Nucleation burst in a coagulating system

The source-enhanced formation and growth of disperse particles is considered assuming the particles born by nucleation grow then by coagulation and condensation of a low volatile vapor onto their surfaces. After formulating the basic equations governing the particle-formation-growth process a realistic process is considered: nucleation-coagulation growth of aerosol particles in a free molecular regime. The kinetics of this process is studied under the assumption that the particle mass spectrum has a log-normal form whose parameters are expressed in terms of three moments of particle mass distribution: particle number concentration, and the moments of the orders 1/3 and 2/3. These three moments together with condensable vapor concentration are shown to meet a set of four first-order nonlinear differential equations that contain a small parameter: relative vapor concentration spent to the disperse particle production. This parameter, however, does not permit a direct application of the perturbation theory: only after two consequent rescalings it becomes possible to remove the small parameter and describe the particle-formation-growth process in terms of universal functions, depending on a specially defined nondimensional group playing the role of time. It is shown that the particle-formation-growth process can be naturally separated into two stages: (i) formation by nucleation and condensational growth of particles, and (ii) growth of formed particles by coagulation and condensation. Each stage is described by its own set of universal functions which are found from the solution of respective differential equations. The asymptotic stage of the process is shown to be described by a self-preserving distribution depending only on two moments: particle number concentration and the moment of particle-mass distribution of the order of 2/3.