Modeling of Highly Viscous Flows in Rotor-Stator Mixing Systems Using a CFD-Coupled Lagrangian Particle-/Immersed Boundary Method and Surrogate Physics-Informed Neural Network Models

In-line multi-stage rotor-stator mixers enable rapid, continuous processing of viscous liquids, but their internal flow dynamics and mixing performance are not yet well understood. This work introduces and evaluates two simulation strategies to address this gap. The first is a hybrid CFD method that integrates massless Lagrangian tracers with an immersed boundary formulation in a finite-volume solver. The tracers provide concentration fields without numerical diffusion, while the immersed boundary approach captures rotor motion without extensive geometric pre-processing. This combination allows efficient analysis of a wide range of mixer configurations with reduced setup time. The second strategy is a mesh-free physics-informed neural network that requires no training data. The governing equations and boundary conditions, including a multiple-reference-frame version of the Navier-Stokes equations, are embedded directly into the loss function. Because the MRF formulation represents only a single rotor-stator phase, two extensions are proposed: transfer learning to adjust a trained model to new angular positions, and parameterization of the geometry and rotor angle as additional network inputs. Both methods produce accurate predictions across different operating conditions. Experimental validation confirms that the CFD approach delivers detailed and reliable flow characterization suitable for integration into existing workflows, while the PINN approach provides flexible parameterization and rapid adaptation to changes in geometry, materials, and operating parameters. Together, these methods form a practical framework for analyzing and designing industrial in-line rotor-stator mixing systems.