PINN-Based Solution for a Diffusion Controlled Droplet Growth

Abstract

We study diffusion-controlled growth of a spherical droplet with a moving boundary using a physics-informed neural network (PINN) formulation. The governing diffusion equation is coupled to the interfacial mass balance, with the droplet radius treated as an additional trainable function of time. The PINN accurately reproduces the self-similar growth law and concentration profiles for a wide range of initial droplet radii, demonstrating convergence toward the asymptotic diffusive regime. The proposed approach provides a flexible and computationally efficient framework for solving moving-boundary diffusion problems and can be readily extended to include additional physical effects.