Instability of viscoelastic curved liquid jets

Abstract

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.

Jet evolution and fiber formation mechanism of amylopectin rich starches in centrifugal spinning system

“…The phenomenon was similar to the M3 model described in industrial prilling process, and the drops could be divided into main drop (larger diameter) and satellite drops (smaller diameter). 29 In this concentration range, the molecular chain is not entangled and caused the jet rapidly breaking up into drops after jet instability occurs.…”

A comprehensive mathematical model for nanofibre formation in centrifugal spinning methods

“…prilling or glass particle production processes, which share similarities with CS in that they produce microfibres or nanofibres. Furthermore, shear thinning and viscoelastic effects have been investigated on the curved jet instability by Uddin, Decent & Simmons A comprehensive mathematical model for nanofibre formation 892 A26-3 (2008), Uddin & Decent (2009, Hawkins et al (2010), , Alsharif, Uddin & Afzaal (2015) and Marheineke et al (2016). Despite their simplicity and popularity, however, the asymptotic methods suffer from near-orifice singularities, strictly limiting their applications to parameters ranges corresponding to low-viscosity jets in slow rotations, as shown in detail by Götz et al (2008) and Arne et al (2010).…”

Convective and absolute instability of viscoelastic liquid jets in the presence of gravity

“…In this paper, we examine the convective and absolute instability of an axisymmetrical viscoelastic liquid jet falling under gravity. This work extends the analysis of Alsharif 16 by including spatial and absolute instability analysis. We use a mapping technique, often referred to as the "Cusp Map Method" developed by Kupfer, Bers, and Ram 1 to find the cusp point, which corresponds to the pinch point for absolute instability.…”

“…They found a new global instability mode for viscous jets. Alsharif 16 investigated the linear temporal instability analysis of a viscoelastic…”