Coagulation in a Continuously Stirred Tank Reactor

Smoluchowski 's coagulation equation with coagulation rates K 0 oc (ij) ~ describing the temporal evaluation of the size distribution ck (concentration of k-mers) is studied in the presence of a source term ark, and a sink term --bCk. With a' a/b 2 one finds that a steady state is reached, exhibiting gelation when w > 1⁄2 and a ' > ao(w), where a0(o~) depends on w (ao(w) = ~ for ~o < 1⁄2, ao(1) = 1⁄4, a0(w) = 0 for w > 1). For a ' < ao(w) the asymptotic behavior of the ck is dominated by exponential decrease, for a ' > ao(w) it has an algebraic tail. The case w = 1 is singular in that also nongelling steady states have an algebraic tail oc k a, where/3 depends on a'. © 1985 Academic Press, Inc.