Thermocapillary effects on absolute and convective instability of viscoelastic liquid jets

Abstract

The effect of heat transmission on the absolute instability (AI) and convective instability (CI) of axisymmetrical disturbances in a viscoelastic liquid jet that falls under gravity is investigated. In general, when heat is included to the interface of a viscoelastic jet, it can be used to process droplet sizes and breakup lengths even more. We describe the jet’s dynamics mathematically using the Upper-Convected Maxwell (UCM) model. On the basis of the jet’s slenderness, an asymptotic approach is used to simplify the problem and obtain solutions of steady basic flow, which are then linearly analyzed for absolute and convective instability. When traveling wave modes are considered, a dispersion relation between the wavenumber and the growth rate of viscoelastic jets is derived, which can then be solved numerically using the Newton–Raphson method. The impact of varying some non-dimensional parameters is shown on absolute and convective instability. In this work, absolute instability is explored by employing a mapping technique called the cusp map method. For a variety of parameter regimes, the convective-to-absolute instability boundary (CAIB) is determined. We have found that absolute-to-convective transitions occur at lower critical Weber numbers when heating is included to the interface of the viscoelastic jets.

Keywords

• Viscoelastic liquid jets
• Absolute instability
• Heat transfer
• Cusp map method