W. Richard Bowen and Nidal Hilal 4

LIST OF SyMbOLS 269
instance it is intended to conduct additional microscopic observations from
beneath the liquid layer. In this way, the current restrictions imposed by the
focal distance can be reduced (it is necessary to use ULWD dry lenses to
document filament formation), and high numerical aperture oil immersion
lenses may be employed to study microscale cavitational effects in the thin
fluid layer prior to the mesoscale deformation process.
ACknowLEDgEMEnTS
The authors would like to acknowledge Prof. W. Richard Bowen and
Prof. Nidal Hilal for their significant contribution to the research content
presented in section 9.6. The authors are grateful for the financial support
of the EPSRC, the work reported here was conducted under EPSRC grant
no. GR/S10438/01.
LIST oF SyMBoLS
A Cantilever vibration amplitude m
an Constant
B Geometric apparatus coefficient m
bp Viscous damping coefficient N s m�1 F Force N
G* Complex modulus Pa
G’′ Elastic modulus Pa
G“″ Viscous modulus Pa
H Separation distance between probe and surface m
K Spring constant N m�1 R Radius of sphere m
T Cantilever thickness m
U Relative separation velocity m s�1 X Cantilever width m
Z Displacement m
� Ratio of cantilever and drive amplitude
�circ Hydrodynamic function for cylindrical cantilever
�rect Hydrodynamic function for rectangular
cantilever
� Rheological phase angle °