While the development of lab-on-chip is increasing, the lack of dedicated computer-aided design tools appears as a bottleneck preventing the emergence of large-scale industrial applications. One of the answer relied on 50 years of CAD experience in microelectronic. Based on this fact, and using this environment, multi-domain libraries (fluidic, biological, chemical) are to be designed. Among other, the development of efficient compact model for microfluidic devices is a first step toward such design tool. This paper deals with a continuous microfluidic mixer. Our model takes as inputs the flow rates and the concentrations of each fluid to mix and returns the flow rate and the concentration profiles across the channel at its output. The model depends also on some physical parameters (e.g. diffusion coefficient of fluids) and mixing channel geometry. The model is validated by comparison with finite-element simulation performed with COMSOL Multiphysics. Comparisons arc made on several cases. We demonstrated that the model gives a good estimation of the concentration profile, with an error of less than 2% compared to the finite element simulator.