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Thermodynamic Analysis of Bridging Bubbles and a Quantitative Comparison with the Measured Hydrophobic

Summary: Thermodynamic Analysis of Bridging Bubbles and a
Quantitative Comparison with the Measured Hydrophobic
Phil Attard
Ian Wark Research Institute, University of South Australia, Mawson Lakes SA 5095, Australia
Received September 2, 1999. In Final Form: February 9, 2000
The shape of a bubble bridging two colloidal spheres is obtained by minimization of the constrained
Gibbs free energy. Bubbles bridging hydrophobic surfaces are concave, whereas hydrophilic surfaces give
rise to convex bubbles. Owing to an energy barrier, metastable submicroscopic 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.
There have been a number of theoretical mechanisms
proposed to account for the long-range attractions mea-


Source: Attard, Phil - School of Chemistry, University of Sydney


Collections: Chemistry