Instability of viscoelastic curved liquid jets

The industrial prilling process is a common technique to produce small pellets which are generated from the break-up of rotating liquid jets. In many cases the fluids used are molten liquid and/or contain small quantities of polymers and thus typically can be modelled as non-Newtonian liquids. Industrial scale set-ups are costly to run and thus mathematical modelling provides an opportunity to assess methods of improving efficiency and introduces greater levels of precision. In order to understand this process, we will consider a mathematical model to capture the essential physics related to a cylindrical drum, which is rotated about its axis. In this paper, we will model the viscoelastic nature of the fluid using the Oldroyd-B model. An asymptotic approach is used to simplify the governing equations into 1D equations. Moreover, a linear instability analysis is examined and the most unstable modes are found to grow along the jet. Furthermore, the non-linear instability is investigated by using a finite difference scheme to find break-up lengths and droplet formation.