This paper reports the modelling and simulation of the acoustic streaming phenomenon, generated by a polymeric piezoelectric transducer, used for promoting fluid mixing in microfluidic devices. The acoustic streaming process consists of the absorption of the acoustic waves by the fluid which results in a pressure drop along the direction of the acoustic propagation. The generated pressure drop promotes the flow and consequently mixing. This process overcomes the slow molecular diffusion resultant from the low Reynolds number that leads to laminar flows in microcuvettes. The numerical model comprises the compressible Navier-Stokes equations, whose variables were expanded in first- and second-order values, to overcome the great difference between the piezoelectric and the fluid flow time scales. The model was implemented in OpenFoam software, through finite volumes numerical methods. It was concluded that the excitation of the transducer above the microcuvette generates a mean global flow with visible recirculation of fluids within the domain, which can be used to predict the fluid flow behaviour.