Modeling sessile drop interfaces using physics-informed neural networks

We investigate the application of physics-informed neural networks (PINNs) to simulate sessile drops interacting with surfaces exhibiting heterogeneous wettability and contact angle hysteresis. Unlike traditional mesh-based numerical methods, the PINN models the drop shape by minimizing a set of loss functions that encode the governing physics and geometric constraints. The mesh-free nature of the PINN framework allows it to simulate a drop spreading over surfaces of heterogeneous wettability without a priori knowledge of the contact line location. The proposed framework evolves from an initial single-droplet shape to the equilibrium in the absence of hysteresis. For drops on hysteretic surfaces, we introduce a memory-based modeling approach. This method incorporates a history-aware loss term that selectively penalizes contact line motion on hysteretic surfaces, allowing the model to realistically capture directional pinning and depinning phenomena. We show that the PINN successfully reproduces asymmetric drop deformation under gravitational tilting and on surfaces with spatially varying wettability. These results demonstrate that the proposed PINN framework provides a mesh-free, physics-informed approach for simulating sessile drops in complex physical environments.