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 to improve efficiency and introduce greater levels of precision. In order to understand this process, we consider a mathematical model to capture the essential physics related to a cylindrical drum which is rotated about its axis and from which a slender liquid jet emerges from a hole placed on the side of the drum. Furthermore, surfactants may be used in such process to manipulate the size of the resulting droplets. In this thesis, we model the viscoelastic nature of the fluid using the Oldroyd-B model. An asymptotic approach is used to simplify the governing equations and then we consider a linear temporal stability analysis of the resulting set of equations.
The effect of gravity on viscoelastic liquid jets has been discussed both with rotation and without rotation. The trajectory of this problem has been plotted in three dimensions. Our results show the effect of many non-dimensional parameters on the linear instability of a viscoelastic curved liquid with gravity and without gravity
