Kinetics of nucleation controlled formation and condensational growth of disperse particles

The kinetics of nucleation controlled formation and condensational growth of disperse particles is considered under the assumptions that: (i) only a small amount of condensable substance nucleates and forms the particles that grow by condensing the rest of the substance. (ii) The condensation efficiency is a power function of the particle mass. A nontrivial perturbation theory with respect to the smallness parameter mu= (the mass of nucleated matter)/(the total mass of condensable matter) is developed allowing one to describe the source-enhanced and free (no source) condensation processes in terms of universal functions: the particle-mass spectrum and the concentration of condensable matter. The theory relies upon a scaling transformation that removes at all the smallness parameter from the evolution equations (if the nucleation rate is a power function of the concentration of condensable matter) or leaves it in the expression for the nucleation rate where this parameter defines only a concentration scale of the nucleation process (for the nucleation rates of general form). The theory is illustrated by the exact analytical solutions of the nucleation-condensation kinetic equations for three practically important cases: (i) gas-to-particle conversion in the free-molecular regime, (ii) formation and diffusion controlled condensational growth of islands on surfaces, and (iii) formation and diffusion controlled growth of disperse particles in the continuum regime. The analytical expressions for the mass spectra of growing particles are found in the case of free condensing particles. The final mass spectra in free condensing systems display rather unusual behavior: they are either singular at small particle masses or not, depending on the value of the power exponent in the mass dependence of the condensation rate.