Coagulation in a continuously stirred tank reactor

Abstract

Smoluchowski's coagulation equation with coagulation rates Kij [is proportial to] (ij)[omega] describing the temporal evaluation of the size distribution ck (concentration of k-mers) is studied in the presence of a source term a[delta]k1, and a sink term -bck. With a' = a/b2 one finds that a steady state is reached, exhibiting gelation when and a' > a0([omega]), where a0([omega]) depends on [omega] (a0([omega]) = [infinity] for , , a0([omega]) = 0 for [omega] > 1). For a' a0([omega]) the asymptotic behavior of the ck is dominated by exponential decrease, for a' > a0([omega]) it has an algebraic tail. The case [omega] = 1 is singular in that also nongelling steady states have an algebraic tail [is proportial to] k[beta], where [beta] depends on a'.