Utilizing Physics-Informed Neural Networks (PINNs) to Estimate Non-Uniform Surface Properties of Active Droplets

We have developed a novel PINN approach to estimate an active droplet’s non-uniform surface properties, such as interfacial tension and velocity. Unraveling these properties is essential for understanding droplet dynamics in various environments, but experimental determination poses significant challenges. While inverse methods are possible, solving inverse flow problems is often costly and requires complex formulations. 

Our study focuses on a spherical oil droplet near a no-slip wall immersed into a water-surfactant solution generating a fluid flow by solubilizing into the aqueous phase. Our PINN model utilizes the droplet’s flow field away from the interface to estimate the surface properties. To ensure the accuracy, the Stokes equation, fluid incompressibility, and no-slip condition on the wall are employed into the loss function. We use the flow field of a squirmer model to test our results. 

Our primary results demonstrate the effectiveness of PINNs in determining the interfacial properties of the droplet and improving noisy experimental data at other points. The model’s flexibility allows it to be applied to any geometry and droplets, with potential applications in various fields, including understanding the propulsion mechanism of active self-phoretic oil droplets and cell deformation and dynamics. Additionally, this method promises substantial advancements in fields that require precise measurements of non-uniform surface properties in fluid dynamics.