Electrohydrodynamic instabilities of a thin confined polymer gel on a saturated porous substrate

Electrohydrodynamic (EHD) instabilities at polymer–porous interfaces play a pivotal role in determining interfacial morphology, wettability and pattern formation, with implications for energy storage, diagnostics and flexible electronics. This study presents a comprehensive general linear stability analysis to examine electric-field-induced instabilities at a confined interface between a viscoelastic polymer gel and a saturated porous medium. By coupling Maxwell stresses with a modified Darcy–Brinkman–Kelvin–Voigt framework, the model captures how porous medium-moderated EHD instabilities influence both the onset and dominant instability modes. Key parameters – including the electric Rayleigh number, Darcy number, dielectric contrast and geometric filling ratio – govern the spatio-temporal features of emerging patterns. The analysis reveals a sigmoidal dependence of characteristic length and time scales on permeability, i.e. Darcy number, establishing three regimes: impermeable, transitional and highly permeable, with a shift toward shorter wavelengths. The length and time scale transitions, triggered by the solid-saturated porous medium, are further moderated by the dielectric contrast – instabilities are suppressed when the contrast is low and amplified when it is high, enabling sub-micron patterning. Geometric confinement, i.e. increasing filling ratio, further intensifies pattern length scales, suggesting the feasibility of fabricating complex ultra-fine nanoscale encapsulated porous patterns. The elasticity of the viscoelastic layer imposes a threshold for instability onset and is critical for identifying wettability transitions at the interface. This framework offers predictive insight into tuning instability modes through permeability–viscoelasticity–electrostatics interplay, laying the foundation for wettability-controlled interfaces and self-organised interfacial patterns in next-generation EHD-driven systems.