Van der Waals Interactions of Microparticles

The aerosol interaction forces discussed in the preceding sections of this chapter have involved only electrically charged particles or neutral particles with multipole moments. The importance of charge on all phases of aerosol dynamics is generally recognized and is exploited in numerous ways. It was argued above (Sect. 

The domain of importance of the van der Waals interaction for aerosol microphysics is typically for particle separations under a radius. For example, consider two identical spherical particles at room temperature with kT 4.14 X ergs. Assume the particles electric susceptibilities e(x) = 2 for 400 

Equation (5.20) can be interpreted to mean that the dispersion energy AE is composed of all the combinations of interactions (disregarding order) among n units 

Now consider the (multipole) eigenfrequencies of each molecule j. If the sums in each term of (5.20) be rearranged in recognition of the fact that 

This is an expression for the dispersion energy of a body in terms of an independent measurable property of its constituents. It shows that the dispersion interaction among molecules in one body generally cannot be approximated by the pairwise interactions among them [first term in (5.23)], but must include all combinations of interactions. Formulation of the two-body dispersion interaction is now clear. Suppose that a dipolse j is located externally to a body A and its interaction with a molecule i in A is sought. That interaction is given by the sum of the dipole fields due to the molecule alone and to its iterated multiple interactions with all the other molecules in A. The resultant dipole field 

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