THEORY OF SELF-PRESERVING SIZE
DISTRIBUTIONS IN A COAGULATING DISPERSION
S. K. FRIEDLANDER
W. M. Keck Engineering Laboratories, California Institute of Technology,
Pasadena, California
ABSTRACT
A reduced form of the particle-size-distribution function, designated
“self-preserving,” satisfies Smoluchowski’s equation of coagulation by
Brownian motion. Both theory and experiment indicate that the self-
preserving form is approached by coagulating systems having a wide
variety of initial distributions. This effect offers an explanation for the
regularities observed in the size distribution of the atmospheric
aerosol.
INTRODUCTION
The theory of self-preserving size distributions was proposed by
Friedlander! to explain experimentally observed regularities in the
particle size distribution of the atmospheric aerosol, The theory was
developed and tested experimentally by Swift and Friedlander.’ In this
paper, abstracted in part from Ref, 2, an account of the theory is given
for the case of Brownian diffusion,
BROWNIAN COAGULATION
The course of a coagulation process can be described by the time
variation of the particle-size-distribution function, This function canbe
defined by using the radius, the area, or the volume as an independent
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