Neural-Network-based Viscosity Closure for Non-Newtonian Multiphase Flows

Abstract

Materials used in polymer-based additive manufacturing processes, such as Digital Light Processing (DLP) and direct ink writing (DIW), typically exhibit non-Newtonian rheology. Carreau-Yasuda and power-law models describe basic shear-thinning and shear-thickening behavior well, but applying them to a new material requires choosing a functional form, deriving it, and re-implementing it inside the flow solver. We present a deployment workflow in which a neural network trained on experimental rheometry data serves as the viscosity closure inside a Cahn-Hilliard-Navier-Stokes (CHNS) finite element solver. The learned closure is generalized Newtonian: viscosity depends only on the local shear rate at the current instant. Lipschitz regularization during training produces smooth viscosity predictions, and the trained network is exported in the Open Neural Network Exchange (ONNX) format and queried by the solver at runtime via the ONNX runtime, without solver modification or network reimplementation. The framework is built on a parallel octree-based adaptive mesh refinement infrastructure that concentrates resolution at the fluid interface. We validate the CHNS solver against benchmark shear-thinning bubble-rise cases from the literature, reproducing reported bubble shapes across varying power-law indices and Weber numbers. We characterized two silicone ink formulations, recorded their rise dynamics in perfluorodecalin on high-speed video, and used the resulting data to test the full workflow. Simulated rise velocities fall within the experimentally measured spread, and the simulated steady-state droplet shape agrees with the observed one. This work contributes to a growing body of literature on integrating neural constitutive closures into multiphysics simulations, and demonstrates a practical path for deploying experimentally trained rheological surrogates inside finite element solvers.