Mathematical Modeling of EGaIn Droplets Sliding Down an Inclined Plane
Discipline: Mathematics and Statistics
Subcategory: Mathematics and Statistics
Session: 1
Room: Chinatown
Luis A. Schneegans III - University of Missouri – St. Louis
Co-Author(s): Shawn Koohy, University of Massachusetts Dartmouth, MA; Kathryn Massey, Marist College, NY; Megan Vezzetti, North Carolina State University, NC; Jessie Chen, North Carolina State University, NC; Souradip Chattopadhyay, North Carolina State University, NC; Carmen Lee, North Carolina State University, NC
Is it possible to numerically simulate a liquid metal sliding down an incline? Specifically, is it possible to not only simulate a liquid metal sliding down but to do so by finding a Partial Differential Equation lubrication model? This project focused on learning more about Eutectic Gallium-Indium (EGaIn), a low-toxicity alternative to liquid mercury. In this study, we present a one-dimensional lubrication model for the dynamics of an EGaIn droplet moving along an inclined plane. Our model incorporates essential physical effects and parameters including oxidation, capillary action, diffusion, gravity, and Marangoni effects. In particular, we incorporate the effects of the electric field, both through electric forces and changes in oxidation flux.Eutectic Gallium-Indium (EGaIn) is a room-temperature liquid metal alloy that dramatically changes its surface tension and dynamics under an applied electric field. EGaIn has been used heavily in soft electronics engineering due to its high conductivity, malleability, and safety. However, the absence of mathematical modeling in the current literature makes its behavior difficult to understand and predict. We model the thin oxide skin of the droplet, which modulates the interfacial surface tension, as an insoluble surfactant at the surface. Oxidation, while observable in the physical setting, cannot be well measured, calling for an alternative method to quantify oxidation flux.Utilizing experimental data, we calibrate system parameters and qualitatively obtain numerical simulation results comparable to experimental observations. Stability analysis was conducted to understand the impacts of physical effects on our model. We find azimuthal curvature to be the main contributor in the process of threading which also promotes the formation of satellite droplets. Our model has demonstrated success in reproducing the observed dynamics of an EGaIn droplet and provides a valuable resource for further investigation and uses of EGaIn.
Funder Acknowledgement(s): We would like to thank Dr. Hangjie Ji and Dr. Karen Daniels for being our mentors for this project. We would also like to extend our thanks to Dr. Mette Olufsen for running this REU and giving us this opportunity. Lastly, we want to acknowledge the support of the National Security Agency (NSA) under Grant No. H98230-23-1-0009 along with the National Science Foundation (NSF) under Grant No. DMS-2051010.
Faculty Advisor: Dr. Hangjie Ji, Karen Daniels, hji5@ncsu.edu
Role: I helped both with parameter estimation, focusing on learning how the model works in reaction to different parameter changes. Additionally, I worked on asymptotic analysis of our coupled 4th-order PDE equation, hoping to find some relationships between variables. Lastly, I worked on finding a similarity solution for the rarefaction part of the solution.