Dynamic break-up and drop formation from a liquid jet spun from a rotating orifice. Part II: Theoretical

We examine the dynamics of a spiralling slender liquid jet which emerges from a rotating cylindrical drum. Such jets arise in the manufacture of fertiliser and magnesium pellts in the prilling process. Exploiting the slenderness of the jet we determine the steady trajectory of the jet, and find that at leading-order it is a function of the rotation rate of the drum, the surface tension and density of the liquid, the exit speed and exit radius of the jet, the radius of the cylinder, but not of the viscosity of the liquid. We carry out a linear stability analysis of the steady solution, using both inviscid and viscous perturbations, and considering both temporal and spatial stability. We extend this approach by considering finite amplitude unsteady disturbances of a steady jet. We derive nonlinear partial differential equations for these disturbances. Solving these equations gives us a better approximation to the break up length of the jet, information on droplet size and distribution, as well as details of the dynamics of the break up of a spiralling jet. The numerical approximations were computed using a finite difference scheme and the time-integration method is a fully implicite scheme. A Lax-Wendroff method is used to solve the nonlinear finite difference equations.