Structural stability of disperse systems and finite nature of a coagulation front

A new discrete model of coagulation, which is a discrete analog of the Oort-van de Hulst-Safronov equation, is derived. It is shown that the familiar version, in contrast with Smoluchowski’s equation, can be used to calculate the propagation of a coagulation front. The relationship between compliance to the mass conservation law and the finite nature of the coagulation front is established, and then estimates of the time of violation of the mass conservation law are made for several classes of coagulation kernels. One of the conclusions is that the mass conservation law can be violated in cases where particles of roughly equal mass cannot coagulate, as occurs, for example, in gravitational coagulation. Estimates of the time for the appearance of structural instability of the system are made for multiplicative coagulation kernels. Zh. éksp. Teor. Fiz. 116, 717–730 (August 1999)