Dynamical modeling and experimental research on capillary flow of gallium-based liquid metal for reconfigurable structures

Gallium and its alloys, as emerging multifunctional metals that melt at room temperature, hold strategic significance in advanced manufacturing and technological innovation. By uniquely integrating the exceptional electrical conductivity of metals with the intrinsic fluidity of liquids, gallium-based liquid metals have garnered immense interest from both academic researchers and industrialists with a wide range of potential applications, including stretchable wires, self-healing circuits, 3D printing and patterning, and reconfigurable antennas. These remarkable properties enable groundbreaking approaches to the patterning and manipulation of gallium-based liquid metals, facilitating the fabrication of reconfigurable and stretchable structures with an unparalleled combination of electrical and mechanical performance. However, an essential yet still unaddressed issue is to establish the quantitative relationship between the interface position of the liquid metal column and the corresponding time of motion. In this study, we have developed a dynamical model based on the momentum theorem and conducted experimental verifications to investigate the capillary flow of gallium-based liquid metals. Our results demonstrate that the theoretical calculations of the time required for eutectic gallium indium to flow from the inlet to the outlet of capillary tubes are in good agreement with experimental measurements obtained from capillary tubes of varying lengths. Consequently, the dynamical model presented here provides quantitative theoretical insights, serving as a valuable tool for guiding the design and fabrication of reconfigurable liquid metal structures and devices in the future.