Biomedical Engineering Reference
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Figure 2. Images of the same two nanobubbles under different amplitude ratios in surfactant solution.
The set-point amplitude is reduced on moving from image a to g and then increased again from h to j.
The nanobubbles appear smaller as the setpoint amplitude is reduced as the nanobubble-tip force is
increased and the tip deforms the nanobubble. Image taken from reference [9].
Zhang et al. [9] have shown that a truer measure of the shape of a nanobubble
is gained by using the information in deflection versus piezo displacement data.
This method which was first developed for measuring nano-droplets [14] allows
the height of the nanobubble at a particular point to be determined accurately and
can be obtained at each point of an image using a technique widely known as force-
volume imaging.
Researchers have consistently reported that the nanobubble shape is accurately
described as a spherical cap (except for the recent report on 'nanopancakes' which
is discussed below). This infers that the curvature of the interface is everywhere the
same and that the pressure drop across the interface is constant. If surface forces had
a significant impact on the stability of nanobubbles one would expect that this would
result in a change in curvature of the interface with separation from the surface [15].
The constant interfacial curvature is evidence that long-range surface forces are not
responsible for the stability of nanobubbles as the magnitude of such forces reduce
rapidly with distance. However, it is typically difficult to determine the shape of the
interface within the last 20 nm of the surface due to the finite size of the cantilever
tip, so the influence of surface forces within the last 20 nm cannot be gauged at this
stage.
When the sectional profile of a nanobubble is accurately determined the con-
tact angle can also be determined with reasonable accuracy. Surprisingly, the
nanoscopic contact angle differs considerably from the macroscopic contact an-
gle. In many cases the contact angle has been reported to be in the range of 10
to 40 [6, 7], where the angle has been measured through the gas phase. However
the correct definition of the contact angle at the three phase line is to measure the
angle through the more dense (i.e., liquid) phase, thus the true value is given by
180
x ,where x
is the angle measured through the gas phase and the con-
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