Linear stability of electroconvection in a viscoelastic electrolyte: polymeric-work pathways and eigenmode selection

Abstract

Electroconvective (EC) instability near ion-selective surfaces plays a key role in electro-chemical transport beyond the diffusion-limited regime. While EC instability in Newtonian electrolytes has been extensively investigated, the influence of viscoelasticity on the instability mechanism remains less understood. In the present study, we investigate the viscoelastic modulation of EC instability using linear stability, eigenspectrum, and mechanical-work analyses, supported by asymptotic pathway ordering. The analysis reveals a non-monotonic dependence on the Weissenberg number Wi, with the maximum growth rate and minimum critical voltage occurring near Wi ~ O(1). The mechanical-work balance separates electric, solvent-viscous, and polymeric contributions, and further decomposes the polymeric work into normal-stress-difference and shear-stress pathways according to their constitutive origins. For Wi << 1, the polymer stress recovers Newtonian viscous dissipation at leading order. As Wi approaches unity, the phase efficiencies of the Newtonian-like polymeric pathways decrease substantially, causing the negative polymeric work to collapse and the instability to intensify. At intermediate Wi, an additional minimum in the critical voltage appears at low wavenumbers. Eigenspectrum analysis attributes this feature to the selection of a slowly propagating mode that retains substantial negative polymeric work. At large Wi, this mode no longer determines the instability threshold, and the low-wavenumber minimum disappears. The normal-stress-difference and shear-stress work then nearly cancel, accompanied by stronger ESC-localized shear deformation and predominantly solvent-viscous dissipation. Thus, the non-monotonic response is governed by stress-deformation phase relations, solvent dissipation, and eigenmode selection rather than stress magnitude or a single polymeric contribution.