Ian Wark Research Institute,
University of South Australia, Mawson Lakes SA 5095 Australia.
Langmuir 16 , 4455-4466 (2000)
Abstract
The shape of a bubble bridging two colloidal spheres is
obtained by minimisation of the constrained Gibbs free energy.
Bubbles bridging hydrophobic surfaces are concave,
whereas hydrophilic surfaces give rise to convex bubbles.
In both cases the optimum contact angle satisfies the Young equation.
Due to an energy barrier, metastable sub-microscopic bubbles
are prevented from expanding to microscopic size,
and vice versa,
and hysteresis is found on approach and on separation
of the hydrophobic spheres.
The force due to the bridging bubble is generally attractive,
except at small separations for both pinned bubbles
and hydrophilic surfaces.
An analytic approximation for the force and bridging bubble size
is derived and shown to be much more accurate for colloidal spheres
than the classic formula for the capillary adhesion.
Dynamic drag on the expanding bubble is shown to
reduce the attraction and to give a repulsion at small separations.
The dynamic results give a quantitative account
of the force measured between hydrophobic surfaces in water
with an atomic force microscope.
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