PINN-Based Solution for a Diffusion Controlled Droplet Growth

TL;DR

This paper introduces a PINN-based method to accurately simulate diffusion-controlled spherical droplet growth with a moving boundary, capturing self-similar growth laws and concentration profiles efficiently.

Contribution

The study develops a novel PINN framework that models moving boundary diffusion problems, demonstrating high accuracy and flexibility in simulating droplet growth.

Findings

PINN accurately reproduces self-similar growth laws.

The method converges to the asymptotic diffusive regime.

Framework is flexible for extending to additional physical effects.

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.