Rigid particles, limiting diffusion

So far the comments on reorientational correlation functions have been general. This subsection describes the form of the decay for a particularly important model a rigid particle undergoing diffusive motion. The diffusive limit is not always applicable for liquids (small molecules and methyl groups can show significant inertial effects), but is generally observed for medium to large molecules in solution and is useful for many analyses. 

For CO 0, Eq. (11-7) reduces to the stream function for steady creeping flow past a rigid sphere, i.e., Eq. (3-7) with k = co. The parameter 3 may be regarded as a characteristic length scale for diffusion of vorticity generated at the particle surface into the surrounding fluid. When co is very large, 3 is small, and the flow can be considered irrotational except in the immediate vicinity of the particle. In the limit co go, Eq. (11-7) reduces to Eq. (1-29), the result for potential flow past a stationary sphere. 

The Stokes-Einstein equation is limited to noninteracting, spherical and rigid spheres. The effect of particle interaction at relatively low particle concentration, c, can be taken into account by expanding the diffusion coefficient into a power series of concentration. 

The list of experimentally accessible properties of colloid solutions is the same as the list of accessible properties of polymer solutions. There are measurements of single-particle diffusion, mutual diffusion and associated relaxation spectra, rotational diffusion (though determined by optical means, not dielectric relaxation), viscosity, and viscoelastic properties (though the number of viscoelastic studies of colloidal fluids is quite limited). One certainly could study sedimentation in or electrophoresis through nondilute colloidal fluids, but such measurements do not appear to have been made. Colloidal particles are rigid, so internal motions within a particle are not hkely to be significant the surface area of colloids, even in a concentrated suspension, is quite small relative to the surface area of an equal weight of dissolved random-coil chains, so it seems unlikely that colloidal particles have the major effect on solvent dynamics that is obtained by dissolved polymer molecules. 

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