Electrohydrodynamic instability of confined viscoelastic liquid jets

Linear stability analysis is performed to study the electrohydrodynamic instability of viscoelastic jets subjected to axisymmetric (m = 0) and first non-axisymmetric (m = 1) perturbations in the creeping-flow limit. The viscoelastic liquid jet is under the influence of a radially applied electric field induced by a concentrically placed electrode located at a finite gap width from the jet. The leaky dielectric model is used to account for the finite conductivity of the fluid. The gap between the liquid jet and the electrode is assumed to be occupied by a hydrodynamically passive gas. The influence of the applied electric potential, electrode width, electrical properties, fluid elasticity, and solvent viscosity on the stability of the jet is analyzed comprehensively. For m = 0 mode, the electric field has a dual effect on the stability of a Newtonian jet above a critical electrode width to jet radius ratio (R-cr). Here, the dual effect means that the electric field has a stabilizing effect for low wavenumbers (k) and a destabilizing effect for higher k. However, for R < R-cr, the electric field has a uniformly destabilizing effect, and the dual nature disappears. In the limit of perfectly conducting Newtonian jet, R-cr = 2.7. The maximum growth rate increases with an increase in Deborah number (De), which is a dimensionless relaxation time of the fluid, but the range of unstable wavenumbers remains unaffected due to an increase in De. For m = 0 mode, there exists a critical Deborah number (De(cr)), for given values of other physical parameters, above which the growth rate diverges. This behavior is similar to the previous results for the planar geometry and is caused due to the neglect of inertia. As the conductivity of the liquid increases, the De(cr), decreases and reaches an asymptotic value in the limit of a perfect conductor. The inclusion of elasticity has no effect on the R-cr, value, thus suggesting that the dual nature of the electric field is independent of fluid elasticity. The singularity in the growth rate is shown to be mitigated by introducing solvent viscous stresses into the model. Thus, the present study shows that finite electrode distance and elasticity have important consequences on the stability of the liquid jet for the axisymmetric mode. For m = 1 mode, the growth rate is singular at low wavenumbers which is due to the neglect of inertia of the system. For the Newtonian case, the range of wavenumbers where the growth rates are singular increases with either increasing the electric potential or decreasing the electrode width. Inclusion of elasticity increases the range of wavenumbers where the growth rates are singular, whereas the range of unstable wavenumbers remains unchanged. Therefore, the neglect of inertia gives rise to non-physical growth rates even in the Newtonian flow limit for m = 1 mode, compared to m = 0 mode where the singularity of growth rate was observed for the Maxwell fluid above De(cr).

Automated summary

Linear stability analysis is used to investigate the electrohydrodynamic instability of viscoelastic jets, showing a dual effect of the electric field on stability and a decrease in the critical Deborah number with increasing conductivity. The presence of elasticity does not affect the stability significantly, indicating that fluid stability is dependent on electrical properties and physical parameters.