Spatial instability analysis and mode transition of a viscoelastic jet in a co-flowing gas stream

Spatial linear instability analysis is employed to investigate the instability of a viscoelastic liquid jet in a co-flowing gas stream. The theoretical model incorporates a non-uniform axial base profile represented by a hyperbolic tangent, capturing the shear layer. The Oldroyd-B model discretised with Chebyshev polynomials is employed, and energy budget analysis is used to interpret underlying mechanisms. At low Weber numbers, the jet evolves axisymmetrically and the instability is governed by interfacial gas-pressure fluctuations; as the Weber number increases, the growing inertia drives a transition of the predominant mode from axisymmetric to helical. At weak elasticity, the instability is also primarily governed by gas-pressure fluctuations. As elasticity increases, the predominant mode transitions from axisymmetric to helical. This transition is accompanied by a migration of disturbance structures from the interface toward the jet interior and an enhanced coupling between velocity perturbation and the basic flow. These trends reveal a new predominant instability mechanism – the elasticity-enhanced shear-driven instability – which is distinct from capillary or Kelvin–Helmholtz instabilities in Newtonian jets. A We – $El$ phase diagram delineates the boundary between predominant modes and experimental results obtained in a flow-focusing configuration validate the theoretical predictions. Compared with temporal stability results, the spatial framework – by directly resolving the convective downstream amplification of disturbances – achieves quantitative agreement with experiments and highlights the superiority of spatial instability analysis in capturing the dynamics of strongly convective, non-parallel jet flows. These findings provide mechanistic insight into viscoelastic jet instabilities and offer guidance for applications involving droplet and fibre formation in co-flow systems.