Analytical solutions for convective fragmentation

Fragmentation of liquid drops occurs in many processes involving convection of dispersions of liquid drops in liquid or gas carrier phases. Such fragmentation is often spatially nonhomogeneous (due, for example, to turbulence induced fragmentation). Recent work has studied a class of pipe flow problems involving convective fragmentation. In the present paper we generalize a version of the problem discussed above to allow for unsteady two-dimensional axisymmetric convective fragmentation and report a corresponding analytical solution. We connect our analytical solution to the grinding solution of Reid (1965) and demonstrate its applicability by applying it to a problem of a pulsating convective fragmentation in an unsteady axisymmetric jet, with the fragmentation characteristics being spatially dependent.

Research highlights▶ Analytical solutions to unsteady discrete population balance model equations. ▶ Applicability to pulsating jet fragmentation. ▶ Demonstrate applicability of grinding solution to a wider class of problems.