In this paper, we present relationships between the intrinsic radial distribution function (RDF) for a three-dimensional, isotropic system of particles and the lower-dimensional RDFs obtained experimentally from either two-dimensional or one-dimensional sampling of the data. The lower-dimensional RDFs are shown to be equivalent to integrals of the three-dimensional function, and as such contain less information than their three-dimensional counterpart. An important consequence is that the lower-dimensional RDFs are attenuated at separation distances below the characteristic length scale of the measurement. In addition, the inverse problem (calculating the three-dimensional RDF from the lower-dimensional measurements) is not well posed. However, recent results from direct numerical simulations (Reade & Collins 2000) showed that the three-dimensional RDF for aerosol particles in a turbulent flow field obeys a power-law dependence on r for r [Lt ] η, where η is the Kolmogorov scale of the turbulence. In this case, the inverse problem is well posed and it is possible to obtain the prefactor and exponent of the power law from one- or two-dimensional measurements. A procedure for inverting the data is given. All of the relationships derived in this paper have been validated by data derived from direct numerical simulations.

The technique of differential electrophoresis can be used to measure subpiconewton forces between Brownian colloidal particles. Previously, this technique was limited by two factors:  (1) forces could be measured only between particles with different average zeta potentials and (2) the particles had to be large enough for observation under a light microscope. This paper focuses on overcoming factor 1 by using a third particle as a “handle”, allowing forces to be measured between particles with identical zeta potentials. Semianalytical solutions to the electrokinetic equations for three spheres were developed, with results similar to those for two spheres, enabling the ready interpretation of experiments. Interparticle forces were then measured for charged polystyrene latex particles 1.5 and 4.5 μm in diameter over a range of aqueous solution conditions. One important finding was that while nearly-touching particles aggregate irreversibly in the absence of the polyelectrolyte sodium polystyrene sulfonate (NaPSS), the addition of trace quantities of NaPSS enables the particles to form triplets that break with forces of O(10 pN).

Interparticle forces have been measured between polystyrene latex particles as small as 85 nm in diameter in KCl solutions. A variant of the differential electrophoresis technique, called particle force light scattering (PFLS), was used to measure forces between Brownian, nearly touching particles for diameters from 4500 nm down to 85 nm. The forces, some less than 0.1 pN, matched to within a factor of 2 with predictions from depletion and DLVO theory.

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