Confined water
Interfacial water and water-gas interfaces
Evidence for nanobubbles
The effect of surface charge on surface tension and nanobubble stability
Nanobubbles are gas-containing cavities in liquid solution (such cavities are often called bubbles).e They are under excess pressure as the surface tension causes a tendency to minimize their surface area, and hence volume.a Nanobubbles grow or shrink by diffusion according to whether the surrounding solution is over-saturated or under-saturated with the dissolved gas relative to the raised cavity pressure. As the solubility of gas is proportional to the gas pressure and this pressure is exerted by the surface tension in inverse proportion to the diameter of the bubbles, there is increasing tendency for gasses to dissolve as the bubbles reduce in size, increases greatly at small bubble diametersa and so accelerating the process. Such dissolution is increased by the bubble's movement and contraction during this process, which aids the removal of any gas-saturated solution around the cavities. Calculations show that nanobubbles should only persist for a few microseconds [1268]. However, the ease with which water forms larger visible bubbles, under slight tensile pressure well below the tensile strength of water, and the greater difficulty that occurs in this on degassing, both indicate the occurrence of gas-containing nanobubbles (cavities). Larger micron-plus sized bubbles can last much longer and have sufficient buoyancy to rise through the solution and release contained gas at the surface before the gas dissolves.
However in contrast to this theoretical view, there is much evidence that sub-micron-sized gas-filled cavities (often called nanobubbles) can also exist for significant periods of time both in aqueous solution [ 974, 1172, 1269, 1433] and at submerged hydrophobic surfaces [506, 1270].d Bulk phase nanobubbles can be detected by light scattering whereas surface nanobubbles can be detected by a number of techniques, prominent amongst which is tapping mode atomic force microscopy [803]. Nanobubbles are commonly found on solid hydrophobic surfaces in solutions open to the air, where they appear to be quite stable [1272]. Bulk nanobubbles are likely to be repelled from each other, and from negatively charged hydrophilic surfaces, at distance but may attach to such surfaces through water separated films, if they closely approach [1273]. Surface and bulk-phase nanobubbles can both give rise to the otherwise difficult to explain long range attraction between hydrophobic surfaces. As the temperature of aqueous solutions rises, the solubility of non-polar gasses drops, so increasing the gas released and nanobubble volume and surface coverage [842] but generally having much lesser effect on nanobubble concentration.
Surface nanobubbles vary considerably in dimensions but typically they might have dimensions of r = 50 nm - 6 µm, rS = 25 - 1000 nm, h = 5 - 20 nm, with contact angles (θ = 135° - 175°) much greater than expected from macroscopic studies. The excess internal pressure is not great when the bubble radius is greater than about a micron.a
The most likely reason for the long-lived presence of nanobubbles is that the nanobubble gas/liquid interface is charged, introducing an opposing force to the surface tension, so slowing or preventing their dissipation. Curved aqueous surfaces may introduce a surface charge due to water’s molecular structure or its ionization. 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. Any effect may be increased by the presence of additional charged materials that favor the gas-liquid interface, such as OH- ions at neutral or basic pH.
It is further probable that the surface charges are stabilized by the higher concentration of dissolved gas in the surface layer, which helps produce an environment favorable to large chaotropic anions.
Nanobubbles have a tendency towards self-organization [1269] in much the same way as charged oil-water emulsions, colloids [1275] and nanoparticles. This is due to their charge, long range attraction [1322] and slow diffusion.
Where there are large numbers of bulk phase nanobubbles, such as in electrolyzed aqueous solutions, there is relatively large amounts of water associated with the surfaces, which can give rise to greater hydration effects due to their greater capacity for forming new hydrogen bonds.
The question arises as to why these surface charge effects are not seen to affect the determination of the surface tension when different conditions such as pH and solute are used. The answer may be partly that small nanobubbles are constantly moving such that they lose counter ions beyond their slip planes, and partly that the effect of the charged surface is stronger through the low-dielectric gas phase formed by the tightly curved surfaces.
[Back to Top 
]
In the analysis that follows it is shown that surface charge can counter the surface tension, so preventing high pressures within the nanobubbles. Clearly the final net charge density at the surface is that required for stability. It may be expected that as the charge density increases, as the nanobubble shrinks, then some charge density will be expelled to the bulk but it is not clear to what extent this will occur; the energy required for expulsionb must be less than the increase in energy due to the approach of the charges. In any case, surface charge density will always slow down the process of nanobubble collapse. Even at the equilibrium charge density, contained gas will dissolve if the solution interface is under-saturated, although this is unlikely if the exposed liquid water surface is also in contact with similar gas at similar pressure.
The effect of charges at the water/gas interface is shown opposite, with the surface negative charges repelling each other and so stretching out the surface. The effect of the charges is to reduce the effect of the surface tension. As the repulsive force between like charges increases inversely as the square of their distances apart the charges cause strongly increasing outwards pressure as bubble diameter lessens. As well as tending to increase the nanobubble diameters, surface charge will clearly also tend to increase the contact angles. The greater van der Waals attraction across the gas bubble also assists in flattening surface nanobubbles [1274].
The surface tension tends to reduce the surface whereas the surface charge tends to expand it. Equilibrium will be reached when these opposing forces are equal.
