Mixing state of bi-component mixtures under aggregation with a product kernel

We analyze the aggregation of a two-component system with a product kernel, to determine its evolution in time during a progressive mixing. The evolution is governed by the Smoluchowski equation, yielding gelation from a certain time. In the past, equilibrium (or asymptotic) solutions have been used to study mixing of bi-component mixtures for non-gelling kernels. In this letter we show that asymptotic solutions are invalid to describe the mixing behavior for the product kernel case (even before gelation). Besides, an equilibrium concentration is not reached. On the contrary, particles with any composition exist all time.