a b s t r a c tThe 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.

Droplet generated from the rupture of a compound liquid jet can be used to produce encapsulated droplets which have applications in a wide variety of industrial processes. In this paper, we examine the instability of a two dimensional axisymmetric inviscid compound jet falling vertically downwards in a surrounding gas under the influence of gravity. The steady state equations are derived using an asymptotic method and the linear instability, including temporal and spatial instability, is determined using a multiple scales approach. The results are analysed to investigate how the gas-to-shell density ratio affects key features of the jet including theoretical breakup lengths.

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