The objective of this work is to describe a model allowing the representation of the mixing phenomenon between two fluids having very different viscosities in an internal mixer, typically a cold plasticizer and a hot molten polymer. We present a dynamic model based on a simplified view of the flow and on mass, energy, and momentum balances. As far as the mass transfer is concerned, we consider simultaneously the mechanical action of the rotors and the diffusive process. Heat transfer has to be considered because of the important temperature difference between the two components and the viscous dissipation. Finally, a momentum balance allows us to calculate the velocity profile and the torque time evolution by considering that the viscosity is concentration and temperature dependent. A sensitivity study has been done to check for the influence of some model parameters on the simulated results. The latter will show a good agreement with experimental results.