Modeling of movement of liquid metal droplets driven by an electric field

The motion of liquid metal has potential applications ranging from micro-pumps and self-fueled motors to rapid cooling and drug delivery. In this study, we systematically investigate the effects of the radius of LMDs (liquid metal droplets), the concentration of electrolyte solution and the applied electric field on the movement behavior of LMDs experimentally. The research also explains the experimental phenomenon with an innovative modeling analysis, which combines pertinent forces (i.e., the driving force induced by the gradient of surface tension, the viscous friction between the droplet and its surrounding electrolyte, and the friction between the droplet and the substrate). The model is highly consistent with the rule that LMDs with a larger radius need smaller actuation voltage, and we can predict the critical voltages of LMDs with r = 2-4 mm through V_electrode = 30.62/r² - 0.998, which is obtained by fitting the parameters. We also obtain the model V = [-66.2Vr²/(259.7-17.7) + 1.253]r², which can predict the average velocity-voltage lines of LMDs with r = 3, 3.5 mm and V = 1-13 V. In addition, the velocity increases upon increasing the concentration of the electrolyte solution from 0.1 mol L^-1 to 0.3 mol L^-1, and tends to be stable at more than 0.3 mol L^-1 owing to the saturation of the EDL (electrical double layer) charge density. Additionally, we discuss the phenomenon of elongation during movement that occurs upon increasing the size of the LMDs. If the size of the LMDs continues to increase, the reverse movement from the anode to the cathode can occur, and the phenomenon can also be explained by the model.