Aggregation process is, in certain cases, a self-similar phenomenon whose modeling can be done through the so-called kernel homogeneity parameter. A new approach for the determination of this parameter is introduced. It is based on analytical expressions derived from the self-preserving theory and applied to the 1st and 2nd moments of the particles size distribution. As aggregation evolves in time, the so determined kernel homogeneity is found to variate in a different way depending on the initial soot volume fraction. The relative convergence between the homogeneity coefficients derived from the 1st and 2nd moments of the particles size distribution is used as a criterion to estimate the time-lag for self-preserving. It is found to be 5 times the characteristic time of coagulation with no relevant dependence on the initial soot volume fraction.