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The behavior of the particle size distribution of coagulating dispersions is studied theoretically. If the collision frequency factor is a homogeneous function of particle volume, the partial integro-differential equation describing the coagulation kinetics can be transformed into an ordinary integro-differential equation by a similarity transformation originally proposed by Friedlander. The solution to the resulting equation, called the self-preserving spectrum, is determined for three different collision mechanisms: (1) constant collision frequency factor, (2) Brownian motion, and (3) simultaneous Brownian motion and shear flow, in which the shear rate decreases with time in a particular way. The results of this study indicate that the shape of the self-preserving spectrum is greatly influenced by the collision mechanism.

If a slip correction for the particle drag is taken into consideration, the coagulation equation for Brownian motion cannot be reduced to an ordinary integro-differential equation. However, the coagulation equation can be written in terms of a reduced size spectrum, By assuming that the reduced size spectrum varies slowly with time, a family of "quasi-self-preserving" spectra are obtained for various values of a parameter [?] which is a function of the mean free path of the fluid, the total volume concentration and the total number concentration of particles.

The self-preserving hypothesis concerning the particle size distribution is proved to be true for the case of constant collision frequency factor. For Brownian coagulation, arguments are presented to support the hypothesis.

In the cases which are worked out, it is assumed that the particles are uncharged and spherical in shape and that their density is conserved in the coagulation process.

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