The numerical simulation of polymer mixing technologies is aimed at supporting the industrial reality for improving process efficiency and productivity. The main challenges are the non-Newtonian rheologies of the materials involved in addition to complex moving domain geometries consisting of rotating screws that mix and push forward the polymer compounds inside the machines. Depending on the amount of polymer compound feeding the machine and on the screw velocity, the mixing device may be only partially filled with material. Hence, multi-phase methods need to be considered. This work integrates a free-surface model within an Immersed Boundary (IB) library [1], based on the open-source CFD software OpenFOAM, that handles complex moving boundaries with a non-conformal treatment with respect to the background fluid mesh. Specifically, we formulated and implemented an Immersed Boundary - Volume Of Fluid (IB-VOF) solution procedure that is able to account for the presence of two materials, air and polymer. The main complexity of free-surface simulations of polymeric materials lays in the extremely large viscosity ratios between the liquid and the gas phases, causing instabilities of the native OpenFOAM solvers, based on a segregated solution of the momentum equation for each velocity component. In order to make the VOF solver more robust, both in conformal and IB framework, a block-coupled approach is employed to treat the whole viscous term of the momentum equation implicitly. This method was successfully employed before in injection moulding simulations, adapting the work by Cardiff P. [2] to the momentum balance of Navier-Stokes equations. The approach is integrated in our polymer mixing library, validated and tested on a realistic case of a single screw extruder. Finally, appropriate Navier-slip boundary conditions [3] are implemented to deal with moving triple contact lines, i. e. intersections of the bi-phase interface with solid walls.