Linear stability of a thixotropic liquid jet in a coaxial swirling gas under an axial electric field

The temporal instability of a thixotropic liquid jet subjected to an axial electric field and a coaxial swirling gas stream is investigated using linear stability analysis. A dispersion relation incorporating thixotropic structural evolution, gas swirl, and Maxwell electric stress is derived based on the Moore thixotropic model and the Taylor–Melcher leaky-dielectric framework, and the resulting complex eigenvalues are solved using the normal-mode method and the Levenberg–Marquardt algorithm. The results show that the axisymmetric disturbance dominates under the reference conditions. Increasing the thixotropic structural parameter, swirl intensity, electric Euler number, or Weber number suppresses disturbance growth and narrows the unstable wavenumber range, whereas increasing the Reynolds number promotes jet instability. A stronger thixotropic structure reduces the maximum growth rate and shifts the most dangerous wavenumber to lower values; gas swirl suppresses short-wave disturbances by modifying the interfacial pressure distribution and momentum exchange; the axial electric field weakens disturbance amplification through Maxwell electric stress; and a larger Weber number suppresses capillary instability, while a larger Reynolds number mainly reflects stronger inertial effects.