| dc.description |
It is assumed that the size distribution c<sub>k</sub>(t) satisfies Smoluchowski's coagulation equation with rate coefficients K(i, j), behaving as K(i, j) approximately i<sup>mu </sup>j<sup>nu </sup> (i<<j), and find the following: in gelling and nongelling systems of class I ( mu >0) the general solution c<sub>k</sub>(t) approaches for t to infinity the exact solution Cb<sub>k</sub>/t(k=1, 2, . . .), where the b<sub>k</sub>'s are independent of the initial conditions c<sub>k</sub>(0), and can be determined from a recursion relation. In class II systems ( mu =0), c<sub>k</sub>(t)/c<sub>1</sub>(t) to b<sub>k</sub> (t to infinity , k=1, 2, . . .), but the b<sub>k</sub>'s depend on c<sub>k</sub>(0). Only in the scaling limit (k to infinity , s(t) to infinity with k/s(t)=finite; s(t) is the mean cluster size) does c<sub>k</sub>(t) approach a form independent of the initial distribution. Class III, where c<sub>k</sub>(t)/c<sub>1</sub>(t) to infinity (t to infinity , k=2, 3, . . .), has not been considered here. |
