Instability of non-isothermal viscous liquid jets

A linear temporal instability analysis of a viscous liquid jet in ambient gas under a thermal field is conducted. The basic temperature profile is derived analytically based on the thermal conduction equation and corresponding boundary conditions. The effects of several control parameters, including the temperature ratio (Tr), Marangoni number (Ma), and Péclet number (Pe), on non-isothermal jet instability are systematically examined through parametric studies. An energy budget method is employed to evaluate the contributions of all physical mechanisms to the kinetic energy. The results reveal that reducing Tr promotes the jet instability. For jets with Tr>1, the maximum growth rate increases with the decrease in Ma or the increase in Pe, indicating that Marangoni stress and thermal conductivity suppress the instability of hot jets. Variations in these control parameters also influence the most dangerous and cutoff wavenumbers. Furthermore, the energy budget analysis reveals a transition in the dominant instability mechanisms between Rayleigh–Plateau and Marangoni instabilities. Specifically, enhancing the Marangoni stress or suppressing the thermal conductivity for hot jets shifts the dominant mechanism from Rayleigh–Plateau instability to Marangoni instability. Phase diagrams in various control parameter spaces are presented to predict transitions in the dominant instability mechanism.