A KINETIC MODEL FOR DROPLET COALESCENCE IN DENSE SPRAYS

Abstract

This paper is devoted to the matematical analysis of a kinetic equation describing the process of droplet coalescence in a spatially homogeneous spray. In the first part, existence of a positive measure valued solution is proved, under very general assumptions on the collision kernel. In the second part, mass conservation and momentum preservation, as well as uniqueness and continuous dependence is established, under some more restrictive — but physically reasonable — assumptions on the model. Lastly, the time-asymptotic behavior of the solution is studied.