Nanobubbles by Quantum Mechanics

YOUNGWOOD, Pa. - Sept. 24, 2013 - PRLog -- Background
Nanobubbles are air containing cavities in liquid water with surface molecules in a continual state of evaporation and condensation. Bubbles grow or shrink by diffusion according to whether the surrounding solution is over or under-saturated with air relative to the pressure. As the solubility of gas is proportional to the Laplace pressure that increases as the diameter decreases, there is increasing tendency for bubbles to shrink in size and dissolve in a few microseconds. However, nanobubbles are observed on submerged surfaces for days, defying the expectation of prompt dissolution.

Recently, the stability of nanobubbles is thought [1] to come from the slow rate of dissolution of gas into the surrounding saturated liquid. Specifically, it is hypothesized the bubble gas cannot enter the surrounding liquid unless it can be transferred through the entire liquid. Depending on the thickness of the liquid layer, therefore, the diffusion can take many hours rather than fractions of a second. The dissolution is slowed down further by the fact that the edge of a nanobubble – where gas, liquid and solid meet – is typically ‘pinned’ in place and does not change over time. In the thumbnail, the radius along the solid and the height of the bubble are depicted by r_S and h, respectively. As the bubble gases dissolve in the liquid, the bubble height h is thought to decrease thereby reducing the curvature, which in turn leads to a reduced internal pressure – the driving force for dissolution.

However, the slow dissolution of gas into the liquid as the mechanism for nanobubble stability is not without controversy. Slow dissolution should show the bubbles ever so slightly shrinking in time, but this is not observed.  Measurement of bubble height h over time for different liquid volume samples is recommended [2] for confirmation. Regardless, it is unlikely if the liquid samples are all truly supersaturated, there should not be any difference in the bubble dissolution rate. See http://www.rsc.org/chemistryworld/2013/02/nanobubbles-sta...

Electrostatic Repulsion
The most likely reason for the stability of nanobubbles is the surface is continually being charged inducing an opposing force to the surface tension, thereby slowing their dissolution. It is clear that the presence of like charges at the interface will reduce the apparent surface tension, with charge repulsion acting in the opposite direction to the surface minimization due to surface tension. Simply put, surface tension tends to dissolve the bubble while surface charge tends to expand the bubble. Based on self-ionization of the water molecule, the bubble charge is thought to be negative comprising hydroxyl OH^- ions while positive hydronium H₃O⁺ are found in the bulk.  http://www.lsbu.ac.uk/water/nanobubble.html

Problem
Classical physics gives the surface tension of nanobubbles by the Laplace pressure and diffusion of gases into the liquid, but does not create charge. Self-ionization of the water molecule creates hydronium H₃O⁺ and hydroxyl OH^- ions, but only at an extremely low probability insufficient to sustain continual charging. How then is continual charging of the nanobubble possible?

QED Induced Charge and Stability
By QM, continuous charging of nanobubbles occurs as air and water molecules continually leave and return to the nanobubble surface. QM stands for quantum mechanics. On the bubble surface, all molecules have thermal kT energy, as they are a part of the liquid continuum. But once the molecules leave and enter the EM confinement of the bubble, QM precludes the molecules from having the heat capacity to conserve their kT energy by an increase in bubble gas temperature. EM stands for electromagnetic. Instead, conservation proceeds by QED creating photons at the TIR mode of the bubble surface having wavelength w = 2nh, where n is the refractive index of the gas, n = 1. QED stands for quantum electrodynamics, and TIR for total internal reflection. The Planck energy E of the QED radiation is, E = h*c/w, where h* is Planck’s constant and c is the velocity of light. For h = 5 to 20 nm, 60 < E < 250 eV, and therefore the QED radiation is sufficient to dissociate the water molecule having an ionization potential of 12.6 eV. Unlike self-ionization, QED induced charging having a high probablity of dissociation provides the nanobubble with a continuous source of  H₃O⁺ and OH^-  ions. See http://www.nanoqed.org at QED Charging of Nanobubbles, 2014.  

Recombination
Recombination of hydronium and hydroxyl ion charges occurs, but the Planck energy of QED radiation produces high velocity ionization fragments that favor separation.  Once separated, the mobility of the hydronium ion is about twice that of the hydroxyl ion, and therefore the hydronium ions tend to move into and charge the bulk positive while the hydroxyl ions remain to charge the nanobubble including the solid surface negative. Hence, the negative charged surfaces of the bubble and solid separated by height h are repulsed from each other to balance the surface tension force. Along the solid surface over distance 2r_S the bubble is pinned and does not move because the electrostatic repulsion is negligible compared to that across h, i.e., 2r_S >> h. Hence, QM allows nanobubbles to display long time stability.

Discussion

1. In liquids, the QM of nanobubbles is similar to nanoparticles in that the respective atoms under TIR confinement are precluded from having the heat capacity to conserve thermal energy from the liquid by an increase in temperature. Instead, QED radiation in the TIR mode produced in the solid nanoparticle or in the bubble gas at the liquid interface creates charge or is emitted to the surroundings.

2. Classical physics always allows the atoms in water molecules to have the heat capacity to conserve EM energy by an increase in temperature, and therefore molecules having kT energy from the interface that enter the bubble from the liquid cannot produce charge.

3. By QM, QED charging only occurs for submicron nanobubbles. Supramicron bubbles do not create charge as the TIR confinement is insufficient to ionize the water molecule.

4. Like interfacial nanobubbles, bulk nanobubbles may be similarly characterized by long lived stability from electrostatic repulsion of hydroxyl ions on the bubble surface created upon the dissociation of the water molecule by QED induced EM radiation.    

References

[1] J H Weijs and D Lohse, "Why Surface Nanobubbles Live for Hours," Phys. Rev. Lett., 2013, 110, 054501
[2] X. Zhang, D Y C Chan, D Wang and N Maeda, "Stability of Interfacial Nanobubbles,"  Langmuir, 2013, 29, 1017.