Mathematical modeling of interfacial fluids

Mentors:
Lead: Hangjie Ji (Mathematics, NCSU)
Collaborator: Karen Daniels (Physics, NCSU)

Intellectual merit and significance:
Interfacial fluids separating two immiscible liquids by a free interface play a crucial role in natural and industrial processes [1]. An interplay between surface tension and physical effects governs the interface evolution. Understanding these mechanisms is critical for practical applications. Eutectic Gallium Indium (EGaIn) is a room-temperature liquid metal alloy widely used in soft electronics/robots, self-healing wires, tunable antennas, and thermal paste [2]. When a positive voltage is applied to EGaIn within an electrolyte solution, the surface tension of the liquid metal decreases due to rapid oxidation, causing interfacial instabilities and pattern formation. This project will study a lubrication-type PDE model [3] for interfacial fluids. Dr. Daniels will open her lab, allowing participants to observe the pattern formation and invite them to perform experiments alongside her group.

Objectives:
Exploration of the PDE model to better understand the spatial instability of interfacial fluid dynamics. The results will be analyzed to estimate the influence of key factors in the experiments.

Outcomes:
A comprehensive numerical study of the interfacial fluids PDE model. This study will provide tools to estimate key model parameters and compare numerical results against experimental observations.

References:
1. Ajaev V. Interfacial Fluid Mechanics. New York, NY: Springer; 2012.
2. Song M, Daniels K, Kiani A, Rashid-Nadimi S, Dickey M. Interfacial tension modulation of liquid metal via electrochemical oxidation. Adv Intell Syst. 2021;3:2100024.
3. Craster R, Matar O. Dynamics and stability of thin liquid films. Rev Mod Phys. 2009;81:1131.