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Mathematical Problems in Engineering
Volume 2016, Article ID 1735897, 8 pages
Research Article

Analytical Solutions for Composition-Dependent Coagulation

1Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
2Jiyang College, Zhejiang Agriculture and Forestry University, Zhuji 311800, China

Received 6 January 2016; Accepted 4 April 2016

Academic Editor: Babak Shotorban

Copyright © 2016 Manli Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Exact solutions of the bicomponent Smoluchowski’s equation with a composition-dependent additive kernel are derived by using the Laplace transform for any initial particle size distribution. The exact solution for an exponential initial distribution is then used to analyse the effects of parameter on mixing degree of such bicomponent mixtures and the conditional distribution of the first component for particles with given mass. The main finding is that the conditional distribution of large particles at larger time is a Gaussian function which is independent of the parameter .