Absolute instability of free-falling viscoelastic liquid jets with surfactants

The effect of surfactants on the absolute instability of a viscoelastic liquid jet falling under gravity is examined for axisymmetrical disturbances. In general, the inclusion of surfactants to the interface of a viscoelastic liquid jet allows for the possibility of further processing droplet sizes and breakup lengths. We use the upper-convected Maxwell model to provide a mathematical description of the dynamics of the jet. An asymptotic approach, based on the slenderness of the jet, is used to render the problem more tractable and obtain steady-state solutions and then perform a linear analysis of the convective and absolute instability on these base solutions. By considering travelling wave modes, we derive a dispersion relationship, which is then solved numerically using the Newton-Raphson method. We show the effect of changing a number of dimensionless parameters, including the initial surfactant concentration, on convective and absolute instability. In this work, we use a mapping technique known as the cusp map method to explore absolute instability. The convective/absolute instability boundary is identified for various parameter regimes