W. Richard Bowen and Nidal Hilal 4

268 9. APPLICATION OF ATOMIC FORCE MICROSCOPy
Therefore when the initial surface separation distance h is large, i.e. the
initial characteristic length of the fluid sample is �1 mm, the attainment
of moderate extensional rates (�100 s �1 ) requires an initial separation
velocity � 100 mm s �1 , which is readily achieved using linear drive systems.
However, the filament length must increase exponentially as a function
of time in order to maintain a constant rate of extension, a situation
which most drive systems are unable to accommodate. Consequently,
many tensile studies involving liquids are restricted to low rates of extension
(�10 s �1 ) or small total strains. In this respect, the recreation of elongational
flows at the mesoscale using piezoceramic technology presents
one possible method by which high extensional strain rates and large total
strains may be achieved. Furthermore, the difficulties encountered when
attempting to measure rapidly changing, small tensile forces, which are
generated within low viscosity, liquid filaments may also be addressed by
utilising the precise force measuring capabilities of the AFM.
The determination of tensile forces in flows which contain a dominant
elongational component is readily achieved using an AFM force sensor;
however, the ability to precisely determine elongational stress at large
strains is only possible when the shape and size of the liquid layer is
clearly understood. In this respect, it is necessary to document the evolution
of a microfilament to ascertain the minimum diameter such that the
maximum tensile stress may be calculated. This is particularly important
as the transient evolution of the profile of Newtonian and non-Newtonian
liquid bridges may vary significantly such that a representation of the
tensile stress through terms such as F/R 2 may not be valid at large separations.
This is because the critical dimension (i.e. the filament diameter) is
not simply related to separation distance and is itself dependent upon the
viscoelastic properties of the material.
The ability of many fluid mechanical systems to perform the desired
function is critically dependent upon the tensile properties of the material,
and the inability of the fluid to sustain large tensions is often beneficial,
e.g. in coating and lubricating flows. Characterisation of the shear, extensional
and cavitational behaviour is clearly important, and the ability of
an AFM to recreate high-rate deformations which are comparable to those
encountered in industrial processes is of particular interest. Moreover, the
ability to experimentally recreate film splitting, fibrillation and cavitational
cohesive failure in one dynamic process is desirable. However, observation
of rapid microscale phenomena is not straightforward, especially so
when cavitational mechanisms are encountered, as the observation of the
growth and collapse of vapourous cavities requires microsecond temporal
resolution. Future work will extend the capabilities of the AFM–optical
microscopy system to further investigate the presence and influence of cavitational
effects prior to the apparent cohesive failure of lubricant layers. As
such, it is necessary to evolve the design of the experiment and in the first