Nonsingular self-preserving regimes of coagulation-condensation process

Growth of disperse particles is considered assuming that the preexisting disperse particles coagulate and grow simultaneously by condensing a low volatile substance (vapor, in what follows) whose concentration is permanently refreshed by a spatially uniform and constant in time source. The kinetics of the condensation-coagulation process is studied under the assumption that the condensation rate and coagulation kernels are homogeneous functions of the particle masses. The power exponents characterizing these functions define the asymptotic self-preserving regimes of the particle growth. Four such regimes are detected: (i) the mass of the disperse phase consumes all vapor and grows linearly with time, while the vapor concentration grows (or even drops) with time as its power s<1; (ii) the mass of the disperse phase grows slower than a linear function of time, while the vapor concentration grows asymptotically as time; (iii) the mass of disperse phase remains finite; and (iv) both, the mass of disperse phase and the vapor concentration grow linearly with time. For all above regimes the equations are derived defining the shape of the asymptotic mass distribution. The latter is shown to depend on a combination of the particle mass and time. The theory is illustrated by two exactly soluble models, and numerical results for the condensation-coagulation growth of aerosol particles in free molecular regime.