Formation of Surface Nanobubbles and the Universality of Their Contact Angles: A Molecular Dynamics Approach

We study surface nanobubbles using molecular dynamics simulation of ternary (gas, liquid, solid) systems of Lennard-Jones fluids. They form for a sufficiently low gas solubility in the liquid, i.e., for a large relative gas concentration. For a strong enough gas-solid attraction, the surface nanobubble is sitting on a gas layer, which forms in between the liquid and the solid. This gas layer is the reason for the universality of the contact angle, which we calculate from the microscopic parameters. Under the present equilibrium conditions the nanobubbles dissolve within less of a microsecond, consistent with the view that the experimentally found nanobubbles are stabilized by a nonequilibrium mechanism.

Figure 1

a) Initial conditions: a liquid layer (blue [dark gray]) is placed on top of a solid substrate (bottom, red [medium gray]). Gas is dissolved inside the liquid layer (green [light gray]). (b) Simulation (${ϵ}_{lg}/{ϵ}_{ll}=0.58$, ${\sigma }_{lg}/{\sigma }_{ll}=1.32$) after about 0.1 ns: nucleation occurs. (c) $t=10\mathrm{ns}$: a surface nanobubble has formed. (d) Parameter space where the solubility of the gas was tuned through the parameters ${ϵ}_{lg}/{ϵ}_{ll}$ and ${\sigma }_{lg}/{\sigma }_{ll}$. As the gas becomes increasingly soluble [going up, left in Fig. 1d] a sudden transition takes place where no nanobubbles nucleate. The gas then remains in a dissolved state and partially escapes to the gas phase above the liquid layer until equilibrium is reached.

Figure 2

The effect of an enhanced gas-solid interaction strength. As the interaction strength ${ϵ}_{\mathrm{sg}}/{ϵ}_{ll}$ is increased, the adsorbed gas density (${\rho }_g^{sl}$, blue squares) increases as well until a saturation limit. As the adsorbed gas density increases, the gas-side contact angle $\theta$ lowers ($\cos \theta$ indicated by red triangles). The red solid line is a fit to the mean-field expression (2) taking into account the screening of the adsorbed gas (see text).

Figure 3

Number of gas molecules $n_{\mathrm{gas}}$ inside the nanobubble as a function of time for nanobubbles on different substrates with different equilibrium contact angles. Initially, the fluid is supersaturated and a bubble quickly forms within a few ns. Shortly after the bubble has formed, the liquid is still supersaturated causing gas to enter the bubble (“Start-up”). After about 20 ns the gas in the liquid achieves the equilibrium concentration, and the nanobubbles start to dissolve (“Dissolution”). The dissolution rate of the nanobubbles is independent of the contact angle. The inset shows the full dissolution of the ${\theta }_{\mathrm{eq}}=93°$ bubble after $0.2\mu \mathrm{s}$.

Figure 4

Local flux of gas through the liquid-vapor interface of a nanobubble attached to a substrate. The gray line indicates the time-averaged local gas flow direction and strength. The gas flow is directed outwards everywhere (iii), except for a small region near the contact line [(i) and (ii)] where in a very small region a strong in- and outflux are observed, indicating that there exists a recirculation current. The net effect of this recirculation current is found to be of the same order as the diffusive outflux.