H

which is the effective range of the van der Waals attractive forces. The bubble will have a layer of surfactant on its surface which will be orientated with its polar end in the water and the hydrophobic end in the air.

The interaction energy is expressed in terms of a net Hamaker constant, A132, which is approximated by Adamson as a simple linear relationship:

Figure 2 Contact angle 8 of liquid droplet on a solid surface.

The binary Hamaker constants expressed above refer to two-surface interactions only. Some of these are physically difficult to interpret, but are nevertheless useful in formulating a conceptual understanding. With these reservations, A12 is the interfacial energy between a solid particle and a bubble separated by a vacuum and A33 is the interaction energy between water molecules.

A13 and A23 are the Hamaker constants representing the particle-water and bubble-water interaction energies. If these energies are low with respect to the mutual interaction energy of the water molecules then A132 will be greater than the interaction A12. The enhanced attraction between the particle and the air bubble in the presence of water reflects hydrophobic bonding.

Leja quotes interaction energy potentials and London dispersion forces for various configurations following integration of atom-atom interaction energies. The dispersion force of attraction between two spheres of radius R1 and R2, for example, is given by:

ar1r2

Solar Panel Basics

Solar Panel Basics

Global warming is a huge problem which will significantly affect every country in the world. Many people all over the world are trying to do whatever they can to help combat the effects of global warming. One of the ways that people can fight global warming is to reduce their dependence on non-renewable energy sources like oil and petroleum based products.

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