A thin film model for statics and dynamics of electro(de)wetting on soft and liquid dielectrics

The contact line dynamics of sessile droplets on soft dielectrics under an electric field is crucial for applications in flexible electronics and point-of-care diagnostics. This study presents a reduced-order model based on lubrication theory to investigate the electrohydrodynamic spreading and retraction dynamics of a sessile droplet on a deformable dielectric under the pinned electrode configuration. The mechanical response of the soft dielectric is characterized using the Kelvin-Voigt model, while the influence of the electric field on the interfacial energy is incorporated based on the electrical energy stored due to dielectric polarization upon electrification. A theoretical framework is established that relates the integrated form of molecular interactions (Hamaker theory) with interfacial tensions of the three phases (Frumkin-Derjaguin theory) and the electric field-dependent equilibrium contact angle (Young-Lippmann law). This enables the incorporation of the coupled effects of dielectric deformation, viscoelastic dissipation, and the imposed electric field in the evolution equations. The set of non-linear evolution equations is solved numerically to obtain the spatiotemporal dynamics of droplet shape and the dielectric deformation. A range of substrate rheologies, ranging from purely elastic to purely viscous limits, are explored. Both the static and dynamic aspects of the spreading and dewetting are shown to be governed by the bulk substrate rheology and the deformation induced by coupling of the substrate softness and the imposed electric field. The model predicts that an increase in substrate softness and viscoelastic dissipation leads to a reduction in the overall rate and extent of both electrowetting and electrodewetting, consistent with previous experimental observations.