258
FRIEDLANDER
can be substituted to give
dN. AikT \»
at
a, Ne
(19)
It has thus been shown that the kinetics of Brownian coagulation of
heterodisperse hydrosols are second order if the self-preservation
hypothesis holds throughout the coagulation process, For heterodisperse hydrosols the value of A; is greater than 4. This value can be
determined from Eq. 18. Thus, if, is known, the effect of heterogeneity
on the rate of coagulation can be determined.
SIGNIFICANCE OF THEORY
been
The theory has been tested experimentally, and the results have
reported by Swift and Friedlander. They found that the size
distributions of coagulating hydrosols, initially unimodal, tend to pre-
serve their Shape when plotted in proper dimensionless form, If the
distribution is self-preserving, it is completely determined by specifying @ and N,,. This result should be useful in correlating and extrapolating experimental data and in calculating the average properties
of disperse phases, When two heterodisperse hydrosols are mixed, the
distribution tends to approach the same shape exhibited by an initially
unimodal system, It appears that the self-preserving form is approached no matter what the initial distribution of the coagulating
dispersion. Computer calculations by Hidy,’® following the studies of
Friedlander! and Swift and Friedlander,? have shown that a self-
preserving
form
is indeed approached asymptotically for several
arbitrarily chosen initial distributions. Hidy’s calculations give the
most accurate representation available for the form of the selfpreserving distribution.
The theory developed in these papers offers an explanation for the
regularities observed in the size distribution of the atmospheric aerosol. It is interesting to note that, if N, ~1/v as is often observed experimentally over part of the size distribution range of the atmospheric aerosol, the self-preserving form requires that
Nn, = 2?
Vv
where A, is a universal dimensionless constant. Thus it is necessary
to measure only ¢@ to establish the size distribution of the suspension
over the range where N, ~ 1/v, provided A, is known, This constant
has been calculated by Friedlander‘ and has a value of about 0.08.
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