Scaling theory for gelling systems: Work in progress

Gelation as it arises in the kinetic equations describing irreversible aggregation–the so-called Smoluchowski equations–is 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 ττ 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)=xμyν+xνyμK(x,y)=xμyν+xνyμ. 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 power-law initial conditions).