The numerical simulation of polymer mixing technologies is aimed at supporting the industrial reality for improving process efficiency and productivity. The mathematical and numerical modeling is continually improving in order to obtain increasingly reliable predictions of the real industrial processes. The main challenges to be dealt with are the non-Newtonian rheologies of the materials involved, leading to highly nonlinear terms inside the Navier-Stokes equations, in addition to complex moving domain geometries consisting of rotating screws that mix and push forward the polymer compounds inside the machines. This work falls within the framework of Immersed Boundary (IB) methods that handle complex solid boundaries inside the fluid domain, avoiding the need of a conformal grid with respect to the fluid mesh. Given a real process, that can be continuous or batch, 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. In order to account for this scenario, we focus on the integration of free-surface models within the currently available immersed boundary method. Specifically, we rely on an Immersed Boundary - Volume Of Fluid (IB-VOF) model that is able to account for the presence of two materials, air and polymer, inside a domain whose boundaries can be treated with the IB method. Appropriate wall boundary conditions are required to deal with contact lines, i. e. intersections of the air-polymer interface with solid walls. The Navier-slip boundary conditions replace the standard no-slip, being able to impose a non-zero tangential velocity proportional to the normal stress at the boundary. Preliminary simulations are carried out to test the IB-VOF method, leading to validation and convergence results.