Applications in Engineering Science (Jun 2020)
On stability of steady nonlinear rotating viscoelastic jets
Abstract
Recently Riahi (2018) studied steady nonlinear rotating viscoelastic jet, which was subjected to the Giesekus constitutive equations for the stress tensor. He applied scaling, perturbation and numerical techniques for the viscoelastic jet with sufficiently small aspect ratio and determined the nonlinear steady solutions for the jet. He then calculated and described the results for the jet quantities such as radius, speed, stretching rate, strain rate and tensile force. In this paper we investigate stability of the nonlinear steady solutions of the time dependent form of such jet system, by superimposing small amplitude disturbances in the form of travelling waves that can grow in time, in space or simultaneously in time and in space. We find, in particular, a main condition for the existence of instability is that the growth rates of the disturbances should depend on the arc length of the jet. Under such condition, the only possible instability of the steady solution is temporal in nature and is due only to disturbances that simultaneously grow in time but decay in space. The growth rates of these disturbances increase with increasing the rotation rate, viscoelasticity and the arc length of the jet. However, the magnitude of such growth rate decreases with increasing the fluid viscosity and surface tension.
