Dynamic behaviour of electrically driven liquid metal droplets in abrasive particle suspensions

Owing to its high electrical conductivity, low melting point and excellent deformability, liquid metal has become a promising functional material for advanced technologies such as flexible electronics, microfluidics and intelligent robotics. However, most existing research has focused on its electrically induced behaviour in homogeneous electrolytes, while the dynamics in abrasive particle suspensions remain poorly understood. This study systematically investigates the electrically actuated motion of liquid metal droplets in sodium hydroxide solutions containing abrasive particles. The effects of particle concentration, size and material on the critical driving voltage and droplet motion are analyzed. A predictive model for the critical driving voltage is developed based on experimental observations, incorporating viscous friction, turbulent resistance and collision forces between particles and droplets. Results show that the critical voltage is inversely proportional to the square of the droplet radius. Furthermore, increasing particle concentration or replacing highly conductive particles with low-conductivity ones significantly raises the threshold voltage required for droplet actuation. The model exhibits strong predictive performance, with average relative error between 2.99% and 9.65% for various particle conditions, demonstrating its suitability for particle-laden flow systems in precision microfabrication.