In this work, we present a numerical method for the simulation of a cell-sorting microfluidic device that exploits small density variations among the various particle types to classify them effectively by creating a stratified flow with several fluid layers of different densities. Previous work on the numerical analysis of this has ignored the effect of diffusion, which we include here, by extending the framework to include the convection-diffusion equations. We analyze how the precision of the device is affected by this phenomenon, and we present a range of validity for our numerical approach. The main motivation of this work is to develop algorithms that couple CFD with convection-diffusion to be able to systematically design and analyze industrial focused cases in microfluidics. For this, we will use finite element discretization. This approach has been applied in other cell separation techniques, but it has not yet been widely developed for gradient-based microfluidic sorting devices.