Nanobubbles at Hydrophobic Surfaces - Drops and Bubbles in Contact with Solid Surfaces - page 160

by a high internal gas pressure. For a bubble of given radius this can be calculated
using the Laplace equation.

γ 1

,

1
r 2

P =

r 1 +

(1)

where P is the pressure change across the interface, γ is the surface tension and
r 1 and r 2 are the principal radii of curvature. Consequently for a spherical bubble
of radius 100 nm in water the internal pressure is 14 atmospheres. An internal

pressure of such magnitude has severe consequences for the existence of such a
bubble as the solubility of the gas in the aqueous phase is significantly enhanced.
An increase in solubility results in loss of gas to the surrounding medium, a con-
sequent decrease in radius and a further increase in pressure and an even greater
driving force for dissolution. Thus lifetimes are expected to be short in the high
pressure world of nano-sized bubbles. For a bubble of radius 100 nm it is calculated
that the bubble lifetime is only 100 µs, [1] therefore it is expected that if nanobub-
bles were produced they would rapidly dissolve under their own internal pressure.
However the substrate has an important role to play in the stability of nanobubbles.
The hydrophobic surface influences the shape of nanobubbles such that their radius
of curvature is much greater. A nanobubble 50 nm in height may have a radius of
curvature of 500 nm. The theoretical lifetime associated with a bubble of this size
is still very short at

∼

1 ms but these calculations assume that there is no supersat-
uration of gas in the aqueous phase and no material at the interface opposing gas
transport or reducing the surface tension.

∼

B. Early Evidence for Nanobubbles

The first report of the existence of nanobubbles in the literature appeared in 1994.
Parker, Claesson and Attard [2] were using a highly sensitive force measurement
device to measure the attractive force between two hydrophobic surfaces in water.
They found that the force exhibited clear steps and they interpreted the attraction
and the presence of these steps as arising from the presence of nanobubbles on
the surfaces. As each nanobubble bridged the gap between the surfaces it would
give rise to a stepwise increase in the attractive force. From the experimental data
they could give an estimate of the height of the nanobubbles and found them to
be < 100 nm. At the time this report was highly controversial as there were the-
oretical objections to the existence of stable nanobubbles as we have seen above.
Significantly this study tied the existence of nanobubbles to the mysterious long-
range hydrophobic attraction which is measurable between hydrophobic surfaces
in aqueous solutions [3].
A much earlier study by Kitchener and Blake [4] into the interaction of macro-
scopic bubbles with glass surfaces could also be cited as possible evidence for the
existence of nanobubbles. They found that when a macroscopic bubble was pushed
towards a native glass (hydrophilic) surface the repulsive electrostatic forces acted