Scaling theory for gelling systems: Work in progress
Abstract
Gelation as it arises in the kinetic equations describing irreversible aggregationthe socalled Smoluchowski equationsis briefly reviewed. The scaling theory near the gel point, immediately before the transition, is presented. The equations presented earlier for the scaling function and the exponent τ are cast in a form more amenable to numerical study. An algorithm to solve them is described and applied to the kernels of the form K(x,y)=x^{μ}y^{ν}+x^{ν}y^{μ}. A theory for the behaviour immediately after the gel transition is also presented and is found to be verified in one special exactly solved case (product kernel with powerlaw initial conditions).
 Publication:

Physica D Nonlinear Phenomena
 Pub Date:
 October 2006
 DOI:
 10.1016/j.physd.2006.08.011
 Bibcode:
 2006PhyD..222...21L