Dynamic modelling of charge transport in solid–liquid systems

Liquid-solid charging systems (LS-CSs) have gained significant attention for their ability to harvest energy from low-power water sources and for their sensitivity in probing the electrical state of droplets. Despite numerous experimental studies, theoretical models remain limited. In this work, we present a comprehensive simulation framework that captures the coupled dynamics of a water droplet sliding on a solid surface, including charge transport via convection, diffusion, and electric migration. The model reproduces the entire process of a one-electrode LS-CS, from initial charging to saturation, and provides new insights into the formation of the electrical double layer and the electrohydrodynamic behavior of bouncing droplets. This approach offers a versatile tool for studying droplet-based energy harvesting and electrostatic systems, enabling systematic analysis and optimization of LS-CS devices and paving the way for broader applications in sensing, energy, and fluid manipulation. A generalized model is established to simulate the charge behavior in a water droplet sliding on a solid surface, which can be utilized to clarify a solid-liquid charging system and the formation of the electric double layer in an impinging droplet, thus paving the way for the simulation of numerous complex systems involving droplets in electric fields. • A universal modeling framework to explore charge behaviors within droplets and droplet-related electrokinetic phenomena are provided. • The understanding of charge behavior within mobile droplets has implications far beyond energy harvesting. • This work delivers a generalizable model applicable to any system involving moving droplets with electrical interactions.