Scaling theory for gelling systems: Work in progress

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• 作者：F. Leyvraz
• 刊名：Physica D
• 出版年：2006
• 出版时间：October 2006
• 年：2006
• 卷：222
• 期：1-2
• 页码：21-28
• 全文大小：313 K

文摘

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 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^μy^ν+x^νy^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 power-law initial conditions).