In the polymer manufacturing industry, numerical simulation tools play an increasingly important role in enhancing both the productivity of mixing processes and the quality of the final products. In recent years, an Immersed Boundary finite-volume solver, based on the open-source CFD software OpenFOAM, has been developed [1] for simulating mixing devices with complex geometries. This solver has been successfully applied to both continuous and batch mixing devices [2]. In this talk, we present recent advancements aimed at extending the solver's capabilities to include partially filled mixing devices. Specifically, we introduce an Immersed Boundary Volume of Fluid (IB-VOF) solver that can track multi-phase flows (e.g., polymer and air) within complex domains. We also address improvements to the stability of the Volume-of-Fluid solver in scenarios involving large viscosity ratios, common in non-Newtonian multi-phase flows, by adopting, in the approximation of the momentum equation, the block-coupled strategy proposed in [3]. Additionally, we discuss the implementation of Navier-slip boundary conditions [4] within the Immersed Boundary framework. The stability and accuracy of the proposed methods are demonstrated through a series of numerical simulations, including benchmark tests and realistic industrial applications. This work has been carried out in collaboration with Giorgio Negrini and Daniele Cerroni (Pirelli Tyre S.p.A.) and Holger Marschall (IANUS Simulation and TU Darmstadt). [1] G. Negrini, N. Parolini and M. Verani, An Immersed Boundary Method for Polymeric Continuous Mixing. To appear in "Emerging Technologies in Computational Sciences for Industry, Sustainability and Innovation - Math to Product", Lecture Notes in Computational Science and Engineering, Springer, 2025. [2] G. Negrini, Non-conforming methods for the simulation of industrial polymer mixing processes. PhD thesis, Politecnico di Milano, 2023. [3] P. Cardiff, Z. Tukovic, H. Jasak and A. Ivankovic, A block-coupled Finite Volume methodology for linear elasticity and unstructured meshes. Computers \& Structures (2016) 175:100-122. [4] L. L. Ferras, J. M. Nobrega and F. T. Pinho, Implementation of slip boundary conditions in the finite volume method: new techniques. Inter. J. Numer. Meth. Fluids (2013) 72:724-747.