Modeling Droplet Spreading Dynamics using Physics-Informed Neural Networks*

This study explores the use of Physics-Informed Neural Networks (PINNs) and their potential in modeling complex physical systems, with a particular focus on droplet spreading dynamics. Droplet spreading on solid surfaces is a phenomenon governed by intricate interactions involving fluid dynamics, surface tension, and contact angle dynamics. By leveraging the capabilities of PINNs, this research aims to integrate these underlying physical principles into the neural network architecture, providing a more comprehensive understanding of the spreading dynamics.

We specifically examine CMAS (calcium-magnesium-aluminosilicate) and water as test cases. CMAS is characterized by its high viscosity, density, and surface tension, making it an ideal candidate for studying the effects of these properties on droplet spreading. Water, with its well-known properties, serves as a contrasting test case to highlight the model's versatility.

We use multiphase many-body dissipative particle dynamics (mDPD) simulations to study the dynamics of CMAS droplets. These simulations are performed in three dimensions, with varying initial droplet sizes and equilibrium contact angles. We also have experimental data for water, obtained through shadowgraphy experiments using the transmitted light method. 

We propose a parametric ordinary differential equation (ODE) to capture the spreading radius behavior of droplets. The ODE parameters are identified using the Physics-Informed Neural Network (PINN) framework. Subsequently, we determine the closed-form dependency of parameter values on initial radii and contact angles through symbolic regression. Additionally, symbolic regression is employed to generate a mathematical expression for each unknown parameter, providing a comprehensive understanding of the factors influencing droplet spreading dynamics.