Condensation/coagulation kinetics for mixture of liquid and solid particles: analytical solutions

Kinetic equations describing a simultaneous coagulation and condensation in a mixture of liquid and solid particles (for example, water drops and ice particles in supercooled cloud) are formulated. New analytical solutions to the equations for coagulation kernels, K(g,s)=2; K(g,s)=g+s; K(g,s)=2gs, and particle condensation rates, v(g)=βg, are obtained and analyzed. The results can be used for verification of numerical methods employed in simulation of microphysical processes in supercooled clouds.