; the lines show the best-fitted probability distribution.

Figure 3

Positions of the nanobubbles in case A2 (left) vs Monte Carlo simulated configurations of a random packing of hard disks with the same size distribution and density as experiment A2 (right). The experimental positions show much more structure than the simulated bubbles.

Figure 4

Radial distribution functions $g\left(r\right)$ as a function of $r$ normalized by the mean radius $⟨R⟩$ for case A (top) and case B (bottom). Black line: experiment; gray line: Monte Carlo simulated configuration of a random packing of hard disks with the same size distribution and density as the associated experiments; dashed line: Poisson point process; dot-dashed line: determinantal point process.

Figure 5

Nearest neighbor distributions $D_{NN}\left(r\right)$ for the four cases A1–B2. The legend is the same as in Fig. 4.