Assume the surface charge density on the inner surface of the bubble (radius r) is Φ (C m-2). The outwards pressure (Pout, Pa) can be found by solving the Navier-Stokes equations to give 
,c where D is the relative dielectric constant of the gas bubble (assumed unity), ε0 is the permittivity of a vacuum (= 8.854 pF m-1). The inwards pressure (Pin, Pa) due to the surface tension on the gas is 
, where γ is the surface tension (0.07198 N m-1, 25°C). Therefore if these pressures are equal, rΦ2 = 2.55x10-12 C2 m-3 = ~ 0.1 (e- nm-2)2 nm. For nanobubble diameters of 5 nm, 10 nm, 20nm, 50 nm and 100 nm the calculated charge density for zero excess internal pressure is 0.20, 0.14, 0.10, 0.06 and 0.04 e- nm-2 bubble surface area respectively. Such charge densities should be achievable; e.g. one surface anion to every about 250 surface water molecules would stabilize a 100 nm diameter nanobubble. The nanobubble radius increases as the total charge on the bubble increases to the power 2/3. Under these circumstances at equilibrium, the ‘effective’ surface tension of the water at the nanobubble surface is zero. The presence of charged gas in the bubble clearly increases the size of the stable nanobubble. Further reduction in the bubble size would not be indicated as it would cause the reduction of the internal pressure to below atmospheric pressure.
The theory above, would predict that greater surface charge would increase the diameter of nanobubbles. This has been shown by means of the variation of nanobubble diameter with pH. Increased pH leads to increased nanobubble diameter together with the increase in OH- concentration [506]. It has recently been shown how the stability of nanobubbles varies with pH and ionic strength [1298] in total agreement with the theory here presented.
It is possible that the bubble would divide to give smaller bubbles due to the surface charge. Assuming that a bubble of radius r and total charge q divides to give two bubbles of shared volume and charge (radius r½= r/21/3, charge q½=0.5q), and ignoring the Coulomb interaction between the bubbles, calculation of the change in energy due to surface tension (ΔEST) and surface charge (ΔEq) gives:
ΔEST = +2 x 4πγr½2 - 4πγr2 = 4πγr2(21/3 – 1)
`
The bubble is metastable if the overall energy change is negative which occurs when ΔEST + ΔEq is negative,
which gives the relationship between the radius and the charge density (Φ):
For nanobubble diameters of 5 nm, 10 nm, 20nm, 50 nm and 100 nm the calculated charge density for bubble splitting is 0.12, 0.08, 0.06, 0.04 and 0.03 e- nm-2 bubble surface area respectively. For the same surface charge density the bubble diameter is always about three times larger for reducing the apparent surface tension to zero than for splitting the bubble in two. Thus, bubbles will never divide unless there is a further energy input.
The presence of salt ions adversely affects nanobubble stability causing aggregation followed by coalescence at higher salt concentrations [1435]. The aggregation behavior appears similar to that of the salting out of colloidal particles due to the screening of the particle charge by the ionic strength of the solution. Coalescence is due to changes at the gas-water interface. [Back to Top ]
a The pressure inside gas cavities is given by the Laplace equation, Pin = Pout + 2γ/r, where Pin and Pout are the cavity internal and external pressures respectively, γ is the surface tension and r is the cavity radius. This equation is simply derived by equating the free energy change on increasing the surface area of a spherical cavity (= γΔA = 4πγ(r+δr)2 - 4πγr2) to the pressure-volume work (= ΔPΔV = ΔP(4/3)π(r+δr)3 - ΔP(4/3)πr3). Although it is not certain that the Laplace equation holds at very small radii [1129] and it has been shown that surface tension may increase almost 20-fold to 1.3 N m-1 for 150 nm diameter droplets [823], in the absence of other effectors, such as surface charge, this equation appears correct down to about a nanometer or so, below which a small correction must be applied [1271]. However, there may well be further contributions to the work required , due to the removal of surface-bound material, as the surface area contracts, that would lower the excess pressure. In the absence of any other surface effects such as solutes or charges, the excess pressures expected in a 50 nm radius spherical nanobubbles and a 50 nm diameter surface nanobubble (rS=50nm, r=1000 nm), due to the surface tension minimizing the cavity surface, are 5.8 MPa and 0.14 MPa respectively. [Back]
b The free energy of surface absorption is expected to vary from about 4-10 kJ mol-1at higher concentrations to 25-40 kJ mol-1 at low surface concentrations (~10-3-10-4 nm-2) [674]. [Back]
c This equation may be simply appreciated (if not rigorously derived) by considering the charge (4πr2Φ) concentrated at the center of the spherical cavity exerting a force on the same charge at the surface. The force would be (4πr2Φ)2/4πDε0r2 from basic electrostatics, and therefore the pressure would be Φ2/Dε0. However the charge has been double counted, therefore the final pressure is half this value. [Back]
d There is some dispute over whether the density depletion often at hydrophobic surfaces is real in some cases [1487]. Hydrophobic liquid-water interfaces behave differently, with no vapor-like layer observed [1484]. [Back]
e Another interesting phenomenom in aqueous solutions is the antibubble where a water drop is held, surrounded by a gaseous film, within the bulk liquid [1491]. [Back]
Home | Site Index | Gas-water interfaces | Solubility of non-polar gases | Hydrophobic hydration | Confined water | LSBU | Top
This page was last updated by Martin Chaplin on 8 December, 2008
