Electrokinetic Thin-Film Model for Electrowetting: The Role of Bulk Charges

The electrowetting behavior of a charge-carrying sessile droplet is relevant to applications such as point-of-care diagnostics. Often biomedical assays involve droplets that contain charged molecules such as dissolved ions, proteins, and DNA. In this work, we develop a reduced-order electrokinetic model for electrowetting of such a charge-carrying droplet under a parallel-plate electrode configuration. An inertial-lubrication model based on the weighted residual integral boundary layer (WRIBL) technique is used to obtain evolution equations that describe the spatiotemporal evolution of the fluid-air interface and the depth-integrated flow rate. The solutions to the evolution equations are obtained numerically by using the spectral collocation method. We investigate the role of domain and surface charges, characterized by the Debye length, on droplet wetting. Under low relaxation timescales, both droplet deformation and wetting alteration under an AC field are shown to be equivalent to that under a root-mean-square (RMS) DC field. We show that an electrolytic sessile droplet can exhibit a larger deformation in comparison to the two asymptotic limits of a perfect conductor and a perfect dielectric droplet, corresponding, respectively, to very low and high Debye lengths. The effects of several other parameters such as the inherent equilibrium wettability, permittivity ratio, and electric field strength are also investigated.