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Effective Spring Constant of Bubbles and Droplets Phil Attard* and Stan J. Miklavcic
 

Summary: Effective Spring Constant of Bubbles and Droplets
Phil Attard* and Stan J. Miklavcic
Ian Wark Research Institute, University of South Australia, Mawson Lakes SA 5095, Australia
Received June 25, 2001. In Final Form: October 3, 2001
It is shown that gas bubbles and liquid droplets respond as hookean springs to applied loads in the
experimental weak force regime. An analytic expression is obtained for the spring constant that is identical
for both, linear in the surface tension , and logarithmically dependent on the lengths (the decay length
of the interaction, the radius of the bubble or droplet, and the radius of the particle or probe). For acute
interior contact angles greater than about 20, it is typically in the range 0.8-1.2, in agreement with
published atomic force microscopy data, and it increases logarithmically for smaller contact angles. Analytic
expressions are also obtained for the deformed profile, the extent of the dimple and of the interaction
region, the wrapping radius, and the rupture force.
Introduction
The interaction of gas bubbles and liquid droplets with
themselves or with particles or substrates is important in
such diverse areas of manufacturing and technology as
froth flotation, oil recovery, printing and deinking, and
emulsion stability. Accordingly, in recent years, direct
quantitativemeasurementsofforcesinwell-definedmodel
systems have been made. In particular, the atomic force

  

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

 

Collections: Chemistry