Physics-informed neural networks for three-dimensional droplet dynamics in two-phase pressure-driven channel flow

The accurate computational modeling of two-phase flows, particularly the tracking of moving interfaces and complex fluid dynamics, remains a significant challenge in applied mechanics. In this work, we present a computational framework that uses physics-informed neural networks (PINNs) to solve the governing multiphase Navier Stokes equations, along with the volume of fluid (VOF) method to capture interface dynamics. To assess the robustness and accuracy of the proposed methodology, we simulate the transient dynamics and deformation of a droplet in a fully developed microchannel flow. The performance of the PINN framework is systematically evaluated across varying capillary numbers, droplet radii, and viscosity ratios. By embedding the physical conservation laws and the VOF advection equation directly into the neural network's loss functions, the PINN approach successfully resolves the complex interplay of inertial, viscous, and interfacial forces. Validation demonstrates that the proposed computational framework accurately captures droplet deformation, achieving maximum droplet deformation errors of less than 8%. These findings establish the proposed PINN-based framework as a physically consistent, data-free in training, and accurate alternative to conventional numerical solvers, advancing the mathematical modeling of complex multiphase systems.