W. Richard Bowen and Nidal Hilal 4
W. Richard Bowen and Nidal Hilal 4
W. Richard Bowen and Nidal Hilal 4
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260 9. APPLICATION OF ATOMIC FORCE MICROSCOPy<br />
Berard et al. (1993) [83] showed that the free energy of a bridging cavity<br />
is lower than that of liquid water when the surfaces are separated as far as<br />
micrometres <strong>and</strong> claim that the fact that such cavities are not observed as<br />
the two surfaces approach contact from far apart indicates that the liquid<br />
between them is metastable, i.e. there is some barrier preventing cavitation.<br />
The theory for the long-ranged hydrophobic attraction relies upon<br />
this notion of induced cavitation – the force between two colloids in a<br />
near-critical or a near-spinodal fluid is attractive <strong>and</strong> long-ranged – <strong>and</strong><br />
the connection between the spinodal attractions in the bulk <strong>and</strong> measured<br />
long-range attractions between hydrophobic surfaces is the observed<br />
cavitation [84].<br />
Computer simulations by Berard et al. [83] on a Lennard–Jones liquid<br />
confined between hard walls showed cavitation at small separations, <strong>and</strong><br />
that there was indeed a spinodal separation. Approaching this separation<br />
it was found that the attractions were much stronger than the van der<br />
Waals attraction <strong>and</strong> longer ranged. Qualitatively, a separation-induced<br />
spinodal can account for the measured hydrophobic attractions.<br />
In the case of cavitation which results from the development of fluid<br />
mechanical stresses (as tension), Joseph [78] has pointed out that the concept<br />
of ‘negative pressure’ is not particularly useful; it is more pertinent to<br />
consider the state of stress experienced by a liquid. In doing so, it is convenient<br />
to decompose the stress into a deviator <strong>and</strong> mean normal stress,<br />
the most positive value of principal stresses being the maximum tension.<br />
In order to facilitate a comparison of a liquid’s cavitation threshold stress<br />
with the principal stresses at each point within the liquid, it is necessary<br />
to know the flow field. In terms of studying cavitation inception within<br />
mesoscale liquid films, this requirement imposes stringent experimental<br />
dem<strong>and</strong>s as it requires a comparison of the cavitation threshold at each<br />
point in a liquid sample with the principal stresses there. For liquids in<br />
motion, cavitation criteria must be based not on the pressure, but on the<br />
stress, <strong>and</strong> a cavitation bubble will open in the direction of maximum tension<br />
in principal coordinates. An important point which emerges is that<br />
a liquid can cavitate as a result of experiencing a shear deformation, the<br />
resulting cavity being pulled open by tension in the direction defined by<br />
principal stresses.<br />
Of the few experimental techniques capable of working at (or below)<br />
the mesoscale, the various ‘force microscopes’, such as the SFA, have been<br />
the most successful, but instances of their use in studies of thin fluid films<br />
are comparatively rare. Notable exceptions are provided by the work of<br />
Israelachvili <strong>and</strong> co-workers [85] who observed the growth <strong>and</strong> disappearance<br />
of vapour cavities in liquid films between separating mica surfaces in<br />
SFA experiments. The growth of a cavity was claimed to represent a ‘new’<br />
cavitation damage mechanism, insofar as surface damage occurred during<br />
cavity inception [86]. This is an interesting finding given that by far