Biomedical Engineering Reference
In-Depth Information
Figure 3. Schematic diagram indicating the influence of the contact angle on shape for two spheri-
cal cap bubbles of equal volume (7.25
10 5
nm 3 ) with the normal macroscopic contact angle (on
×
170 ). The radius
of curvature is much smaller for the macroscopic contact angle, ( R 1 = 88 nm <R 2 = 1000 nm)
as is the bubble diameter ( D 1 = 83 nm <D 2 = 174 nm). Whilst the maximum height is larger
( H 1 = 58 nm >H 2 = 15 . 2 nm) for the bubble with the macroscopic contact angle. The increase
in the radius of curvature associated with the nanoscopic contact angle results in a much reduced
internal pressure and is responsible for the stability of nanobubbles.
110 ) and the observed nanoscopic contact angle (R. H. S., θ 2 =
the left, θ 1 =
tact angles are more correctly reported as being in the range of 140 -170 [6, 9].
These exceptionally high contact angles are much larger than the corresponding
macroscopic contact angles which are in the range of 90 -120 .Thishasseveral
significant implications. The first is on the shape of a nanobubble. This is illustrated
in Fig. 3 where two bubbles of the same volume are depicted one with the macro-
scopic contact angle and the other with the nanoscopic contact angle. The shape
is influenced dramatically. When the contact angle is 170 the bubble has a maxi-
mum height of only 15 nm and the diameter of the base is 347 nm, whereas for a
contact angle of 110 the bubble has a maximum height of 58 nm and the diameter
of the base is only 165 nm. The curvature of the interface is greatly reduced by an
increase in nanobubble contact angle, in the example in Fig. 3 the radius of curva-
ture is 1000 nm for a contact angle of 170 (see the bubble on the right), whereas
the same volume with a contact angle of 110 has a radius of curvature of 88 nm
(left bubble). Thus the Laplace pressure is also greatly reduced, for the high contact
angle case it is
16.4 atmospheres for the lower
contact angle. In this case the greater contact angle reduces the Laplace pressure by
a factor of 11.7. A reduction in interfacial curvature and a consequent significant
reduction in the internal pressure within a bubble aids greatly in our understanding
of the stability of nanobubbles, as this means that the driving force for dissolution
is greatly reduced and with a small degree of supersaturation we can expect that the
bubbles are kinetically stable for hours and even days. Whilst the surprisingly high
1.4 atmospheres compared to
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