Supersingular mass distributions in gelling systems

Abstract

This paper considers the time evolution of disperse systems in which binary coagulation is so rapid that it leads to formation of gels during a finite but nonzero interval of time. Right before the transition point an algebraic particle mass spectrum forms whose behavior at small particle masses does not permit one to define the total particle mass concentration as ∫(0) (∞)gc(g,t)dg, because the integral diverges at low limit. This divergency prevents the formulation of an asymptotic self-similarity spectrum in its traditional form. This difficulty is avoided by introducing the second moment of the particle mass spectrum as a basic scale defining its behavior at the pregelation stage. The equations for the universality mass spectra are formulated. It is shown that these equations correctly reproduce the asymptotic form of the particle mass spectrum for the system with the product kernel. The postcritical behavior in this case is investigated. The time dependencies of the gel mass, the second moment, and particle number concentrations in the postcritical period are found.