Ionic-electrostatic modeling of solid-liquid triboelectric nanogenerators

Solid-liquid triboelectric nanogenerators (SL-TENGs) are promising for blue-energy harvesting and self-powered sensing, yet a quantitative framework linking interfacial charge dynamics to electrical waveforms remains lacking. Here, we develop a unified ionic-electrostatic framework that integrates solid-liquid contact electrification, electrical double layer (EDL) screening, electrode induction, and droplet hydrodynamics. The model follows a two-stage operation principle. In Stage I, charge accumulates and approaches saturation on the dielectric. In Stage II, the response is dominated by induction current driven by the time-varying wetted area. EDL screening is incorporated through a capacitance-partition factor, which establishes a direct link between electrolyte properties and both output attenuation and sensing sensitivity. Using a reciprocity-based weighting potential, we derive a generalized induced-charge source term. This formulation explicitly accounts for electrode geometry and droplet position. A closed-form contact-radius model further yields analytical current and voltage waveforms, capturing peak scaling and polarity reversal. The framework reveals systematic dependencies on electrolyte concentration, droplet height, and load impedance. These dependencies are translated into design guidelines for dielectric properties, contact-line dynamics, and electrode architecture. Overall, this work establishes a unified and predictive foundation linking interfacial physics, signal formation, and device design in SL-TENGs.