Emergence of fractal behavior in condensationdriven aggregation
Abstract
We investigate the condensationdriven aggregation model that we recently proposed whereby an initial ensemble of chemically identical Brownian particles are continuously growing by condensation and at the same time undergo aggregation upon collision. We solved the model exactly by using scaling theory for the case when a particle, say of size x , grows by an amount αx over the time it takes to collide with another particle of any size. It is shown that the particle size spectra exhibit transition to scaling c(x,t)∼t^{β}ϕ(x/t^{z}) accompanied by the emergence of a fractal of dimension d_{f}=1/(1+2α) . A remarkable feature of this model is that it is governed by a nontrivial conservation law, namely, the d_{f}th moment of c(x,t) is time invariant. The reason why it remains conserved is explained. Exact values for the exponents β , z , and d_{f} are obtained and it is shown that they obey a generalized scaling relation β=(1+d_{f})z .
 Publication:

Physical Review E
 Pub Date:
 February 2009
 DOI:
 10.1103/PhysRevE.79.021406
 arXiv:
 arXiv:0901.2761
 Bibcode:
 2009PhRvE..79b1406H
 Keywords:

 61.43.Hv;
 64.60.Ht;
 68.03.Fg;
 82.70.Dd;
 Fractals;
 macroscopic aggregates;
 Dynamic critical phenomena;
 Evaporation and condensation;
 Colloids;
 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Soft Condensed Matter
 EPrint:
 8 pages, 6 figures, to appear in Phys. Rev. E