Аннотация
A mathematical model is constructed for the dynamics of a raindrop moving in a gravity field through an atmosphere containing fine particles, taking into account the processes of relaxation of its velocity and the capture of fine particles. It has been established that the equation of motion of a drop in the problem posed belongs to the class of singularly perturbed equations, for the integration of which it is necessary to involve special algorithms. In the limiting modes of droplet motion, analytical solutions of the problem are obtained that describe the dependence of the droplet velocity and coordinate on time. In the complete formulation, the solutions of the problem are obtained numerically for different values of the defining parameters. The influence of the droplet size on the parameters of its motion in a concentrated aerodispersed mixture has been studied. The dependences of the limiting volume fraction of the solid component in the composition of the drop and the intensity of the precipitation of particles (washed out by the drop) on the earth’s surface on the size of the drop are obtained. Comparison of the calculated, approximate-analytical and experimental dependences of the steady-state rate of fall of a drop on its size was carried out, which showed their good agreement.