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Abstract
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.