1. Coagulation in a continuously stirred tank reactor
- Author
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Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA; Institut f??r Theoretische Physik, Universit??t zu K??ln, Z??lpicher Str. 77, D-5000, K??ln 41, West Germany, Hendriks, E.M., Ziff, Robert M., Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA; Institut f??r Theoretische Physik, Universit??t zu K??ln, Z??lpicher Str. 77, D-5000, K??ln 41, West Germany, Hendriks, E.M., and Ziff, Robert M.
- 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'.
- Published
- 2006