A study of the fluid flow in a mixing device proposed to dissolve alloying elements in iron baths is performed through a mathematical model in order to predict the best operating conditions for a proper melting/dissolution of solid alloying particles. The mathematical model consists in the mass and momentum conservation equations (continuity and Turbulent Navier-Stokes equations), and the standard two k-epsilon turbulence model. The model is numerically solved in transient regime with the Volume of Fluid algorithm (VOF) to calculate the vortex shape. VOF is built-in the CFD (Computational Fluid Dynamics) software ANSYS FLUENT 14. A flow of metal enters tangentially in the mixing chamber of the proposed mixing device (taken from an open patent) to generate a vortex. The shape and height of the vortex reached in this chamber depends on several design variables, but in this work only the presence or absence of a barrier in the device is analyzed. Results are obtained on the vortex sizes and shapes, liquid flow patterns, turbulent structure, residence times of the particles of alloying elements added to the melt and mixing times (Residence time distribution curves) of two devices: one with a barrier and the other without this barrier. It is found that the presence of the barrier in the device increases turbulence, destroys the vortex, decreases the residence time of the particles, and decreases the volume of fluid in the device. Most of the features of the barrier are detrimental for mixing and inhibits melting/dissolution of the alloying elements. Then, it is suggested a device without the presence of barrier for better performance.