  An overview of the author's papers on the new approach to the Brownian
coagulation theory and its generalization to the diffusion-limited reaction
rate theory is presented. The traditional diffusion approach of the
Smoluchowski theory for coagulation of colloids is critically analyzed and
shown to be valid only in the particular case of coalescence of small particles
with large ones. It is shown that, owing to rapid diffusion mixing, coalescence
of comparable size particles occurs in the kinetic regime, realized under
condition of homogeneous spatial distribution of particles, in the two modes,
continuum and free molecular. Transition from the continuum to the free
molecular mode can be described by the interpolation expression derived within
the new analytical approach with fitting parameters that can be specified
numerically, avoiding semi-empirical assumptions of the traditional models. A
similar restriction arises in the traditional approach to the diffusion-limited
reaction rate theory, based on generalization of the Smoluchowski theory for
coagulation of colloids. In particular, it is shown that the traditional
approach is applicable only to the special case of reactions with a large
reaction radius, and becomes inappropriate to calculation of the reaction rate
in the case of a relatively small reaction radius. In the latter, more general
case particles collisions occur mainly in the kinetic regime (rather than in
the diffusion one) characterized by homogeneous (at random) spatial
distribution of particles. The calculated reaction rate for a small reaction
radius in 3-d formally coincides with the expression derived in the traditional
approach for reactions with a large reaction radius, however, notably deviates
at large times from the traditional result in the plane (2-d) geometry, that
has wide applications also in the membrane biology as well as in some other
important areas.
