Ian Wark Research Institute,
University of South Australia, Mawson Lakes SA 5095 Australia.
J. Phys. A (submitted, 19 June, 2001)
Abstract
The exact equation describing the shape of a fluid drop under the
action of local surface stresses induced by colloidal interactions is
derived without resorting to any of the approximations inherent in the
profile equation currently employed in the literature. The exact equation
implies, and numerical examples confirm, that repulsive external (i.e.,
positive) surface energies assist in stabilising the drop against
deformation, while attractive (i.e., negative) energies destabilise the
drop, promoting or enhancing deformation. An inherent singularity in the
governing differential equation (absent from the approximate equations
currently used) when the surface energy (surface tension) is identically
matched by an external attractive energy represents an instability limit.
Explicit bounds are established for a further instability criterion and for
the hydrostatic pressure difference across the interface. An exact equation
for the radial extent of the sessile drop and some numerical examples are
also presented.
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